Realization of space-time inversion-invariant topological semimetal-bands in superconducting quantum circuits.

NASA Astrophysics Data System (ADS)

Yu, Y.; Tan, X.; Liu, Q.; Xue, G.; Yu, H.; Zhao, Y.; Wang, Z.

Topological band theory has attracted much attention since several types of topological metals and semimetals have been explored. These robustness of nodal band structures are symmetry-protected, whose topological features have deepened and widened the understandings of condensed matter physics. Meanwhile, as artificial quantum systems superconducting circuits possess high controllability, supplying a powerful approach to investigate topological properties of condensed matter systems. We realize a Hamiltonian with space-time (PT) symmetry by mapping momentum space of nodal band structure to parameter space in a superconducting quantum circuit. By measuring energy spectrum of the system, we observe the gapless band structure of topological semimetals, shown as Dirac points in momentum space. The phase transition from topological semimetal to topological insulator can be realized by continuously tuning the parameter in Hamiltonian. We add perturbation to broken time reversal symmetry. As long as the combined PT symmetry is preserved, the Dirac points of the topological semimetal are still observable, suggesting the robustness of the topological protection of the gapless energy band. Our work open a platform to simulate the relation between the symmetry and topological stability in condensed matter systems. Supported by the NKRDP of China (2016YFA0301802) and the GRF of Hong Kong (HKU173051/14P&HKU173055/15P).

Entanglement in 3D Kitaev spin liquids

NASA Astrophysics Data System (ADS)

Matern, S.; Hermanns, M.

2018-06-01

Quantum spin liquids are highly fascinating quantum liquids in which the spin degrees of freedom fractionalize. An interesting class of spin liquids are the exactly solvable, three-dimensional Kitaev spin liquids. Their fractionalized excitations are Majonara fermions, which may exhibit a variety of topological band structures—ranging from topologically protected Weyl semi-metals over nodal semi-metals to systems with Majorana Fermi surfaces. We study the entanglement spectrum of such Kitaev spin liquids and verify that it is closely related to the topologically protected edge spectrum. Moreover, we find that in some cases the entanglement spectrum contains even more information about the topological features than the surface spectrum, and thus provides a simple and reliable tool to probe the topology of a system.

Hidden-Symmetry-Protected Topological Semimetals on a Square Lattice

NASA Astrophysics Data System (ADS)

Hou, Jing-Min

2014-03-01

We study a two-dimensional fermionic square lattice, which supports the existence of two-dimensional Weyl semimetal, quantum anomalous Hall effect, and 2 π -flux topological semimetal in different parameter ranges. We show that the band degenerate points of the two-dimensional Weyl semimetal and 2 π -flux topological semimetal are protected by two distinct novel hidden symmetries, which both corresponds to antiunitary composite operations. When these hidden symmetries are broken, a gap opens between the conduction and valence bands, turning the system into a insulator. With appropriate parameters, a quantum anomalous Hall effect emerges. The degenerate point at the boundary between the quantum anomalous Hall insulator and trivial band insulator is also protected by the hidden symmetry. [PRL 111, 130403(2013)] This work was supported by the National Natural Science Foundation of China under Grants No. 11004028 and No. 11274061.

Exploring photonic topological insulator states in a circuit-QED lattice

NASA Astrophysics Data System (ADS)

Li, Jing-Ling; Shan, Chuan-Jia; Zhao, Feng

2018-04-01

We propose a simple protocol to explore the topological properties of photonic integer quantum Hall states in a one-dimensional circiut-QED lattice. By periodically modulating the on-site photonic energies in such a lattice, we demonstrate that this one-dimensional lattice model can be mapped into a two-dimensional integer quantum Hall insulator model. Based on the lattice-based cavity input-output theory, we show that both the photonic topological protected edge states and topological invariants can be clearly measured from the final steady state of the resonator lattice after taking into account cavity dissipation. Interestingly, we also find that the measurement signals associated with the above topological features are quite unambitious even in five coupled dissipative resonators. Our work opens up a new prospect of exploring topological states with a small-size dissipative quantum artificial lattice, which is quite attractive to the current quantum optics community.

Hidden Order and Symmetry Protected Topological States in Quantum Link Ladders

NASA Astrophysics Data System (ADS)

Cardarelli, L.; Greschner, S.; Santos, L.

2017-11-01

We show that, whereas spin-1 /2 one-dimensional U(1) quantum-link models (QLMs) are topologically trivial, when implemented in ladderlike lattices these models may present an intriguing ground-state phase diagram, which includes a symmetry protected topological (SPT) phase that may be readily revealed by analyzing long-range string spin correlations along the ladder legs. We propose a simple scheme for the realization of spin-1 /2 U(1) QLMs based on single-component fermions loaded in an optical lattice with s and p bands, showing that the SPT phase may be experimentally realized by adiabatic preparation.

Blind topological measurement-based quantum computation.

PubMed

Morimae, Tomoyuki; Fujii, Keisuke

2012-01-01

Blind quantum computation is a novel secure quantum-computing protocol that enables Alice, who does not have sufficient quantum technology at her disposal, to delegate her quantum computation to Bob, who has a fully fledged quantum computer, in such a way that Bob cannot learn anything about Alice's input, output and algorithm. A recent proof-of-principle experiment demonstrating blind quantum computation in an optical system has raised new challenges regarding the scalability of blind quantum computation in realistic noisy conditions. Here we show that fault-tolerant blind quantum computation is possible in a topologically protected manner using the Raussendorf-Harrington-Goyal scheme. The error threshold of our scheme is 4.3 × 10(-3), which is comparable to that (7.5 × 10(-3)) of non-blind topological quantum computation. As the error per gate of the order 10(-3) was already achieved in some experimental systems, our result implies that secure cloud quantum computation is within reach.

Blind topological measurement-based quantum computation

NASA Astrophysics Data System (ADS)

Morimae, Tomoyuki; Fujii, Keisuke

2012-09-01

Blind quantum computation is a novel secure quantum-computing protocol that enables Alice, who does not have sufficient quantum technology at her disposal, to delegate her quantum computation to Bob, who has a fully fledged quantum computer, in such a way that Bob cannot learn anything about Alice's input, output and algorithm. A recent proof-of-principle experiment demonstrating blind quantum computation in an optical system has raised new challenges regarding the scalability of blind quantum computation in realistic noisy conditions. Here we show that fault-tolerant blind quantum computation is possible in a topologically protected manner using the Raussendorf-Harrington-Goyal scheme. The error threshold of our scheme is 4.3×10-3, which is comparable to that (7.5×10-3) of non-blind topological quantum computation. As the error per gate of the order 10-3 was already achieved in some experimental systems, our result implies that secure cloud quantum computation is within reach.

Universal measurement-based quantum computation in two-dimensional symmetry-protected topological phases

NASA Astrophysics Data System (ADS)

Wei, Tzu-Chieh; Huang, Ching-Yu

2017-09-01

Recent progress in the characterization of gapped quantum phases has also triggered the search for a universal resource for quantum computation in symmetric gapped phases. Prior works in one dimension suggest that it is a feature more common than previously thought, in that nontrivial one-dimensional symmetry-protected topological (SPT) phases provide quantum computational power characterized by the algebraic structure defining these phases. Progress in two and higher dimensions so far has been limited to special fixed points. Here we provide two families of two-dimensional Z2 symmetric wave functions such that there exists a finite region of the parameter in the SPT phases that supports universal quantum computation. The quantum computational power appears to lose its universality at the boundary between the SPT and the symmetry-breaking phases.

Resource quality of a symmetry-protected topologically ordered phase for quantum computation.

PubMed

Miller, Jacob; Miyake, Akimasa

2015-03-27

We investigate entanglement naturally present in the 1D topologically ordered phase protected with the on-site symmetry group of an octahedron as a potential resource for teleportation-based quantum computation. We show that, as long as certain characteristic lengths are finite, all its ground states have the capability to implement any unit-fidelity one-qubit gate operation asymptotically as a key computational building block. This feature is intrinsic to the entire phase, in that perfect gate fidelity coincides with perfect string order parameters under a state-insensitive renormalization procedure. Our approach may pave the way toward a novel program to classify quantum many-body systems based on their operational use for quantum information processing.

Resource Quality of a Symmetry-Protected Topologically Ordered Phase for Quantum Computation

NASA Astrophysics Data System (ADS)

Miller, Jacob; Miyake, Akimasa

2015-03-01

We investigate entanglement naturally present in the 1D topologically ordered phase protected with the on-site symmetry group of an octahedron as a potential resource for teleportation-based quantum computation. We show that, as long as certain characteristic lengths are finite, all its ground states have the capability to implement any unit-fidelity one-qubit gate operation asymptotically as a key computational building block. This feature is intrinsic to the entire phase, in that perfect gate fidelity coincides with perfect string order parameters under a state-insensitive renormalization procedure. Our approach may pave the way toward a novel program to classify quantum many-body systems based on their operational use for quantum information processing.

Quantum spin Hall effect and topological phase transition in InN x Bi y Sb1-x-y /InSb quantum wells

NASA Astrophysics Data System (ADS)

Song, Zhigang; Bose, Sumanta; Fan, Weijun; Zhang, Dao Hua; Zhang, Yan Yang; Shen Li, Shu

2017-07-01

Quantum spin Hall (QSH) effect, a fundamentally new quantum state of matter and topological phase transitions are characteristics of a kind of electronic material, popularly referred to as topological insulators (TIs). TIs are similar to ordinary insulator in terms of their bulk bandgap, but have gapless conducting edge-states that are topologically protected. These edge-states are facilitated by the time-reversal symmetry and they are robust against nonmagnetic impurity scattering. Recently, the quest for new materials exhibiting non-trivial topological state of matter has been of great research interest, as TIs find applications in new electronics and spintronics and quantum-computing devices. Here, we propose and demonstrate as a proof-of-concept that QSH effect and topological phase transitions can be realized in {{InN}}x{{Bi}}y{{Sb}}1-x-y/InSb semiconductor quantum wells (QWs). The simultaneous incorporation of nitrogen and bismuth in InSb is instrumental in lowering the bandgap, while inducing opposite kinds of strain to attain a near-lattice-matching conducive for lattice growth. Phase diagram for bandgap shows that as we increase the QW thickness, at a critical thickness, the electronic bandstructure switches from a normal to an inverted type. We confirm that such transition are topological phase transitions between a traditional insulator and a TI exhibiting QSH effect—by demonstrating the topologically protected edge-states using the bandstructure, edge-localized distribution of the wavefunctions and edge-state spin-momentum locking phenomenon, presence of non-zero conductance in spite of the Fermi energy lying in the bandgap window, crossover points of Landau levels in the zero-mode indicating topological band inversion in the absence of any magnetic field and presence of large Rashba spin-splitting, which is essential for spin-manipulation in TIs.

Topological Phase Transitions in Line-nodal Superconductors

NASA Astrophysics Data System (ADS)

Cho, Gil Young; Han, Sangeun; Moon, Eun-Gook

Fathoming interplay between symmetry and topology of many-electron wave-functions deepens our understanding in quantum nature of many particle systems. Topology often protects zero-energy excitation, and in a certain class, symmetry is intrinsically tied to the topological protection. Namely, unless symmetry is broken, topological nature is intact. We study one specific case of such class, symmetry-protected line-nodal superconductors in three spatial dimensions (3d). Mismatch between phase spaces of order parameter fluctuation and line-nodal fermion excitation induces an exotic universality class in a drastic contrast to one of the conventional ϕ4 theory in 3d. Hyper-scaling violation and relativistic dynamic scaling with unusually large quantum critical region are main characteristics, and their implication in experiments is discussed. For example, continuous phase transition out of line-nodal superconductors has a linear phase boundary in a temperature-tuning parameter phase-diagram. This work was supported by the Brain Korea 21 PLUS Project of Korea Government and KAIST start-up funding.

Robustness of edge states in topological quantum dots against global electric field

NASA Astrophysics Data System (ADS)

Qu, Jin-Xian; Zhang, Shu-Hui; Liu, Ding-Yang; Wang, Ping; Yang, Wen

2017-07-01

The topological insulator has attracted increasing attention as a new state of quantum matter featured by the symmetry-protected edge states. Although the qualitative robustness of the edge states against local perturbations has been well established, it is not clear how these topological edge states respond quantitatively to a global perturbation. Here, we study the response of topological edge states in a HgTe quantum dot to an external in-plane electric field—a paradigmatic global perturbation in solid-state environments. We find that the stability of the topological edge state could be larger than that of the ground bulk state by several orders of magnitudes. This robustness may be verified by standard transport measurements in the Coulomb blockage regime. Our work may pave the way towards utilizing these topological edge states as stable memory devices for charge and/or spin information and stable emitter of single terahertz photons or entangled terahertz photon pairs for quantum communication.

Role of helical edge modes in the chiral quantum anomalous Hall state.

PubMed

Mani, Arjun; Benjamin, Colin

2018-01-22

Although indications are that a single chiral quantum anomalous Hall(QAH) edge mode might have been experimentally detected. There have been very many recent experiments which conjecture that a chiral QAH edge mode always materializes along with a pair of quasi-helical quantum spin Hall (QSH) edge modes. In this work we deal with a substantial 'What If?' question- in case the QSH edge modes, from which these QAH edge modes evolve, are not topologically-protected then the QAH edge modes wont be topologically-protected too and thus unfit for use in any applications. Further, as a corollary one can also ask if the topological-protection of QSH edge modes does not carry over during the evolution process to QAH edge modes then again our 'What if?' scenario becomes apparent. The 'how' of the resolution of this 'What if?' conundrum is the main objective of our work. We show in similar set-ups affected by disorder and inelastic scattering, transport via trivial QAH edge mode leads to quantization of Hall resistance and not that via topological QAH edge modes. This perhaps begs a substantial reinterpretation of those experiments which purported to find signatures of chiral(topological) QAH edge modes albeit in conjunction with quasi helical QSH edge modes.

Photonic zero mode in a non-Hermitian photonic lattice.

PubMed

Pan, Mingsen; Zhao, Han; Miao, Pei; Longhi, Stefano; Feng, Liang

2018-04-03

Zero-energy particles (such as Majorana fermions) are newly predicted quasiparticles and are expected to play an important role in fault-tolerant quantum computation. In conventional Hermitian quantum systems, however, such zero states are vulnerable and even become vanishing if couplings with surroundings are of the same topological nature. Here we demonstrate a robust photonic zero mode sustained by a spatial non-Hermitian phase transition in a parity-time (PT) symmetric lattice, despite the same topological order across the entire system. The non-Hermitian-enhanced topological protection ensures the reemergence of the zero mode at the phase transition interface when the two semi-lattices under different PT phases are decoupled effectively in their real spectra. Residing at the midgap level of the PT symmetric spectrum, the zero mode is topologically protected against topological disorder. We experimentally validated the robustness of the zero-energy mode by ultrafast heterodyne measurements of light transport dynamics in a silicon waveguide lattice.

Topological triplon modes and bound states in a Shastry-Sutherland magnet

NASA Astrophysics Data System (ADS)

McClarty, P. A.; Krüger, F.; Guidi, T.; Parker, S. F.; Refson, K.; Parker, A. W.; Prabhakaran, D.; Coldea, R.

2017-08-01

The twin discoveries of the quantum Hall effect, in the 1980s, and of topological band insulators, in the 2000s, were landmarks in physics that enriched our view of the electronic properties of solids. In a nutshell, these discoveries have taught us that quantum mechanical wavefunctions in crystalline solids may carry nontrivial topological invariants which have ramifications for the observable physics. One of the side effects of the recent topological insulator revolution has been that such physics is much more widespread than was appreciated ten years ago. For example, while topological insulators were originally studied in the context of electron wavefunctions, recent work has initiated a hunt for topological insulators in bosonic systems: in photonic crystals, in the vibrational modes of crystals, and in the excitations of ordered magnets. Using inelastic neutron scattering along with theoretical calculations, we demonstrate that, in a weak magnetic field, the dimerized quantum magnet SrCu2(BO3)2 is a bosonic topological insulator with topologically protected chiral edge modes of triplon excitations.

Blind topological measurement-based quantum computation

PubMed Central

Morimae, Tomoyuki; Fujii, Keisuke

2012-01-01

Blind quantum computation is a novel secure quantum-computing protocol that enables Alice, who does not have sufficient quantum technology at her disposal, to delegate her quantum computation to Bob, who has a fully fledged quantum computer, in such a way that Bob cannot learn anything about Alice's input, output and algorithm. A recent proof-of-principle experiment demonstrating blind quantum computation in an optical system has raised new challenges regarding the scalability of blind quantum computation in realistic noisy conditions. Here we show that fault-tolerant blind quantum computation is possible in a topologically protected manner using the Raussendorf–Harrington–Goyal scheme. The error threshold of our scheme is 4.3×10−3, which is comparable to that (7.5×10−3) of non-blind topological quantum computation. As the error per gate of the order 10−3 was already achieved in some experimental systems, our result implies that secure cloud quantum computation is within reach. PMID:22948818

Scalable designs for quasiparticle-poisoning-protected topological quantum computation with Majorana zero modes

NASA Astrophysics Data System (ADS)

Karzig, Torsten; Knapp, Christina; Lutchyn, Roman M.; Bonderson, Parsa; Hastings, Matthew B.; Nayak, Chetan; Alicea, Jason; Flensberg, Karsten; Plugge, Stephan; Oreg, Yuval; Marcus, Charles M.; Freedman, Michael H.

2017-06-01

We present designs for scalable quantum computers composed of qubits encoded in aggregates of four or more Majorana zero modes, realized at the ends of topological superconducting wire segments that are assembled into superconducting islands with significant charging energy. Quantum information can be manipulated according to a measurement-only protocol, which is facilitated by tunable couplings between Majorana zero modes and nearby semiconductor quantum dots. Our proposed architecture designs have the following principal virtues: (1) the magnetic field can be aligned in the direction of all of the topological superconducting wires since they are all parallel; (2) topological T junctions are not used, obviating possible difficulties in their fabrication and utilization; (3) quasiparticle poisoning is abated by the charging energy; (4) Clifford operations are executed by a relatively standard measurement: detection of corrections to quantum dot energy, charge, or differential capacitance induced by quantum fluctuations; (5) it is compatible with strategies for producing good approximate magic states.

Topological protection of multiparticle dissipative transport

NASA Astrophysics Data System (ADS)

Loehr, Johannes; Loenne, Michael; Ernst, Adrian; de Las Heras, Daniel; Fischer, Thomas M.

2016-06-01

Topological protection allows robust transport of localized phenomena such as quantum information, solitons and dislocations. The transport can be either dissipative or non-dissipative. Here, we experimentally demonstrate and theoretically explain the topologically protected dissipative motion of colloidal particles above a periodic hexagonal magnetic pattern. By driving the system with periodic modulation loops of an external and spatially homogeneous magnetic field, we achieve total control over the motion of diamagnetic and paramagnetic colloids. We can transport simultaneously and independently each type of colloid along any of the six crystallographic directions of the pattern via adiabatic or deterministic ratchet motion. Both types of motion are topologically protected. As an application, we implement an automatic topologically protected quality control of a chemical reaction between functionalized colloids. Our results are relevant to other systems with the same symmetry.

Local characterization of one-dimensional topologically ordered states

NASA Astrophysics Data System (ADS)

Cui, Jian; Amico, Luigi; Fan, Heng; Gu, Mile; Hamma, Alioscia; Vedral, Vlatko

2013-09-01

We consider one-dimensional Hamiltonian systems whose ground states display symmetry-protected topological order. We show that ground states within the topological phase cannot be connected with each other through local operations and classical communication between a bipartition of the system. Our claim is demonstrated by analyzing the entanglement spectrum and Rényi entropies of different physical systems that provide examples for symmetry-protected topological phases. Specifically, we consider the spin-1/2 cluster-Ising model and a class of spin-1 models undergoing quantum phase transitions to the Haldane phase. Our results provide a probe for symmetry-protected topological order. Since the picture holds even at the system's local scale, our analysis can serve as a local experimental test for topological order.

Experimental verification of acoustic pseudospin multipoles in a symmetry-broken snowflakelike topological insulator

NASA Astrophysics Data System (ADS)

Zhang, Zhiwang; Tian, Ye; Cheng, Ying; Liu, Xiaojun; Christensen, Johan

2017-12-01

Topologically protected wave engineering in artificially structured media resides at the frontier of ongoing metamaterials research, which is inspired by quantum mechanics. Acoustic analogs of electronic topological insulators have recently led to a wealth of new opportunities in manipulating sound propagation by means of robust edge mode excitations through analogies drawn to exotic quantum states. A variety of artificial acoustic systems hosting topological edge states have been proposed analogous to the quantum Hall effect, topological insulators, and Floquet topological insulators in electronic systems. However, those systems were characterized by a fixed geometry and a very narrow frequency response, which severely hinders the exploration and design of useful applications. Here we establish acoustic multipolar pseudospin states as an engineering degree of freedom in time-reversal invariant flow-free phononic crystals and develop reconfigurable topological insulators through rotation of their meta-atoms and reshaping of the metamolecules. Specifically, we show how rotation forms man-made snowflakelike molecules, whose topological phase mimics pseudospin-down (pseudospin-up) dipolar and quadrupolar states, which are responsible for a plethora of robust edge confined properties and topological controlled refraction disobeying Snell's law.

Fermionic Symmetry-Protected Topological Phase in a Two-Dimensional Hubbard Model

DOE PAGES

Chen, Cheng-Chien; Muechler, Lukas; Car, Roberto; ...

2016-08-25

We study the two-dimensional (2D) Hubbard model using exact diagonalization for spin-1/2 fermions on the triangular and honeycomb lattices decorated with a single hexagon per site. In certain parameter ranges, the Hubbard model maps to a quantum compass model on those lattices. On the triangular lattice, the compass model exhibits collinear stripe antiferromagnetism, implying d-density wave charge order in the original Hubbard model. On the honeycomb lattice, the compass model has a unique, quantum disordered ground state that transforms nontrivially under lattice reflection. The ground state of the Hubbard model on the decorated honeycomb lattice is thus a 2D fermionicmore » symmetry-protected topological phase. This state—protected by time-reversal and reflection symmetries—cannot be connected adiabatically to a free-fermion topological phase.« less

Crystalline Symmetry-Protected Majorana Mode in Number-Conserving Dirac Semimetal Nanowires

NASA Astrophysics Data System (ADS)

Zhang, Rui-Xing; Liu, Chao-Xing

2018-04-01

One of the cornerstones for topological quantum computations is the Majorana zero mode, which has been intensively searched in fractional quantum Hall systems and topological superconductors. Several recent works suggest that such an exotic mode can also exist in a one-dimensional (1D) interacting double-wire setup even without long-range superconductivity. A notable instability in these proposals comes from interchannel single-particle tunneling that spoils the topological ground state degeneracy. Here we show that a 1D Dirac semimetal (DSM) nanowire is an ideal number-conserving platform to realize such Majorana physics. By inserting magnetic flux, a DSM nanowire is driven into a 1D crystalline-symmetry-protected semimetallic phase. Interaction enables the emergence of boundary Majorana zero modes, which is robust as a result of crystalline symmetry protection. We also explore several experimental consequences of Majorana signals.

Skyrme insulators: insulators at the brink of superconductivity

DOE PAGES

Ertem, Onur; Chang, Po -Yao; Coleman, Piers; ...

2017-08-04

Current theories of superfluidity are based on the idea of a coherent quantum state with topologically protected, quantized circulation. When this topological protection is absent, as in the case of 3He-A, the coherent quantum state no longer supports persistent superflow. In this paper, we argue that the loss of topological protection in a superconductor gives rise to an insulating ground state. Specifically, we introduce the concept of a Skyrme insulator to describe the coherent dielectric state that results from the topological failure of superflow carried by a complex vector order parameter. Here, we apply this idea to the case ofmore » SmB6, arguing that the observation of a diamagnetic Fermi surface within an insulating bulk can be understood as a realization of this state. Our theory enables us to understand the linear specific heat of SmB6 in terms of a neutral Majorana Fermi sea and leads us to predict that in low fields of order a Gauss, SmB6 will develop a Meissner effect.« less

Skyrme Insulators: Insulators at the Brink of Superconductivity

NASA Astrophysics Data System (ADS)

Erten, Onur; Chang, Po-Yao; Coleman, Piers; Tsvelik, Alexei M.

2017-08-01

Current theories of superfluidity are based on the idea of a coherent quantum state with topologically protected quantized circulation. When this topological protection is absent, as in the case of 3He -A , the coherent quantum state no longer supports persistent superflow. Here, we argue that the loss of topological protection in a superconductor gives rise to an insulating ground state. We specifically introduce the concept of a Skyrme insulator to describe the coherent dielectric state that results from the topological failure of superflow carried by a complex-vector order parameter. We apply this idea to the case of SmB6 , arguing that the observation of a diamagnetic Fermi surface within an insulating bulk can be understood as a realization of this state. Our theory enables us to understand the linear specific heat of SmB6 in terms of a neutral Majorana Fermi sea and leads us to predict that in low fields of order a Gauss, SmB6 will develop a Meissner effect.

Topological Qubits from Valence Bond Solids

NASA Astrophysics Data System (ADS)

Wang, Dong-Sheng; Affleck, Ian; Raussendorf, Robert

2018-05-01

Topological qubits based on S U (N )-symmetric valence-bond solid models are constructed. A logical topological qubit is the ground subspace with twofold degeneracy, which is due to the spontaneous breaking of a global parity symmetry. A logical Z rotation by an angle 2 π /N , for any integer N >2 , is provided by a global twist operation, which is of a topological nature and protected by the energy gap. A general concatenation scheme with standard quantum error-correction codes is also proposed, which can lead to better codes. Generic error-correction properties of symmetry-protected topological order are also demonstrated.

Electrically controlled band gap and topological phase transition in two-dimensional multilayer germanane

NASA Astrophysics Data System (ADS)

Qi, Jingshan; Li, Xiao; Qian, Xiaofeng

2016-06-01

Electrically controlled band gap and topological electronic states are important for the next-generation topological quantum devices. In this letter, we study the electric field control of band gap and topological phase transitions in multilayer germanane. We find that although the monolayer and multilayer germananes are normal insulators, a vertical electric field can significantly reduce the band gap of multilayer germananes owing to the giant Stark effect. The decrease of band gap eventually leads to band inversion, transforming them into topological insulators with nontrivial Z2 invariant. The electrically controlled topological phase transition in multilayer germananes provides a potential route to manipulate topologically protected edge states and design topological quantum devices. This strategy should be generally applicable to a broad range of materials, including other two-dimensional materials and ultrathin films with controlled growth.

Quasiparticles in condensed matter systems

NASA Astrophysics Data System (ADS)

Wölfle, Peter

2018-03-01

Quasiparticles are a powerful concept of condensed matter quantum theory. In this review, the appearence and the properties of quasiparticles are presented in a unifying perspective. The principles behind the existence of quasiparticle excitations in both quantum disordered and ordered phases of fermionic and bosonic systems are discussed. The lifetime of quasiparticles is considered in particular near a continuous classical or quantum phase transition, when the nature of quasiparticles on both sides of a transition into an ordered state changes. A new concept of critical quasiparticles near a quantum critical point is introduced, and applied to quantum phase transitions in heavy fermion metals. Fractional quasiparticles in systems of restricted dimensionality are reviewed. Dirac quasiparticles emerging in so-called Dirac materials are discussed. The more recent discoveries of topologically protected chiral quasiparticles in topological matter and Majorana quasiparticles in topological superconductors are briefly reviewed.

High-Threshold Fault-Tolerant Quantum Computation with Analog Quantum Error Correction

NASA Astrophysics Data System (ADS)

Fukui, Kosuke; Tomita, Akihisa; Okamoto, Atsushi; Fujii, Keisuke

2018-04-01

To implement fault-tolerant quantum computation with continuous variables, the Gottesman-Kitaev-Preskill (GKP) qubit has been recognized as an important technological element. However, it is still challenging to experimentally generate the GKP qubit with the required squeezing level, 14.8 dB, of the existing fault-tolerant quantum computation. To reduce this requirement, we propose a high-threshold fault-tolerant quantum computation with GKP qubits using topologically protected measurement-based quantum computation with the surface code. By harnessing analog information contained in the GKP qubits, we apply analog quantum error correction to the surface code. Furthermore, we develop a method to prevent the squeezing level from decreasing during the construction of the large-scale cluster states for the topologically protected, measurement-based, quantum computation. We numerically show that the required squeezing level can be relaxed to less than 10 dB, which is within the reach of the current experimental technology. Hence, this work can considerably alleviate this experimental requirement and take a step closer to the realization of large-scale quantum computation.

Tensor Network Wavefunctions for Topological Phases

NASA Astrophysics Data System (ADS)

Ware, Brayden Alexander

The combination of quantum effects and interactions in quantum many-body systems can result in exotic phases with fundamentally entangled ground state wavefunctions--topological phases. Topological phases come in two types, both of which will be studied in this thesis. In topologically ordered phases, the pattern of entanglement in the ground state wavefunction encodes the statistics of exotic emergent excitations, a universal indicator of a phase that is robust to all types of perturbations. In symmetry protected topological phases, the entanglement instead encodes a universal response of the system to symmetry defects, an indicator that is robust only to perturbations respecting the protecting symmetry. Finding and creating these phases in physical systems is a motivating challenge that tests all aspects--analytical, numerical, and experimental--of our understanding of the quantum many-body problem. Nearly three decades ago, the creation of simple ansatz wavefunctions--such as the Laughlin fractional quantum hall state, the AKLT state, and the resonating valence bond state--spurred analytical understanding of both the role of entanglement in topological physics and physical mechanisms by which it can arise. However, quantitative understanding of the relevant phase diagrams is still challenging. For this purpose, tensor networks provide a toolbox for systematically improving wavefunction ansatz while still capturing the relevant entanglement properties. In this thesis, we use the tools of entanglement and tensor networks to analyze ansatz states for several proposed new phases. In the first part, we study a featureless phase of bosons on the honeycomb lattice and argue that this phase can be topologically protected under any one of several distinct subsets of the crystalline lattice symmetries. We discuss methods of detecting such phases with entanglement and without. In the second part, we consider the problem of constructing fixed-point wavefunctions for intrinsically fermionic topological phases, i.e. topological phases contructed out of fermions with a nontrivial response to fermion parity defects. A zero correlation length wavefunction and a commuting projector Hamiltonian that realizes this wavefunction as its ground state are constructed. Using an appropriate generalization of the minimally entangled states method for extraction of topological order from the ground states on a torus to the intrinsically fermionic case, we fully characterize the corresponding topological order as Ising x (px - ipy). We argue that this phase can be captured using fermionic tensor networks, expanding the applicability of tensor network methods.

Computational Power of Symmetry-Protected Topological Phases.

PubMed

Stephen, David T; Wang, Dong-Sheng; Prakash, Abhishodh; Wei, Tzu-Chieh; Raussendorf, Robert

2017-07-07

We consider ground states of quantum spin chains with symmetry-protected topological (SPT) order as resources for measurement-based quantum computation (MBQC). We show that, for a wide range of SPT phases, the computational power of ground states is uniform throughout each phase. This computational power, defined as the Lie group of executable gates in MBQC, is determined by the same algebraic information that labels the SPT phase itself. We prove that these Lie groups always contain a full set of single-qubit gates, thereby affirming the long-standing conjecture that general SPT phases can serve as computationally useful phases of matter.

Computational Power of Symmetry-Protected Topological Phases

NASA Astrophysics Data System (ADS)

Stephen, David T.; Wang, Dong-Sheng; Prakash, Abhishodh; Wei, Tzu-Chieh; Raussendorf, Robert

2017-07-01

We consider ground states of quantum spin chains with symmetry-protected topological (SPT) order as resources for measurement-based quantum computation (MBQC). We show that, for a wide range of SPT phases, the computational power of ground states is uniform throughout each phase. This computational power, defined as the Lie group of executable gates in MBQC, is determined by the same algebraic information that labels the SPT phase itself. We prove that these Lie groups always contain a full set of single-qubit gates, thereby affirming the long-standing conjecture that general SPT phases can serve as computationally useful phases of matter.

Electrically controlled band gap and topological phase transition in two-dimensional multilayer germanane

DOE Office of Scientific and Technical Information (OSTI.GOV)

Qi, Jingshan, E-mail: qijingshan@jsnu.edu.cn, E-mail: feng@tamu.edu; Li, Xiao; Qian, Xiaofeng, E-mail: qijingshan@jsnu.edu.cn, E-mail: feng@tamu.edu

2016-06-20

Electrically controlled band gap and topological electronic states are important for the next-generation topological quantum devices. In this letter, we study the electric field control of band gap and topological phase transitions in multilayer germanane. We find that although the monolayer and multilayer germananes are normal insulators, a vertical electric field can significantly reduce the band gap of multilayer germananes owing to the giant Stark effect. The decrease of band gap eventually leads to band inversion, transforming them into topological insulators with nontrivial Z{sub 2} invariant. The electrically controlled topological phase transition in multilayer germananes provides a potential route tomore » manipulate topologically protected edge states and design topological quantum devices. This strategy should be generally applicable to a broad range of materials, including other two-dimensional materials and ultrathin films with controlled growth.« less

Correlated spin currents generated by resonant-crossed Andreev reflections in topological superconductors

PubMed Central

He, James J.; Wu, Jiansheng; Choy, Ting-Pong; Liu, Xiong-Jun; Tanaka, Y.; Law, K. T.

2014-01-01

Topological superconductors, which support Majorana fermion excitations, have been the subject of intense studies due to their novel transport properties and their potential applications in fault-tolerant quantum computations. Here we propose a new type of topological superconductors that can be used as a novel source of correlated spin currents. We show that inducing superconductivity on a AIII class topological insulator wire, which respects a chiral symmetry and supports protected fermionic end states, will result in a topological superconductor. This topological superconductor supports two topological phases with one or two Majorana fermion end states, respectively. In the phase with two Majorana fermions, the superconductor can split Cooper pairs efficiently into electrons in two spatially separated leads due to Majorana-induced resonant-crossed Andreev reflections. The resulting currents in the leads are correlated and spin-polarized. Importantly, the proposed topological superconductors can be realized using quantum anomalous Hall insulators in proximity to superconductors. PMID:24492649

A quantized microwave quadrupole insulator with topologically protected corner states

NASA Astrophysics Data System (ADS)

Peterson, Christopher W.; Benalcazar, Wladimir A.; Hughes, Taylor L.; Bahl, Gaurav

2018-03-01

The theory of electric polarization in crystals defines the dipole moment of an insulator in terms of a Berry phase (geometric phase) associated with its electronic ground state. This concept not only solves the long-standing puzzle of how to calculate dipole moments in crystals, but also explains topological band structures in insulators and superconductors, including the quantum anomalous Hall insulator and the quantum spin Hall insulator, as well as quantized adiabatic pumping processes. A recent theoretical study has extended the Berry phase framework to also account for higher electric multipole moments, revealing the existence of higher-order topological phases that have not previously been observed. Here we demonstrate experimentally a member of this predicted class of materials—a quantized quadrupole topological insulator—produced using a gigahertz-frequency reconfigurable microwave circuit. We confirm the non-trivial topological phase using spectroscopic measurements and by identifying corner states that result from the bulk topology. In addition, we test the critical prediction that these corner states are protected by the topology of the bulk, and are not due to surface artefacts, by deforming the edges of the crystal lattice from the topological to the trivial regime. Our results provide conclusive evidence of a unique form of robustness against disorder and deformation, which is characteristic of higher-order topological insulators.

Proximity-Induced Superconductivity and Quantum Interference in Topological Crystalline Insulator SnTe Thin-Film Devices.

PubMed

Klett, Robin; Schönle, Joachim; Becker, Andreas; Dyck, Denis; Borisov, Kiril; Rott, Karsten; Ramermann, Daniela; Büker, Björn; Haskenhoff, Jan; Krieft, Jan; Hübner, Torsten; Reimer, Oliver; Shekhar, Chandra; Schmalhorst, Jan-Michael; Hütten, Andreas; Felser, Claudia; Wernsdorfer, Wolfgang; Reiss, Günter

2018-02-14

Topological crystalline insulators represent a new state of matter, in which the electronic transport is governed by mirror-symmetry protected Dirac surface states. Due to the helical spin-polarization of these surface states, the proximity of topological crystalline matter to a nearby superconductor is predicted to induce unconventional superconductivity and, thus, to host Majorana physics. We report on the preparation and characterization of Nb-based superconducting quantum interference devices patterned on top of topological crystalline insulator SnTe thin films. The SnTe films show weak anti-localization, and the weak links of the superconducting quantum interference devices (SQUID) exhibit fully gapped proximity-induced superconductivity. Both properties give a coinciding coherence length of 120 nm. The SQUID oscillations induced by a magnetic field show 2π periodicity, possibly dominated by the bulk conductivity.

Topological Triplon Modes and Bound States in a Shastry-Sutherland Magnet

NASA Astrophysics Data System (ADS)

McClarty, Paul; Kruger, Frank; Guidi, Tatiana; Parker, Stewart; Refson, Keith; Parker, Tony; Prabhakaran, Dharmalingam; Coldea, Radu

The twin discoveries of the quantum Hall effect, in the 1980's, and of topoogical band insulators, in the 2000's, were landmarks in physics that enriched our view of the electronic properties of solids. In a nutshell, these discoveries have taught us that quantum mechanical wavefunctions in crystalline solids may carry nontrivial topological invariants which have ramifications for the observable physics. One of the side effects of the recent topological insulator revolution has been that such physics is much more widespread than was appreciated ten years ago. For example, while topological insulators were originally studied in the context of electron wavefunctions, recent work has led to proposals of topological insulators in bosonic systems: in photonic crystals, in the vibrational modes of crystals, and in the excitations of ordered magnets. Using inelastic neutron scattering along with theoretical calculations we demonstrate that, in a weak magnetic field, the dimerized quantum magnet SrCu2(BO3)2 is a bosonic topological insulator with nonzero Chern number in the triplon bands and topologically protected chiral edge excitations.

The phase transitions between Z n × Z n bosonic topological phases in 1 + 1D, and a constraint on the central charge for the critical points between bosonic symmetry protected topological phases

DOE PAGES

Tsui, Lokman; Huang, Yen-Ta; Jiang, Hong-Chen; ...

2017-03-27

The study of continuous phase transitions triggered by spontaneous symmetry breaking has brought revolutionary ideas to physics. Recently, through the discovery of symmetry protected topological phases, it is realized that continuous quantum phase transition can also occur between states with the same symmetry but different topology. Here in this paper we study a specific class of such phase transitions in 1+1 dimensions – the phase transition between bosonic topological phases protected by Z n × Z n. We find in all cases the critical point possesses two gap opening relevant operators: one leads to a Landau-forbidden symmetry breaking phase transitionmore » and the other to the topological phase transition. We also obtained a constraint on the central charge for general phase transitions between symmetry protected bosonic topological phases in 1+1D.« less

The phase transitions between Z n × Z n bosonic topological phases in 1 + 1D, and a constraint on the central charge for the critical points between bosonic symmetry protected topological phases

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tsui, Lokman; Huang, Yen-Ta; Jiang, Hong-Chen

The study of continuous phase transitions triggered by spontaneous symmetry breaking has brought revolutionary ideas to physics. Recently, through the discovery of symmetry protected topological phases, it is realized that continuous quantum phase transition can also occur between states with the same symmetry but different topology. Here in this paper we study a specific class of such phase transitions in 1+1 dimensions – the phase transition between bosonic topological phases protected by Z n × Z n. We find in all cases the critical point possesses two gap opening relevant operators: one leads to a Landau-forbidden symmetry breaking phase transitionmore » and the other to the topological phase transition. We also obtained a constraint on the central charge for general phase transitions between symmetry protected bosonic topological phases in 1+1D.« less

Superconducting quantum simulator for topological order and the toric code

NASA Astrophysics Data System (ADS)

Sameti, Mahdi; Potočnik, Anton; Browne, Dan E.; Wallraff, Andreas; Hartmann, Michael J.

2017-04-01

Topological order is now being established as a central criterion for characterizing and classifying ground states of condensed matter systems and complements categorizations based on symmetries. Fractional quantum Hall systems and quantum spin liquids are receiving substantial interest because of their intriguing quantum correlations, their exotic excitations, and prospects for protecting stored quantum information against errors. Here, we show that the Hamiltonian of the central model of this class of systems, the toric code, can be directly implemented as an analog quantum simulator in lattices of superconducting circuits. The four-body interactions, which lie at its heart, are in our concept realized via superconducting quantum interference devices (SQUIDs) that are driven by a suitably oscillating flux bias. All physical qubits and coupling SQUIDs can be individually controlled with high precision. Topologically ordered states can be prepared via an adiabatic ramp of the stabilizer interactions. Strings of qubit operators, including the stabilizers and correlations along noncontractible loops, can be read out via a capacitive coupling to read-out resonators. Moreover, the available single-qubit operations allow to create and propagate elementary excitations of the toric code and to verify their fractional statistics. The architecture we propose allows to implement a large variety of many-body interactions and thus provides a versatile analog quantum simulator for topological order and lattice gauge theories.

Fidelity of Majorana-based quantum operations

NASA Astrophysics Data System (ADS)

Tanhayi Ahari, Mostafa; Ortiz, Gerardo; Seradjeh, Babak

2015-03-01

It is well known that one-dimensional p-wave superconductor, the so-called Kitaev model, has topologically distinct phases that are distinguished by the presence of Majorana fermions. Owing to their topological protection, these Majorana fermions have emerged as candidates for fault-tolerant quantum computation. They furnish the operation of such a computation via processes that produce, braid, and annihilate them in pairs. In this work we study some of these processes from the dynamical perspective. In particular, we determine the fidelity of the Majorana fermions when they are produced or annihilated by tuning the system through the corresponding topological phase transition. For a simple linear protocol, we derive analytical expressions for fidelity and test various perturbative schemes. For more general protocols, we present exact numerics. Our results are relevant for the operation of Majorana-based quantum gates and quantum memories.

Topological bound states of a quantum walk with cold atoms

NASA Astrophysics Data System (ADS)

Mugel, Samuel; Celi, Alessio; Massignan, Pietro; Asbóth, János K.; Lewenstein, Maciej; Lobo, Carlos

2016-08-01

We suggest a method for engineering a quantum walk, with cold atoms as walkers, which presents topologically nontrivial properties. We derive the phase diagram, and show that we are able to produce a boundary between topologically distinct phases using the finite beam width of the applied lasers. A topologically protected bound state can then be observed, which is pinned to the interface and is robust to perturbations. We show that it is possible to identify this bound state by averaging over spin sensitive measures of the atom's position, based on the spin distribution that these states display. Interestingly, there exists a parameter regime in which our system maps on to the Creutz ladder.

Numerical investigation of gapped edge states in fractional quantum Hall-superconductor heterostructures

NASA Astrophysics Data System (ADS)

Repellin, Cécile; Cook, Ashley M.; Neupert, Titus; Regnault, Nicolas

2018-03-01

Fractional quantum Hall-superconductor heterostructures may provide a platform towards non-abelian topological modes beyond Majoranas. However their quantitative theoretical study remains extremely challenging. We propose and implement a numerical setup for studying edge states of fractional quantum Hall droplets with a superconducting instability. The fully gapped edges carry a topological degree of freedom that can encode quantum information protected against local perturbations. We simulate such a system numerically using exact diagonalization by restricting the calculation to the quasihole-subspace of a (time-reversal symmetric) bilayer fractional quantum Hall system of Laughlin ν = 1/3 states. We show that the edge ground states are permuted by spin-dependent flux insertion and demonstrate their fractional 6π Josephson effect, evidencing their topological nature and the Cooper pairing of fractionalized quasiparticles. The versatility and efficiency of our setup make it a well suited method to tackle wider questions of edge phases and phase transitions in fractional quantum Hall systems.

Quantum strain sensor with a topological insulator HgTe quantum dot

PubMed Central

Korkusinski, Marek; Hawrylak, Pawel

2014-01-01

We present a theory of electronic properties of HgTe quantum dot and propose a strain sensor based on a strain-driven transition from a HgTe quantum dot with inverted bandstructure and robust topologically protected quantum edge states to a normal state without edge states in the energy gap. The presence or absence of edge states leads to large on/off ratio of conductivity across the quantum dot, tunable by adjusting the number of conduction channels in the source-drain voltage window. The electronic properties of a HgTe quantum dot as a function of size and applied strain are described using eight-band Luttinger and Bir-Pikus Hamiltonians, with surface states identified with chirality of Luttinger spinors and obtained through extensive numerical diagonalization of the Hamiltonian. PMID:24811674

Quantum computation on the edge of a symmetry-protected topological order.

PubMed

Miyake, Akimasa

2010-07-23

We elaborate the idea of quantum computation through measuring the correlation of a gapped ground state, while the bulk Hamiltonian is utilized to stabilize the resource. A simple computational primitive, by pulling out a single spin adiabatically from the bulk followed by its measurement, is shown to make any ground state of the one-dimensional isotropic Haldane phase useful ubiquitously as a quantum logical wire. The primitive is compatible with certain discrete symmetries that protect this topological order, and the antiferromagnetic Heisenberg spin-1 finite chain is practically available. Our approach manifests a holographic principle in that the logical information of a universal quantum computer can be written and processed perfectly on the edge state (i.e., boundary) of the system, supported by the persistent entanglement from the bulk even when the ground state and its evolution cannot be exactly analyzed.

Probing the Topology of Density Matrices

NASA Astrophysics Data System (ADS)

Bardyn, Charles-Edouard; Wawer, Lukas; Altland, Alexander; Fleischhauer, Michael; Diehl, Sebastian

2018-01-01

The mixedness of a quantum state is usually seen as an adversary to topological quantization of observables. For example, exact quantization of the charge transported in a so-called Thouless adiabatic pump is lifted at any finite temperature in symmetry-protected topological insulators. Here, we show that certain directly observable many-body correlators preserve the integrity of topological invariants for mixed Gaussian quantum states in one dimension. Our approach relies on the expectation value of the many-body momentum-translation operator and leads to a physical observable—the "ensemble geometric phase" (EGP)—which represents a bona fide geometric phase for mixed quantum states, in the thermodynamic limit. In cyclic protocols, the EGP provides a topologically quantized observable that detects encircled spectral singularities ("purity-gap" closing points) of density matrices. While we identify the many-body nature of the EGP as a key ingredient, we propose a conceptually simple, interferometric setup to directly measure the latter in experiments with mesoscopic ensembles of ultracold atoms.

Electron–hole asymmetry of the topological surface states in strained HgTe

PubMed Central

Jost, Andreas; Bendias, Michel; Böttcher, Jan; Hankiewicz, Ewelina; Brüne, Christoph; Buhmann, Hartmut; Molenkamp, Laurens W.; Maan, Jan C.; Zeitler, Uli; Hussey, Nigel; Wiedmann, Steffen

2017-01-01

Topological insulators are a new class of materials with an insulating bulk and topologically protected metallic surface states. Although it is widely assumed that these surface states display a Dirac-type dispersion that is symmetric above and below the Dirac point, this exact equivalence across the Fermi level has yet to be established experimentally. Here, we present a detailed transport study of the 3D topological insulator-strained HgTe that strongly challenges this prevailing viewpoint. First, we establish the existence of exclusively surface-dominated transport via the observation of an ambipolar surface quantum Hall effect and quantum oscillations in the Seebeck and Nernst effect. Second, we show that, whereas the thermopower is diffusion driven for surface electrons, both diffusion and phonon drag contributions are essential for the hole surface carriers. This distinct behavior in the thermoelectric response is explained by a strong deviation from the linear dispersion relation for the surface states, with a much flatter dispersion for holes compared with electrons. These findings show that the metallic surface states in topological insulators can exhibit both strong electron–hole asymmetry and a strong deviation from a linear dispersion but remain topologically protected. PMID:28280101

Topological gapped edge states in fractional quantum Hall-superconductor heterostructures

NASA Astrophysics Data System (ADS)

Cook, Ashley; Repellin, Cécile; Regnault, Nicolas; Neupert, Titus

We propose and implement a numerical setup for studying edge states of fractional quantum Hall droplets with a superconducting instability. We focus on a time-reversal symmetric bilayer fractional quantum Hall system of Laughlin ν = 1 / 3 states. The fully gapped edges carry a topological parafermionic degree of freedom that can encode quantum information protected against local perturbations. We numerically simulate such a system using exact diagonalization by restricting the calculation to the Laughlin quasihole subspace. We study the quantization of the total charge on each edge and show that the ground states are permuted by spin flux insertion and the parafermionic Josephson effect, evidencing their topological nature and the Cooper pairing of fractionalized quasiparticles. The full affiliation for Author 3 is: Laboratoire Pierre Aigrain, Ecole Normale Supérieure-PSL Research University, CNRS, Université Pierre et Marie Curie-Sorbonne Universités, Université Paris Diderot-Sorbonne Paris Cité, 24 rue Lhomond, 75231 Paris.

Machine learning topological states

NASA Astrophysics Data System (ADS)

Deng, Dong-Ling; Li, Xiaopeng; Das Sarma, S.

2017-11-01

Artificial neural networks and machine learning have now reached a new era after several decades of improvement where applications are to explode in many fields of science, industry, and technology. Here, we use artificial neural networks to study an intriguing phenomenon in quantum physics—the topological phases of matter. We find that certain topological states, either symmetry-protected or with intrinsic topological order, can be represented with classical artificial neural networks. This is demonstrated by using three concrete spin systems, the one-dimensional (1D) symmetry-protected topological cluster state and the 2D and 3D toric code states with intrinsic topological orders. For all three cases, we show rigorously that the topological ground states can be represented by short-range neural networks in an exact and efficient fashion—the required number of hidden neurons is as small as the number of physical spins and the number of parameters scales only linearly with the system size. For the 2D toric-code model, we find that the proposed short-range neural networks can describe the excited states with Abelian anyons and their nontrivial mutual statistics as well. In addition, by using reinforcement learning we show that neural networks are capable of finding the topological ground states of nonintegrable Hamiltonians with strong interactions and studying their topological phase transitions. Our results demonstrate explicitly the exceptional power of neural networks in describing topological quantum states, and at the same time provide valuable guidance to machine learning of topological phases in generic lattice models.

Symmetry enriched U(1) quantum spin liquids

NASA Astrophysics Data System (ADS)

Zou, Liujun; Wang, Chong; Senthil, T.

2018-05-01

We classify and characterize three-dimensional U (1 ) quantum spin liquids [deconfined U (1 ) gauge theories] with global symmetries. These spin liquids have an emergent gapless photon and emergent electric/magnetic excitations (which we assume are gapped). We first discuss in great detail the case with time-reversal and SO(3 ) spin rotational symmetries. We find there are 15 distinct such quantum spin liquids based on the properties of bulk excitations. We show how to interpret them as gauged symmetry-protected topological states (SPTs). Some of these states possess fractional response to an external SO (3 ) gauge field, due to which we dub them "fractional topological paramagnets." We identify 11 other anomalous states that can be grouped into three anomaly classes. The classification is further refined by weakly coupling these quantum spin liquids to bosonic symmetry protected topological (SPT) phases with the same symmetry. This refinement does not modify the bulk excitation structure but modifies universal surface properties. Taking this refinement into account, we find there are 168 distinct such U (1 ) quantum spin liquids. After this warm-up, we provide a general framework to classify symmetry enriched U (1 ) quantum spin liquids for a large class of symmetries. As a more complex example, we discuss U (1 ) quantum spin liquids with time-reversal and Z2 symmetries in detail. Based on the properties of the bulk excitations, we find there are 38 distinct such spin liquids that are anomaly-free. There are also 37 anomalous U (1 ) quantum spin liquids with this symmetry. Finally, we briefly discuss the classification of U (1 ) quantum spin liquids enriched by some other symmetries.

Topological entanglement entropy of fracton stabilizer codes

NASA Astrophysics Data System (ADS)

Ma, Han; Schmitz, A. T.; Parameswaran, S. A.; Hermele, Michael; Nandkishore, Rahul M.

2018-03-01

Entanglement entropy provides a powerful characterization of two-dimensional gapped topological phases of quantum matter, intimately tied to their description by topological quantum field theories (TQFTs). Fracton topological orders are three-dimensional gapped topologically ordered states of matter that lack a TQFT description. We show that three-dimensional fracton phases are nevertheless characterized, at least partially, by universal structure in the entanglement entropy of their ground-state wave functions. We explicitly compute the entanglement entropy for two archetypal fracton models, the "X-cube model" and "Haah's code," and demonstrate the existence of a nonlocal contribution that scales linearly in subsystem size. We show via Schrieffer-Wolff transformations that this piece of the entanglement entropy of fracton models is robust against arbitrary local perturbations of the Hamiltonian. Finally, we argue that these results may be extended to characterize localization-protected fracton topological order in excited states of disordered fracton models.

Quantum transport in topological semimetals under magnetic fields

NASA Astrophysics Data System (ADS)

Lu, Hai-Zhou; Shen, Shun-Qing

2017-06-01

Topological semimetals are three-dimensional topological states of matter, in which the conduction and valence bands touch at a finite number of points, i.e., the Weyl nodes. Topological semimetals host paired monopoles and antimonopoles of Berry curvature at the Weyl nodes and topologically protected Fermi arcs at certain surfaces. We review our recent works on quantum transport in topological semimetals, according to the strength of the magnetic field. At weak magnetic fields, there are competitions between the positive magnetoresistivity induced by the weak anti-localization effect and negative magnetoresistivity related to the nontrivial Berry curvature. We propose a fitting formula for the magnetoconductivity of the weak anti-localization. We expect that the weak localization may be induced by inter-valley effects and interaction effect, and occur in double-Weyl semimetals. For the negative magnetoresistance induced by the nontrivial Berry curvature in topological semimetals, we show the dependence of the negative magnetoresistance on the carrier density. At strong magnetic fields, specifically, in the quantum limit, the magnetoconductivity depends on the type and range of the scattering potential of disorder. The high-field positive magnetoconductivity may not be a compelling signature of the chiral anomaly. For long-range Gaussian scattering potential and half filling, the magnetoconductivity can be linear in the quantum limit. A minimal conductivity is found at the Weyl nodes although the density of states vanishes there.

Topological mirror superconductivity.

PubMed

Zhang, Fan; Kane, C L; Mele, E J

2013-08-02

We demonstrate the existence of topological superconductors (SCs) protected by mirror and time-reversal symmetries. D-dimensional (D=1, 2, 3) crystalline SCs are characterized by 2(D-1) independent integer topological invariants, which take the form of mirror Berry phases. These invariants determine the distribution of Majorana modes on a mirror symmetric boundary. The parity of total mirror Berry phase is the Z(2) index of a class DIII SC, implying that a DIII topological SC with a mirror line must also be a topological mirror SC but not vice versa and that a DIII SC with a mirror plane is always time-reversal trivial but can be mirror topological. We introduce representative models and suggest experimental signatures in feasible systems. Advances in quantum computing, the case for nodal SCs, the case for class D, and topological SCs protected by rotational symmetries are pointed out.

Self-organized pseudo-graphene on grain boundaries in topological band insulators

NASA Astrophysics Data System (ADS)

Slager, Robert-Jan; Juričić, Vladimir; Lahtinen, Ville; Zaanen, Jan

2016-06-01

Semimetals are characterized by nodal band structures that give rise to exotic electronic properties. The stability of Dirac semimetals, such as graphene in two spatial dimensions, requires the presence of lattice symmetries, while akin to the surface states of topological band insulators, Weyl semimetals in three spatial dimensions are protected by band topology. Here we show that in the bulk of topological band insulators, self-organized topologically protected semimetals can emerge along a grain boundary, a ubiquitous extended lattice defect in any crystalline material. In addition to experimentally accessible electronic transport measurements, these states exhibit a valley anomaly in two dimensions influencing edge spin transport, whereas in three dimensions they appear as graphenelike states that may exhibit an odd-integer quantum Hall effect. The general mechanism underlying these semimetals—the hybridization of spinon modes bound to the grain boundary—suggests that topological semimetals can emerge in any topological material where lattice dislocations bind localized topological modes.

Latent Computational Complexity of Symmetry-Protected Topological Order with Fractional Symmetry.

PubMed

Miller, Jacob; Miyake, Akimasa

2018-04-27

An emerging insight is that ground states of symmetry-protected topological orders (SPTOs) possess latent computational complexity in terms of their many-body entanglement. By introducing a fractional symmetry of SPTO, which requires the invariance under 3-colorable symmetries of a lattice, we prove that every renormalization fixed-point state of 2D (Z_{2})^{m} SPTO with fractional symmetry can be utilized for universal quantum computation using only Pauli measurements, as long as it belongs to a nontrivial 2D SPTO phase. Our infinite family of fixed-point states may serve as a base model to demonstrate the idea of a "quantum computational phase" of matter, whose states share universal computational complexity ubiquitously.

Majorana-Based Fermionic Quantum Computation.

PubMed

O'Brien, T E; Rożek, P; Akhmerov, A R

2018-06-01

Because Majorana zero modes store quantum information nonlocally, they are protected from noise, and have been proposed as a building block for a quantum computer. We show how to use the same protection from noise to implement universal fermionic quantum computation. Our architecture requires only two Majorana modes to encode a fermionic quantum degree of freedom, compared to alternative implementations which require a minimum of four Majorana modes for a spin quantum degree of freedom. The fermionic degrees of freedom support both unitary coupled cluster variational quantum eigensolver and quantum phase estimation algorithms, proposed for quantum chemistry simulations. Because we avoid the Jordan-Wigner transformation, our scheme has a lower overhead for implementing both of these algorithms, allowing for simulation of the Trotterized Hubbard Hamiltonian in O(1) time per unitary step. We finally demonstrate magic state distillation in our fermionic architecture, giving a universal set of topologically protected fermionic quantum gates.

Majorana-Based Fermionic Quantum Computation

NASA Astrophysics Data System (ADS)

O'Brien, T. E.; RoŻek, P.; Akhmerov, A. R.

2018-06-01

Because Majorana zero modes store quantum information nonlocally, they are protected from noise, and have been proposed as a building block for a quantum computer. We show how to use the same protection from noise to implement universal fermionic quantum computation. Our architecture requires only two Majorana modes to encode a fermionic quantum degree of freedom, compared to alternative implementations which require a minimum of four Majorana modes for a spin quantum degree of freedom. The fermionic degrees of freedom support both unitary coupled cluster variational quantum eigensolver and quantum phase estimation algorithms, proposed for quantum chemistry simulations. Because we avoid the Jordan-Wigner transformation, our scheme has a lower overhead for implementing both of these algorithms, allowing for simulation of the Trotterized Hubbard Hamiltonian in O (1 ) time per unitary step. We finally demonstrate magic state distillation in our fermionic architecture, giving a universal set of topologically protected fermionic quantum gates.

Topological surface states in nodal superconductors.

PubMed

Schnyder, Andreas P; Brydon, Philip M R

2015-06-24

Topological superconductors have become a subject of intense research due to their potential use for technical applications in device fabrication and quantum information. Besides fully gapped superconductors, unconventional superconductors with point or line nodes in their order parameter can also exhibit nontrivial topological characteristics. This article reviews recent progress in the theoretical understanding of nodal topological superconductors, with a focus on Weyl and noncentrosymmetric superconductors and their protected surface states. Using selected examples, we review the bulk topological properties of these systems, study different types of topological surface states, and examine their unusual properties. Furthermore, we survey some candidate materials for topological superconductivity and discuss different experimental signatures of topological surface states.

Topological Anderson insulator phase in a Dirac-semimetal thin film

NASA Astrophysics Data System (ADS)

Chen, Rui; Xu, Dong-Hui; Zhou, Bin

2017-06-01

The recently discovered topological Dirac semimetal represents a new exotic quantum state of matter. Topological Dirac semimetals can be viewed as three-dimensional analogues of graphene, in which the Dirac nodes are protected by crystalline symmetry. It has been found that the quantum confinement effect can gap out Dirac nodes and convert Dirac semimetal to a band insulator. The band insulator is either a normal insulator or quantum spin Hall insulator, depending on the thin-film thickness. We present the study of disorder effects in a thin film of Dirac semimetals. It is found that moderate Anderson disorder strength can drive a topological phase transition from a normal band insulator to a topological Anderson insulator in a Dirac-semimetal thin film. The numerical calculation based on the model parameters of Dirac semimetal Na3Bi shows that in the topological Anderson insulator phase, a quantized conductance plateau occurs in the bulk gap of the band insulator, and the distributions of local currents further confirm that the quantized conductance plateau arises from the helical edge states induced by disorder. Finally, an effective medium theory based on the Born approximation fits the numerical data.

Unexpected Giant-Gap Quantum Spin Hall Insulator in Chemically Decorated Plumbene Monolayer

PubMed Central

Zhao, Hui; Zhang, Chang-wen; Ji, Wei-xiao; Zhang, Run-wu; Li, Sheng-shi; Yan, Shi-shen; Zhang, Bao-min; Li, Ping; Wang, Pei-ji

2016-01-01

Quantum spin Hall (QSH) effect of two-dimensional (2D) materials features edge states that are topologically protected from backscattering by time-reversal symmetry. However, the major obstacles to the application for QSH effect are the lack of suitable QSH insulators with a large bulk gap. Here, we predict a novel class of 2D QSH insulators in X-decorated plumbene monolayers (PbX; X = H, F, Cl, Br, I) with extraordinarily giant bulk gaps from 1.03 eV to a record value of 1.34 eV. The topological characteristic of PbX mainly originates from s-px,y band inversion related to the lattice symmetry, while the effect of spin-orbital coupling (SOC) is only to open up a giant gap. Their QSH states are identified by nontrivial topological invariant Z2 = 1, as well as a single pair of topologically protected helical edge states locating inside the bulk gap. Noticeably, the QSH gaps of PbX are tunable and robust via external strain. We also propose high-dielectric-constant BN as an ideal substrate for the experimental realization of PbX, maintaining its nontrivial topology. These novel QSH insulators with giant gaps are a promising platform to enrich topological phenomena and expand potential applications at high temperature. PMID:26833133

Topological Acoustic Delay Line

NASA Astrophysics Data System (ADS)

Zhang, Zhiwang; Tian, Ye; Cheng, Ying; Wei, Qi; Liu, Xiaojun; Christensen, Johan

2018-03-01

Topological protected wave engineering in artificially structured media is at the frontier of ongoing metamaterials research that is inspired by quantum mechanics. Acoustic analogues of electronic topological insulators have recently led to a wealth of new opportunities in manipulating sound propagation with strikingly unconventional acoustic edge modes immune to backscattering. Earlier fabrications of topological insulators are characterized by an unreconfigurable geometry and a very narrow frequency response, which severely hinders the exploration and design of useful devices. Here we establish topologically protected sound in reconfigurable phononic crystals that can be switched on and off simply by rotating its three-legged "atoms" without altering the lattice structure. In particular, we engineer robust phase delay defects that take advantage of the ultrabroadband reflection-free sound propagation. Such topological delay lines serve as a paradigm in compact acoustic devices, interconnects, and electroacoustic integrated circuits.

Applications of Atomic Systems in Quantum Simulation, Quantum Computation and Topological Phases of Matter

NASA Astrophysics Data System (ADS)

Wang, Shengtao

The ability to precisely and coherently control atomic systems has improved dramatically in the last two decades, driving remarkable advancements in quantum computation and simulation. In recent years, atomic and atom-like systems have also been served as a platform to study topological phases of matter and non-equilibrium many-body physics. Integrated with rapid theoretical progress, the employment of these systems is expanding the realm of our understanding on a range of physical phenomena. In this dissertation, I draw on state-of-the-art experimental technology to develop several new ideas for controlling and applying atomic systems. In the first part of this dissertation, we propose several novel schemes to realize, detect, and probe topological phases in atomic and atom-like systems. We first theoretically study the intriguing properties of Hopf insulators, a peculiar type of topological insulators beyond the standard classification paradigm of topological phases. Using a solid-state quantum simulator, we report the first experimental observation of Hopf insulators. We demonstrate the Hopf fibration with fascinating topological links in the experiment, showing clear signals of topological phase transitions for the underlying Hamiltonian. Next, we propose a feasible experimental scheme to realize the chiral topological insulator in three dimensions. They are a type of topological insulators protected by the chiral symmetry and have thus far remained unobserved in experiment. We then introduce a method to directly measure topological invariants in cold-atom experiments. This detection scheme is general and applicable to probe of different topological insulators in any spatial dimension. In another study, we theoretically discover a new type of topological gapless rings, dubbed a Weyl exceptional ring, in three-dimensional dissipative cold atomic systems. In the second part of this dissertation, we focus on the application of atomic systems in quantum computation and simulation. Trapped atomic ions are one of the leading platforms to build a scalable, universal quantum computer. The common one-dimensional setup, however, greatly limits the system's scalability. By solving the critical problem of micromotion, we propose a two-dimensional architecture for scalable trapped-ion quantum computation. Hamiltonian tomography for many-body quantum systems is essential for benchmarking quantum computation and simulation. By employing dynamical decoupling, we propose a scalable scheme for full Hamiltonian tomography. The required number of measurements increases only polynomially with the system size, in contrast to an exponential scaling in common methods. Finally, we work toward the goal of demonstrating quantum supremacy. A number of sampling tasks, such as the boson sampling problem, have been proposed to be classically intractable under mild assumptions. An intermediate quantum computer can efficiently solve the sampling problem, but the correct operation of the device is not known to be classically verifiable. Toward practical verification, we present an experimental friendly scheme to extract useful and robust information from the quantum boson samplers based on coarse-grained measurements. In a separate study, we introduce a new model built from translation-invariant Ising-interacting spins. This model possesses several advantageous properties, catalyzing the ultimate experimental demonstration of quantum supremacy.

Impurity-generated non-Abelions

NASA Astrophysics Data System (ADS)

Simion, G.; Kazakov, A.; Rokhinson, L. P.; Wojtowicz, T.; Lyanda-Geller, Y. B.

2018-06-01

Two classes of topological superconductors and Majorana modes in condensed matter systems are known to date: one in which disorder induced by impurities strongly suppresses topological superconducting gap and is detrimental to Majorana modes, and another where Majorana fermions are protected by a disorder-robust topological superconductor gap. Observation and control of Majorana fermions and other non-Abelions often requires a symmetry of an underlying system leading to a gap in the single-particle or quasiparticle spectra. In semiconductor structures, impurities that provide charge carriers introduce states into the gap and enable conductance and proximity-induced superconductivity via the in-gap states. Thus a third class of topological superconductivity and Majorana modes emerges, in which topological superconductivity and Majorana fermions appear exclusively when impurities generate in-gap states. We show that impurity-enabled topological superconductivity is realized in a quantum Hall ferromagnet, when a helical domain wall is coupled to an s -wave superconductor. As an example of emergence of topological superconductivity in quantum Hall ferromagnets, we consider the integer quantum Hall effect in Mn-doped CdTe quantum wells. Recent experiments on transport through the quantum Hall ferromagnet domain wall in this system indicated a vital role of impurities in the conductance, but left unresolved the question whether impurities preclude generation of Majorana fermions and other non-Abelions in such systems in general. Here, solving a general quantum-mechanical problem of impurity bound states in a system of spin-orbit coupled Landau levels, we demonstrate that impurity-induced Majorana modes emerge at boundaries between topological and conventional superconducting states generated in a domain wall due to proximity to an s superconductor. We consider both short-range disorder and a smooth random potential. The phase diagram of the system is defined by characteristic disorder, gate voltage induced angular momentum splitting of impurity levels, and by a proximity superconducting gap. The phase diagram exhibits two ranges of gate voltage with conventional superconducting order separated by a gate voltage range with topological superconductivity. We show that electrostatic control of domain walls in an integer quantum Hall ferromagnet allows manipulation of Majorana fermions. Ferromagnetic transitions in the fractional quantum Hall regime may lead to the formation and electrostatic control of higher order non-Abelian excitations.

Topological phase transition and evolution of edge states in In-rich InGaN/GaN quantum wells under hydrostatic pressure

NASA Astrophysics Data System (ADS)

Łepkowski, S. P.; Bardyszewski, W.

2017-02-01

Combining the k · p method with the third-order elasticity theory, we perform a theoretical study of the pressure-induced topological phase transition and the pressure evolution of topologically protected edge states in InN/GaN and In-rich InGaN/GaN quantum wells. We show that for a certain range of the quantum well parameters, thanks to a negative band gap pressure coefficient, it is possible to continuously drive the system from the normal insulator state through the topological insulator into the semimetal phase. The critical pressure for the topological phase transition depends not only on the quantum well thickness but also on the width of the Hall bar, which determines the coupling between the edge states localized at the opposite edges. We also find that in narrow Hall bar structures, near the topological phase transition, a significant Rashba-type spin splitting of the lower and upper branches of the edge state dispersion curve appears. This effect originates from the lack of the mirror symmetry of the quantum well potential caused by the built-in electric field, and can be suppressed by increasing the Hall bar width. When the pressure increases, the energy dispersion of the edge states becomes more parabolic-like and the spin splitting decreases. A further increase of pressure leads to the transition to a semimetal phase, which occurs due to the closure of the indirect 2D bulk band gap. The difference between the critical pressure at which the system becomes semimetallic, and the pressure for the topological phase transition, correlates with the variation of the pressure coefficient of the band gap in the normal insulator state.

Topological phase transition and evolution of edge states in In-rich InGaN/GaN quantum wells under hydrostatic pressure.

PubMed

Łepkowski, S P; Bardyszewski, W

2017-02-08

Combining the k · p method with the third-order elasticity theory, we perform a theoretical study of the pressure-induced topological phase transition and the pressure evolution of topologically protected edge states in InN/GaN and In-rich InGaN/GaN quantum wells. We show that for a certain range of the quantum well parameters, thanks to a negative band gap pressure coefficient, it is possible to continuously drive the system from the normal insulator state through the topological insulator into the semimetal phase. The critical pressure for the topological phase transition depends not only on the quantum well thickness but also on the width of the Hall bar, which determines the coupling between the edge states localized at the opposite edges. We also find that in narrow Hall bar structures, near the topological phase transition, a significant Rashba-type spin splitting of the lower and upper branches of the edge state dispersion curve appears. This effect originates from the lack of the mirror symmetry of the quantum well potential caused by the built-in electric field, and can be suppressed by increasing the Hall bar width. When the pressure increases, the energy dispersion of the edge states becomes more parabolic-like and the spin splitting decreases. A further increase of pressure leads to the transition to a semimetal phase, which occurs due to the closure of the indirect 2D bulk band gap. The difference between the critical pressure at which the system becomes semimetallic, and the pressure for the topological phase transition, correlates with the variation of the pressure coefficient of the band gap in the normal insulator state.

Unconventional Topological Phase Transition in Two-Dimensional Systems with Space-Time Inversion Symmetry

NASA Astrophysics Data System (ADS)

Ahn, Junyeong; Yang, Bohm-Jung

2017-04-01

We study a topological phase transition between a normal insulator and a quantum spin Hall insulator in two-dimensional (2D) systems with time-reversal and twofold rotation symmetries. Contrary to the case of ordinary time-reversal invariant systems, where a direct transition between two insulators is generally predicted, we find that the topological phase transition in systems with an additional twofold rotation symmetry is mediated by an emergent stable 2D Weyl semimetal phase between two insulators. Here the central role is played by the so-called space-time inversion symmetry, the combination of time-reversal and twofold rotation symmetries, which guarantees the quantization of the Berry phase around a 2D Weyl point even in the presence of strong spin-orbit coupling. Pair creation and pair annihilation of Weyl points accompanying partner exchange between different pairs induces a jump of a 2D Z2 topological invariant leading to a topological phase transition. According to our theory, the topological phase transition in HgTe /CdTe quantum well structure is mediated by a stable 2D Weyl semimetal phase because the quantum well, lacking inversion symmetry intrinsically, has twofold rotation about the growth direction. Namely, the HgTe /CdTe quantum well can show 2D Weyl semimetallic behavior within a small but finite interval in the thickness of HgTe layers between a normal insulator and a quantum spin Hall insulator. We also propose that few-layer black phosphorus under perpendicular electric field is another candidate system to observe the unconventional topological phase transition mechanism accompanied by the emerging 2D Weyl semimetal phase protected by space-time inversion symmetry.

Andreev spectrum with high spin-orbit interactions: Revealing spin splitting and topologically protected crossings

NASA Astrophysics Data System (ADS)

Murani, A.; Chepelianskii, A.; Guéron, S.; Bouchiat, H.

2017-10-01

In order to point out experimentally accessible signatures of spin-orbit interaction, we investigate numerically the Andreev spectrum of a multichannel mesoscopic quantum wire (N) with high spin-orbit interaction coupled to superconducting electrodes (S), contrasting topological and nontopological behaviors. In the nontopological case (square lattice with Rashba interactions), we find that the Kramers degeneracy of Andreev levels is lifted by a phase difference between the S reservoirs except at multiples of π , when the normal quantum wires can host several conduction channels. The level crossings at these points invariant by time-reversal symmetry are not lifted by disorder. Whereas the dc Josephson current is insensitive to these level crossings, the high-frequency admittance (susceptibility) at finite temperature reveals these level crossings and the lifting of their degeneracy at π by a small Zeeman field. We have also investigated the hexagonal lattice with intrinsic spin-orbit interaction in the range of parameters where it is a two-dimensional topological insulator with one-dimensional helical edges protected against disorder. Nontopological superconducting contacts can induce topological superconductivity in this system characterized by zero-energy level crossing of Andreev levels. Both Josephson current and finite-frequency admittance carry then very specific signatures at low temperature of this disorder-protected Andreev level crossing at π and zero energy.

From bosonic topological transition to symmetric fermion mass generation

NASA Astrophysics Data System (ADS)

You, Yi-Zhuang; He, Yin-Chen; Vishwanath, Ashvin; Xu, Cenke

2018-03-01

A bosonic topological transition (BTT) is a quantum critical point between the bosonic symmetry-protected topological phase and the trivial phase. In this work, we investigate such a transition in a (2+1)-dimensional lattice model with the maximal microscopic symmetry: an internal SO (4 ) symmetry. We derive a description for this transition in terms of compact quantum electrodynamics (QED) with four fermion flavors (Nf=4 ). Within a systematic renormalization group analysis, we identify the critical point with the desired O (4 ) emergent symmetry and all expected deformations. By lowering the microscopic symmetry, we recover the previous Nf=2 noncompact QED description of the BTT. Finally, by merging two BTTs we recover a previously discussed theory of symmetric mass generation, as an SU (2 ) quantum chromodynamics-Higgs theory with Nf=4 flavors of SU (2 ) fundamental fermions and one SU (2 ) fundamental Higgs boson. This provides a consistency check on both theories.

Synthesis of Arbitrary Quantum Circuits to Topological Assembly: Systematic, Online and Compact.

PubMed

Paler, Alexandru; Fowler, Austin G; Wille, Robert

2017-09-05

It is challenging to transform an arbitrary quantum circuit into a form protected by surface code quantum error correcting codes (a variant of topological quantum error correction), especially if the goal is to minimise overhead. One of the issues is the efficient placement of magic state distillation sub circuits, so-called distillation boxes, in the space-time volume that abstracts the computation's required resources. This work presents a general, systematic, online method for the synthesis of such circuits. Distillation box placement is controlled by so-called schedulers. The work introduces a greedy scheduler generating compact box placements. The implemented software, whose source code is available at www.github.com/alexandrupaler/tqec, is used to illustrate and discuss synthesis examples. Synthesis and optimisation improvements are proposed.

Unexpected mass acquisition of Dirac fermions at the quantum phase transition of a topological insulator

NASA Astrophysics Data System (ADS)

Sato, T.; Segawa, Kouji; Kosaka, K.; Souma, S.; Nakayama, K.; Eto, K.; Minami, T.; Ando, Yoichi; Takahashi, T.

2011-11-01

The three-dimensional (3D) topological insulator is a novel quantum state of matter where an insulating bulk hosts a linearly dispersing surface state, which can be viewed as a sea of massless Dirac fermions protected by the time-reversal symmetry (TRS). Breaking the TRS by a magnetic order leads to the opening of a gap in the surface state, and consequently the Dirac fermions become massive. It has been proposed theoretically that such a mass acquisition is necessary to realize novel topological phenomena, but achieving a sufficiently large mass is an experimental challenge. Here we report an unexpected discovery that the surface Dirac fermions in a solid-solution system TlBi(S1-xSex)2 acquire a mass without explicitly breaking the TRS. We found that this system goes through a quantum phase transition from the topological to the non-topological phase, and, by tracing the evolution of the electronic states using the angle-resolved photoemission, we observed that the massless Dirac state in TlBiSe2 switches to a massive state before it disappears in the non-topological phase. This result suggests the existence of a condensed-matter version of the `Higgs mechanism' where particles acquire a mass through spontaneous symmetry breaking.

Emergence, evolution, and control of multistability in a hybrid topological quantum/classical system.

PubMed

Wang, Guanglei; Xu, Hongya; Lai, Ying-Cheng

2018-03-01

We present a novel class of nonlinear dynamical systems-a hybrid of relativistic quantum and classical systems and demonstrate that multistability is ubiquitous. A representative setting is coupled systems of a topological insulator and an insulating ferromagnet, where the former possesses an insulating bulk with topologically protected, dissipationless, and conducting surface electronic states governed by the relativistic quantum Dirac Hamiltonian and the latter is described by the nonlinear classical evolution of its magnetization vector. The interactions between the two are essentially the spin transfer torque from the topological insulator to the ferromagnet and the local proximity induced exchange coupling in the opposite direction. The hybrid system exhibits a rich variety of nonlinear dynamical phenomena besides multistability such as bifurcations, chaos, and phase synchronization. The degree of multistability can be controlled by an external voltage. In the case of two coexisting states, the system is effectively binary, opening a door to exploitation for developing spintronic memory devices. Because of the dissipationless and spin-momentum locking nature of the surface currents of the topological insulator, little power is needed for generating a significant current, making the system appealing for potential applications in next generation of low power memory devices.

Emergence, evolution, and control of multistability in a hybrid topological quantum/classical system

NASA Astrophysics Data System (ADS)

Wang, Guanglei; Xu, Hongya; Lai, Ying-Cheng

2018-03-01

We present a novel class of nonlinear dynamical systems—a hybrid of relativistic quantum and classical systems and demonstrate that multistability is ubiquitous. A representative setting is coupled systems of a topological insulator and an insulating ferromagnet, where the former possesses an insulating bulk with topologically protected, dissipationless, and conducting surface electronic states governed by the relativistic quantum Dirac Hamiltonian and the latter is described by the nonlinear classical evolution of its magnetization vector. The interactions between the two are essentially the spin transfer torque from the topological insulator to the ferromagnet and the local proximity induced exchange coupling in the opposite direction. The hybrid system exhibits a rich variety of nonlinear dynamical phenomena besides multistability such as bifurcations, chaos, and phase synchronization. The degree of multistability can be controlled by an external voltage. In the case of two coexisting states, the system is effectively binary, opening a door to exploitation for developing spintronic memory devices. Because of the dissipationless and spin-momentum locking nature of the surface currents of the topological insulator, little power is needed for generating a significant current, making the system appealing for potential applications in next generation of low power memory devices.

Different Topological Quantum States in Ternary Zintl compounds: BaCaX (X = Si, Ge, Sn and Pb)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Lin-Lin; Kaminski, Adam; Canfield, Paul C.

Topological quantum states require stringent combination of crystal symmetry and spin–orbit coupling (SOC) strength. Here in this paper, we report that the ternary Zintl compound series BaCaX (X = Si, Ge, Sn and Pb, Group IV) in the same crystal structure having eight valence electrons per formula unit can host two different topological quantum phases, controlled by atomic size and SOC strength. BaCaSi is a nodal-line semimetal (NLSM) with band inversion protected by mirror symmetry and hosts a strong topological insulator (TI) state when SOC is turned on, thus, a NLSM-TI phase. Moving to larger atomic sizes and heavier atoms,more » BaCaGe and BaCaSn are normal insulators (NIs); then, with the strongest SOC in BaCaPb, a different band inversion is induced, giving a strong TI phase without the need of NLSM. Thus, we also predict two types of topological transitions in a phase diagram for BaCaX: (1) NLSM-TI to NI, then to TI by tuning atomic size and SOC strength via alloying, and (2) NI or TI to NLSM-TI via pressure.« less

Different Topological Quantum States in Ternary Zintl compounds: BaCaX (X = Si, Ge, Sn and Pb)

DOE PAGES

Wang, Lin-Lin; Kaminski, Adam; Canfield, Paul C.; ...

2017-12-14

Topological quantum states require stringent combination of crystal symmetry and spin–orbit coupling (SOC) strength. Here in this paper, we report that the ternary Zintl compound series BaCaX (X = Si, Ge, Sn and Pb, Group IV) in the same crystal structure having eight valence electrons per formula unit can host two different topological quantum phases, controlled by atomic size and SOC strength. BaCaSi is a nodal-line semimetal (NLSM) with band inversion protected by mirror symmetry and hosts a strong topological insulator (TI) state when SOC is turned on, thus, a NLSM-TI phase. Moving to larger atomic sizes and heavier atoms,more » BaCaGe and BaCaSn are normal insulators (NIs); then, with the strongest SOC in BaCaPb, a different band inversion is induced, giving a strong TI phase without the need of NLSM. Thus, we also predict two types of topological transitions in a phase diagram for BaCaX: (1) NLSM-TI to NI, then to TI by tuning atomic size and SOC strength via alloying, and (2) NI or TI to NLSM-TI via pressure.« less

Charge 2e/3 Superconductivity and Topological Degeneracies without Localized Zero Modes in Bilayer Fractional Quantum Hall States.

PubMed

Barkeshli, Maissam

2016-08-26

It has been recently shown that non-Abelian defects with localized parafermion zero modes can arise in conventional Abelian fractional quantum Hall (FQH) states. Here we propose an alternate route to creating, manipulating, and measuring topologically protected degeneracies in bilayer FQH states coupled to superconductors, without the creation of localized parafermion zero modes. We focus mainly on electron-hole bilayers, with a ±1/3 Laughlin FQH state in each layer, with boundaries that are proximity coupled to a superconductor. We show that the superconductor induces charge 2e/3 quasiparticle-pair condensation at each boundary of the FQH state, and that this leads to (i) topologically protected degeneracies that can be measured through charge sensing experiments and (ii) a fractional charge 2e/3 ac Josephson effect. We demonstrate that an analog of non-Abelian braiding is possible, despite the absence of a localized zero mode. We discuss several practical advantages of this proposal over previous work, and also several generalizations.

Robust integer and fractional helical modes in the quantum Hall effect

NASA Astrophysics Data System (ADS)

Ronen, Yuval; Cohen, Yonatan; Banitt, Daniel; Heiblum, Moty; Umansky, Vladimir

2018-04-01

Electronic systems harboring one-dimensional helical modes, where spin and momentum are locked, have lately become an important field of their own. When coupled to a conventional superconductor, such systems are expected to manifest topological superconductivity; a unique phase hosting exotic Majorana zero modes. Even more interesting are fractional helical modes, yet to be observed, which open the route for realizing generalized parafermions. Possessing non-Abelian exchange statistics, these quasiparticles may serve as building blocks in topological quantum computing. Here, we present a new approach to form protected one-dimensional helical edge modes in the quantum Hall regime. The novel platform is based on a carefully designed double-quantum-well structure in a GaAs-based system hosting two electronic sub-bands; each tuned to the quantum Hall effect regime. By electrostatic gating of different areas of the structure, counter-propagating integer, as well as fractional, edge modes with opposite spins are formed. We demonstrate that, due to spin protection, these helical modes remain ballistic over large distances. In addition to the formation of helical modes, this platform can serve as a rich playground for artificial induction of compounded fractional edge modes, and for construction of edge-mode-based interferometers.

Spin and topological order in a periodically driven spin chain

NASA Astrophysics Data System (ADS)

Russomanno, Angelo; Friedman, Bat-el; Dalla Torre, Emanuele G.

2017-07-01

The periodically driven quantum Ising chain has recently attracted a large attention in the context of Floquet engineering. In addition to the common paramagnet and ferromagnet, this driven model can give rise to new topological phases. In this work, we systematically explore its quantum phase diagram by examining the properties of its Floquet ground state. We specifically focus on driving protocols with time-reversal invariant points, and demonstrate the existence of an infinite number of distinct phases. These phases are separated by second-order quantum phase transitions, accompanied by continuous changes of local and string order parameters, as well as sudden changes of a topological winding number and of the number of protected edge states. When one of these phase transitions is adiabatically crossed, the correlator associated to the order parameter is nonvanishing over a length scale which shows a Kibble-Zurek scaling. In some phases, the Floquet ground state spontaneously breaks the discrete time-translation symmetry of the Hamiltonian. Our findings provide a better understanding of topological phases in periodically driven clean integrable models.

Controllable band structure and topological phase transition in two-dimensional hydrogenated arsenene

PubMed Central

Wang, Ya-ping; Ji, Wei-xiao; Zhang, Chang-wen; Li, Ping; Li, Feng; Ren, Miao-juan; Chen, Xin-Lian; Yuan, Min; Wang, Pei-ji

2016-01-01

Discovery of two-dimensional (2D) topological insulator such as group-V films initiates challenges in exploring exotic quantum states in low dimensions. Here, we perform first-principles calculations to study the geometric and electronic properties in 2D arsenene monolayer with hydrogenation (HAsH). We predict a new σ-type Dirac cone related to the px,y orbitals of As atoms in HAsH, dependent on in-plane tensile strain. Noticeably, the spin-orbit coupling (SOC) opens a quantum spin Hall (QSH) gap of 193 meV at the Dirac cone. A single pair of topologically protected helical edge states is established for the edges, and its QSH phase is confirmed with topological invariant Z2 = 1. We also propose a 2D quantum well (QW) encapsulating HAsH with the h-BN sheet on each side, which harbors a nontrivial QSH state with the Dirac cone lying within the band gap of cladding BN substrate. These findings provide a promising innovative platform for QSH device design and fabrication operating at room temperature. PMID:26839209

Controllable band structure and topological phase transition in two-dimensional hydrogenated arsenene

NASA Astrophysics Data System (ADS)

Wang, Ya-Ping; Ji, Wei-Xiao; Zhang, Chang-Wen; Li, Ping; Li, Feng; Ren, Miao-Juan; Chen, Xin-Lian; Yuan, Min; Wang, Pei-Ji

2016-02-01

Discovery of two-dimensional (2D) topological insulator such as group-V films initiates challenges in exploring exotic quantum states in low dimensions. Here, we perform first-principles calculations to study the geometric and electronic properties in 2D arsenene monolayer with hydrogenation (HAsH). We predict a new σ-type Dirac cone related to the px,y orbitals of As atoms in HAsH, dependent on in-plane tensile strain. Noticeably, the spin-orbit coupling (SOC) opens a quantum spin Hall (QSH) gap of 193 meV at the Dirac cone. A single pair of topologically protected helical edge states is established for the edges, and its QSH phase is confirmed with topological invariant Z2 = 1. We also propose a 2D quantum well (QW) encapsulating HAsH with the h-BN sheet on each side, which harbors a nontrivial QSH state with the Dirac cone lying within the band gap of cladding BN substrate. These findings provide a promising innovative platform for QSH device design and fabrication operating at room temperature.

Two-dimensional topological photonic systems

NASA Astrophysics Data System (ADS)

Sun, Xiao-Chen; He, Cheng; Liu, Xiao-Ping; Lu, Ming-Hui; Zhu, Shi-Ning; Chen, Yan-Feng

2017-09-01

The topological phase of matter, originally proposed and first demonstrated in fermionic electronic systems, has drawn considerable research attention in the past decades due to its robust transport of edge states and its potential with respect to future quantum information, communication, and computation. Recently, searching for such a unique material phase in bosonic systems has become a hot research topic worldwide. So far, many bosonic topological models and methods for realizing them have been discovered in photonic systems, acoustic systems, mechanical systems, etc. These discoveries have certainly yielded vast opportunities in designing material phases and related properties in the topological domain. In this review, we first focus on some of the representative photonic topological models and employ the underlying Dirac model to analyze the edge states and geometric phase. On the basis of these models, three common types of two-dimensional topological photonic systems are discussed: 1) photonic quantum Hall effect with broken time-reversal symmetry; 2) photonic topological insulator and the associated pseudo-time-reversal symmetry-protected mechanism; 3) time/space periodically modulated photonic Floquet topological insulator. Finally, we provide a summary and extension of this emerging field, including a brief introduction to the Weyl point in three-dimensional systems.

Dynamically enriched topological orders in driven two-dimensional systems

NASA Astrophysics Data System (ADS)

Potter, Andrew C.; Morimoto, Takahiro

2017-04-01

Time-periodic driving of a quantum system can enable new dynamical topological phases of matter that could not exist in thermal equilibrium. We investigate two related classes of dynamical topological phenomena in 2D systems: Floquet symmetry-protected topological phases (FSPTs) and Floquet enriched topological orders (FETs). By constructing solvable lattice models for a complete set of 2D bosonic FSPT phases, we show that bosonic FSPTs can be understood as topological pumps which deposit loops of 1D SPT chains onto the boundary during each driving cycle, which protects a nontrivial edge state by dynamically tuning the edge to a self-dual point poised between the 1D SPT and trivial phases of the edge. By coupling these FSPT models to dynamical gauge fields, we construct solvable models of FET orders in which anyon excitations are dynamically transmuted into topologically distinct anyon types during each driving period. These bosonic FSPT and gauged FSPT models are classified by group cohomology methods. In addition, we also construct examples of "beyond cohomology" FET orders, which can be viewed as topological pumps of 1D topological chains formed of emergent anyonic quasiparticles.

Quasiparticle Interference Studies of Quantum Materials.

PubMed

Avraham, Nurit; Reiner, Jonathan; Kumar-Nayak, Abhay; Morali, Noam; Batabyal, Rajib; Yan, Binghai; Beidenkopf, Haim

2018-06-03

Exotic electronic states are realized in novel quantum materials. This field is revolutionized by the topological classification of materials. Such compounds necessarily host unique states on their boundaries. Scanning tunneling microscopy studies of these surface states have provided a wealth of spectroscopic characterization, with the successful cooperation of ab initio calculations. The method of quasiparticle interference imaging proves to be particularly useful for probing the dispersion relation of the surface bands. Herein, how a variety of additional fundamental electronic properties can be probed via this method is reviewed. It is demonstrated how quasiparticle interference measurements entail mesoscopic size quantization and the electronic phase coherence in semiconducting nanowires; helical spin protection and energy-momentum fluctuations in a topological insulator; and the structure of the Bloch wave function and the relative insusceptibility of topological electronic states to surface potential in a topological Weyl semimetal. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Complete theory of symmetry-based indicators of band topology.

PubMed

Po, Hoi Chun; Vishwanath, Ashvin; Watanabe, Haruki

2017-06-30

The interplay between symmetry and topology leads to a rich variety of electronic topological phases, protecting states such as the topological insulators and Dirac semimetals. Previous results, like the Fu-Kane parity criterion for inversion-symmetric topological insulators, demonstrate that symmetry labels can sometimes unambiguously indicate underlying band topology. Here we develop a systematic approach to expose all such symmetry-based indicators of band topology in all the 230 space groups. This is achieved by first developing an efficient way to represent band structures in terms of elementary basis states, and then isolating the topological ones by removing the subset of atomic insulators, defined by the existence of localized symmetric Wannier functions. Aside from encompassing all earlier results on such indicators, including in particular the notion of filling-enforced quantum band insulators, our theory identifies symmetry settings with previously hidden forms of band topology, and can be applied to the search for topological materials.Understanding the role of topology in determining electronic structure can lead to the discovery, or appreciation, of materials with exotic properties such as protected surface states. Here, the authors present a framework for identifying topologically distinct band-structures for all 3D space groups.

(DARPA) Topologically Protected Quantum Information Processing In Spin-Orbit Compled Semiconductors

DTIC Science & Technology

2013-12-17

expression for the disorder suppression of the superconducting quasiparticle gap in the topological superconducting states carrying MFs. Our principle...assisted electron transfer amplitude (derived from the fractionalization property of the MFs) the quasiparticle tunneling from to through the...mesoscopic rings, the energy-level of such a quasiparticle excitation spectrum in the ring is expected to develop a periodic dependence on

Superconducting quantum spin-Hall systems with giant orbital g-factors

NASA Astrophysics Data System (ADS)

Hankiewicz, Ewelina; Reinthaler, Rolf; Tkachov, Grigory

Topological aspects of superconductivity in quantum spin-Hall systems (QSHSs) such as thin layers of three-dimensional topological insulators (3D Tis) or two-dimensional Tis are in the focus of current research. Here, we describe a novel superconducting quantum spin-Hall effect (quantum spin Hall system in the proximity to the s-wave superconductor and in the orbital in-plane magnetic field), which is protected against elastic backscattering by combined time-reversal and particle-hole symmetry. This effect is characterized by spin-polarized edge states, which can be manipulated in weak magnetic fields due to a giant effective orbital g-factor, allowing the generation of spin currents. The phenomenon provides a novel solution to the outstanding challenge of detecting the spin-polarization of the edge states. Here we propose the detection of the edge polarization in the three-terminal junction using unusual transport properties of superconducting quantum Hall-effect: a non-monotonic excess current and a zero-bias conductance splitting. We thank for the financial support the German Science Foundation (DFG), Grants No HA 5893/4-1 within SPP 1666, HA5893/5-2 within FOR1162 and TK60/1-1 (G.T.), as well the ENB graduate school ``Topological insulators''.

Electrostatically defined isolated domain wall in integer quantum Hall regime as precursor for reconfigurable Majorana network

NASA Astrophysics Data System (ADS)

Kazakov, Alexander; Simion, George; Kolkovsky, Valery; Adamus, Zbigniew; Karczewski, Grzegorz; Wojtowicz, Tomasz; Lyanda-Geller, Yuli; Rokhinson, Leonid

Development of a two-dimensional systems with reconfigurable one-dimensional topological superconductor channels became primary direction in experimental branch of Majorana physics. Such system would allow to probe non-Abelian properties of Majorana quasiparticles and realize the ultimate goal of Majorana research - topological qubit for topologically protected quantum computations. In order to create and exchange Majorana quasiparticles desired system may be spin-full, but fermion doubling should be lifted. These requirements may be fulfilled in domain walls (DW) which are formed during quantum Hall ferromagnet (QHF) transition when two Landau levels with opposite spin polarization become degenerate. We developed a system based on CdMnTe quantum well with engineered placement of Mn ions where exchange interaction and, consequently, QHF transition can be controlled by electrostatic gating. Using electrostatic control of exchange we create conductive channels of DWs which, unlike conventional edge channels, are not chiral and should contain both spin polarizations. We will present results on the formation of isolated DWs of various widths and discuss their transport properties. Department of Defence Office of Naval research Award N000141410339.

Experimental Identification of Non-Abelian Topological Orders on a Quantum Simulator.

PubMed

Li, Keren; Wan, Yidun; Hung, Ling-Yan; Lan, Tian; Long, Guilu; Lu, Dawei; Zeng, Bei; Laflamme, Raymond

2017-02-24

Topological orders can be used as media for topological quantum computing-a promising quantum computation model due to its invulnerability against local errors. Conversely, a quantum simulator, often regarded as a quantum computing device for special purposes, also offers a way of characterizing topological orders. Here, we show how to identify distinct topological orders via measuring their modular S and T matrices. In particular, we employ a nuclear magnetic resonance quantum simulator to study the properties of three topologically ordered matter phases described by the string-net model with two string types, including the Z_{2} toric code, doubled semion, and doubled Fibonacci. The third one, non-Abelian Fibonacci order is notably expected to be the simplest candidate for universal topological quantum computing. Our experiment serves as the basic module, built on which one can simulate braiding of non-Abelian anyons and ultimately, topological quantum computation via the braiding, and thus provides a new approach of investigating topological orders using quantum computers.

Invariance of Topological Indices Under Hilbert Space Truncation

DOE PAGES

Huang, Zhoushen; Zhu, Wei; Arovas, Daniel P.; ...

2018-01-05

Here, we show that the topological index of a wave function, computed in the space of twisted boundary phases, is preserved under Hilbert space truncation, provided the truncated state remains normalizable. If truncation affects the boundary condition of the resulting state, the invariant index may acquire a different physical interpretation. If the index is symmetry protected, the truncation should preserve the protecting symmetry. We discuss implications of this invariance using paradigmatic integer and fractional Chern insulators, Z 2 topological insulators, and spin-1 Affleck-Kennedy-Lieb-Tasaki and Heisenberg chains, as well as its relation with the notion of bulk entanglement. As a possiblemore » application, we propose a partial quantum tomography scheme from which the topological index of a generic multicomponent wave function can be extracted by measuring only a small subset of wave function components, equivalent to the measurement of a bulk entanglement topological index.« less

Invariance of Topological Indices Under Hilbert Space Truncation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huang, Zhoushen; Zhu, Wei; Arovas, Daniel P.

Here, we show that the topological index of a wave function, computed in the space of twisted boundary phases, is preserved under Hilbert space truncation, provided the truncated state remains normalizable. If truncation affects the boundary condition of the resulting state, the invariant index may acquire a different physical interpretation. If the index is symmetry protected, the truncation should preserve the protecting symmetry. We discuss implications of this invariance using paradigmatic integer and fractional Chern insulators, Z 2 topological insulators, and spin-1 Affleck-Kennedy-Lieb-Tasaki and Heisenberg chains, as well as its relation with the notion of bulk entanglement. As a possiblemore » application, we propose a partial quantum tomography scheme from which the topological index of a generic multicomponent wave function can be extracted by measuring only a small subset of wave function components, equivalent to the measurement of a bulk entanglement topological index.« less

Transport and magnetic properties in topological materials

NASA Astrophysics Data System (ADS)

Liang, Tian

The notion of topology has been the central topic of the condensed matter physics in recent years, ranging from 2D quantum hall (QH) and quantum spin hall (QSH) states, 3D topological insulators (TIs), topological crystalline insulators (TCIs), 3D Dirac/Weyl semimetals, and topological superconductors (TSCs) etc. The key notion of the topological materials is the bulk edge correspondence, i.e., in order to preserve the symmetry of the whole system (bulk+edge), edge states must exist to counter-compensate the broken symmetry of the bulk. Combined with the fact that the bulk is topologically protected, the edge states are robust due to the bulk edge correspondence. This leads to interesting phenomena of chiral edge states in 2D QH, helical edge states in 2D QSH, "parity anomaly'' (time reversal anomaly) in 3D TI, helical edge states in the mirror plane of TCI, chiral anomaly in Dirac/Weyl semimetals, Majorana fermions in the TSCs. Transport and magnetic properties of topological materials are investigated to yield intriguing phenomena. For 3D TI Bi1.1Sb0.9Te 2S, anomalous Hall effect (AHE) is observed, and for TCI Pb1-x SnxSe, Seebeck/Nernst measurements reveal the anomalous sign change of Nernst signals as well as the massive Dirac fermions. Ferroelectricity and pressure measurements show that TCI Pb1-xSnxTe undergoes quantum phase transition (QPT) from trivial insulator through Weyl semimetal to anomalous insulator. Dirac semimetals Cd3As2, Na 3Bi show interesting results such as the ultrahigh mobility 10 7cm2V-1s-1 protected from backscattering at zero magnetic field, as well as anomalous Nernst effect (ANE) for Cd3As2, and the negative longitudinal magnetoresistance (MR) due to chiral anomaly for Na3Bi. In-plane and out-of-plane AHE are observed for semimetal ZrTe5 by in-situ double-axes rotation measurements. For interacting system Eu2Ir2O7, full angle torque magnetometry measurements reveal the existence of orthogonal magnetization breaking the symmetry of handedness, as well as additional order parameter which breaks the underlying lattice symmetry. Heat capacity measurements for CoNb2O6 detect the neutral gapless fermion-like excitations near the quantum critical point (QCP) under transverse magnetic field. The implications of these phenomena are discussed.

Atomic-Ordering-Induced Quantum Phase Transition between Topological Crystalline Insulator and Z 2 Topological Insulator

NASA Astrophysics Data System (ADS)

Deng, Hui-Xiong; Song, Zhi-Gang; Li, Shu-Shen; Wei, Su-Huai; Luo, Jun-Wei

2018-05-01

Topological phase transition in a single material usually refers to transitions between a trivial band insulator and a topological Dirac phase, but the transition may also occur between different classes of topological Dirac phases. However, it is a fundamental challenge to realize quantum transition between Z2 nontrivial topological insulator (TI) and topological crystalline insulator (TCI) in one material because Z2 TI and TCI are hardly both co-exist in a single material due to their contradictory requirement on the number of band inversions. The Z2 TIs must have an odd number of band inversions over all the time-reversal invariant momenta, whereas, the newly discovered TCIs, as a distinct class of the topological Dirac materials protected by the underlying crystalline symmetry, owns an even number of band inversions. Here, take PbSnTe2 alloy as an example, we show that at proper alloy composition the atomic-ordering is an effective way to tune the symmetry of the alloy so that we can electrically switch between TCI phase and Z2 TI phase when the alloy is ordered from a random phase into a stable CuPt phase. Our results suggest that atomic-ordering provides a new platform to switch between different topological phases.

Optimal diabatic dynamics of Majorana-based quantum gates

NASA Astrophysics Data System (ADS)

Rahmani, Armin; Seradjeh, Babak; Franz, Marcel

2017-08-01

In topological quantum computing, unitary operations on qubits are performed by adiabatic braiding of non-Abelian quasiparticles, such as Majorana zero modes, and are protected from local environmental perturbations. In the adiabatic regime, with timescales set by the inverse gap of the system, the errors can be made arbitrarily small by performing the process more slowly. To enhance the performance of quantum information processing with Majorana zero modes, we apply the theory of optimal control to the diabatic dynamics of Majorana-based qubits. While we sacrifice complete topological protection, we impose constraints on the optimal protocol to take advantage of the nonlocal nature of topological information and increase the robustness of our gates. By using the Pontryagin's maximum principle, we show that robust equivalent gates to perfect adiabatic braiding can be implemented in finite times through optimal pulses. In our implementation, modifications to the device Hamiltonian are avoided. Focusing on thermally isolated systems, we study the effects of calibration errors and external white and 1 /f (pink) noise on Majorana-based gates. While a noise-induced antiadiabatic behavior, where a slower process creates more diabatic excitations, prohibits indefinite enhancement of the robustness of the adiabatic scheme, our fast optimal protocols exhibit remarkable stability to noise and have the potential to significantly enhance the practical performance of Majorana-based information processing.

Topological Quantum Buses: Coherent Quantum Information Transfer between Topological and Conventional Qubits

NASA Astrophysics Data System (ADS)

Bonderson, Parsa; Lutchyn, Roman M.

2011-04-01

We propose computing bus devices that enable quantum information to be coherently transferred between topological and conventional qubits. We describe a concrete realization of such a topological quantum bus acting between a topological qubit in a Majorana wire network and a conventional semiconductor double quantum dot qubit. Specifically, this device measures the joint (fermion) parity of these two different qubits by using the Aharonov-Casher effect in conjunction with an ancilliary superconducting flux qubit that facilitates the measurement. Such a parity measurement, together with the ability to apply Hadamard gates to the two qubits, allows one to produce states in which the topological and conventional qubits are maximally entangled and to teleport quantum states between the topological and conventional quantum systems.

Chiral Haldane phases of SU(N ) quantum spin chains

NASA Astrophysics Data System (ADS)

Roy, Abhishek; Quella, Thomas

2018-04-01

Gapped quantum spin chains with symmetry PSU(N ) =SU(N ) /ZN are known to possess N distinct symmetry protected topological phases. Besides the trivial phase, there are N -1 Haldane phases which are distinguished by the occurrence of massless boundary spins. We give an expression for a universal AKLT Hamiltonian for an arbitrary symmetry group, including the case where inversion symmetry is broken. Using a diagrammatic method, we construct Hamiltonians for two of the topological classes in SU(N ) that arise when the physical spin is in the adjoint representation. Since our results are valid for all N , we also discuss the large-N limit.

Topological quantum buses: coherent quantum information transfer between topological and conventional qubits.

PubMed

Bonderson, Parsa; Lutchyn, Roman M

2011-04-01

We propose computing bus devices that enable quantum information to be coherently transferred between topological and conventional qubits. We describe a concrete realization of such a topological quantum bus acting between a topological qubit in a Majorana wire network and a conventional semiconductor double quantum dot qubit. Specifically, this device measures the joint (fermion) parity of these two different qubits by using the Aharonov-Casher effect in conjunction with an ancilliary superconducting flux qubit that facilitates the measurement. Such a parity measurement, together with the ability to apply Hadamard gates to the two qubits, allows one to produce states in which the topological and conventional qubits are maximally entangled and to teleport quantum states between the topological and conventional quantum systems. © 2011 American Physical Society

Hidden edge Dirac point and robust quantum edge transport in InAs/GaSb quantum wells

NASA Astrophysics Data System (ADS)

Li, Chang-An; Zhang, Song-Bo; Shen, Shun-Qing

2018-01-01

The robustness of quantum edge transport in InAs/GaSb quantum wells in the presence of magnetic fields raises an issue on the fate of topological phases of matter under time-reversal symmetry breaking. A peculiar band structure evolution in InAs/GaSb quantum wells is revealed: the electron subbands cross the heavy hole subbands but anticross the light hole subbands. The topologically protected band crossing point (Dirac point) of the helical edge states is pulled to be close to and even buried in the bulk valence bands when the system is in a deeply inverted regime, which is attributed to the existence of the light hole subbands. A sizable Zeeman energy gap verified by the effective g factors of edge states opens at the Dirac point by an in-plane or perpendicular magnetic field; however, it can also be hidden in the bulk valance bands. This provides a plausible explanation for the recent observation on the robustness of quantum edge transport in InAs/GaSb quantum wells subjected to strong magnetic fields.

Entanglement convertibility by sweeping through the quantum phases of the alternating bonds XXZ chain

PubMed Central

Tzeng, Yu-Chin; Dai, Li; Chung, Ming-Chiang; Amico, Luigi; Kwek, Leong-Chuan

2016-01-01

We study the entanglement structure and the topological edge states of the ground state of the spin-1/2 XXZ model with bond alternation. We employ parity-density matrix renormalization group with periodic boundary conditions. The finite-size scaling of Rényi entropies S2 and S∞ are used to construct the phase diagram of the system. The phase diagram displays three possible phases: Haldane type (an example of symmetry protected topological ordered phases), Classical Dimer and Néel phases, the latter bounded by two continuous quantum phase transitions. The entanglement and non-locality in the ground state are studied and quantified by the entanglement convertibility. We found that, at small spatial scales, the ground state is not convertible within the topological Haldane dimer phase. The phenomenology we observe can be described in terms of correlations between edge states. We found that the entanglement spectrum also exhibits a distinctive response in the topological phase: the effective rank of the reduced density matrix displays a specifically large “susceptibility” in the topological phase. These findings support the idea that although the topological order in the ground state cannot be detected by local inspection, the ground state response at local scale can tell the topological phases apart from the non-topological phases. PMID:27216970

Entanglement convertibility by sweeping through the quantum phases of the alternating bonds XXZ chain.

PubMed

Tzeng, Yu-Chin; Dai, Li; Chung, Ming-Chiang; Amico, Luigi; Kwek, Leong-Chuan

2016-05-24

We study the entanglement structure and the topological edge states of the ground state of the spin-1/2 XXZ model with bond alternation. We employ parity-density matrix renormalization group with periodic boundary conditions. The finite-size scaling of Rényi entropies S2 and S∞ are used to construct the phase diagram of the system. The phase diagram displays three possible phases: Haldane type (an example of symmetry protected topological ordered phases), Classical Dimer and Néel phases, the latter bounded by two continuous quantum phase transitions. The entanglement and non-locality in the ground state are studied and quantified by the entanglement convertibility. We found that, at small spatial scales, the ground state is not convertible within the topological Haldane dimer phase. The phenomenology we observe can be described in terms of correlations between edge states. We found that the entanglement spectrum also exhibits a distinctive response in the topological phase: the effective rank of the reduced density matrix displays a specifically large "susceptibility" in the topological phase. These findings support the idea that although the topological order in the ground state cannot be detected by local inspection, the ground state response at local scale can tell the topological phases apart from the non-topological phases.

Thickness dependent quantum oscillations of transport properties in topological insulator Bi2Te3 thin films

NASA Astrophysics Data System (ADS)

Rogacheva, E. I.; Budnik, A. V.; Sipatov, A. Yu.; Nashchekina, O. N.; Dresselhaus, M. S.

2015-02-01

The dependences of the electrical conductivity, the Hall coefficient, and the Seebeck coefficient on the layer thickness d (d = 18-600 nm) of p-type topological insulator Bi2Te3 thin films grown by thermal evaporation in vacuum on glass substrates were obtained at room temperature. In the thickness range of d = 18-100 nm, sustained oscillations with a substantial amplitude were revealed. The observed oscillations are well approximated by a harmonic function with a period Δd = (9.5 ± 0.5) nm. At d > 100 nm, the transport coefficients practically do not change as d is increased. The oscillations of the kinetic properties are attributed to the quantum size effects due to the hole confinement in the Bi2Te3 quantum wells. The results of the theoretical calculations of Δd within the framework of a model of an infinitely deep potential well are in good agreement with the experimental results. It is suggested that the substantial amplitude of the oscillations and their sustained character as a function of d are connected with the topologically protected gapless surface states of Bi2Te3 and are inherent to topological insulators.

Noise Threshold and Resource Cost of Fault-Tolerant Quantum Computing with Majorana Fermions in Hybrid Systems.

PubMed

Li, Ying

2016-09-16

Fault-tolerant quantum computing in systems composed of both Majorana fermions and topologically unprotected quantum systems, e.g., superconducting circuits or quantum dots, is studied in this Letter. Errors caused by topologically unprotected quantum systems need to be corrected with error-correction schemes, for instance, the surface code. We find that the error-correction performance of such a hybrid topological quantum computer is not superior to a normal quantum computer unless the topological charge of Majorana fermions is insusceptible to noise. If errors changing the topological charge are rare, the fault-tolerance threshold is much higher than the threshold of a normal quantum computer and a surface-code logical qubit could be encoded in only tens of topological qubits instead of about 1,000 normal qubits.

Topological π Junctions from Crossed Andreev Reflection in the Quantum Hall Regime

NASA Astrophysics Data System (ADS)

Finocchiaro, F.; Guinea, F.; San-Jose, P.

2018-03-01

We consider a two-dimensional electron gas (2DEG) in the quantum Hall regime in the presence of a Zeeman field, with the Fermi level tuned to a filling factor of ν =1 . We show that, in the presence of spin-orbit coupling, contacting the 2DEG with a narrow strip of an s -wave superconductor produces a topological superconducting gap along the contact as a result of crossed Andreev reflection (CAR) processes across the strip. The sign of the topological gap, controlled by the CAR amplitude, depends periodically on the Fermi wavelength and strip width and can be externally tuned. An interface between two halves of a long strip with topological gaps of opposite sign implements a robust π junction, hosting a pair of Majorana zero modes that do not split despite their overlap. We show that such a configuration can be exploited to perform protected non-Abelian tunnel-braid operations without any fine tuning.

Observation of nodal line in non-symmorphic topological semimetal InBi

DOE PAGES

Ekahana, Sandy Adhitia; Wu, Shu-Chun; Jiang, Juan; ...

2017-05-30

Topological nodal semimetal (TNS), characterized by its touching conduction and valence bands, is a newly discovered state of quantum matter which exhibits various exotic physical phenomena. Recently, a new type of TNS called topological nodal line semimetal (TNLS) is predicted where its conduction and valence band form a degenerate one-dimension line which is further protected by its crystal symmetry. In this work, we systematically investigated the bulk and surface electronic structure of the non-symmorphic, TNLS in InBi (which is also a type II Dirac semimetal) with strong spin–orbit coupling by using angle resolved photoemission spectroscopy. By tracking the crossing points of the bulk bands at the Brillouin zone boundary, we discovered the nodal-line feature along themore » $${{k}}_{{z}}$$ direction, in agreement with the ab initio calculations and confirmed it to be a new compound in the TNLS family. Our discovery provides a new material platform for the study of these exotic topological quantum phases and paves the way for possible future applications.« less

Manipulation of Dirac Cones in Mechanical Graphene

PubMed Central

Kariyado, Toshikaze; Hatsugai, Yasuhiro

2015-01-01

Recently, quantum Hall state analogs in classical mechanics attract much attention from topological points of view. Topology is not only for mathematicians but also quite useful in a quantum world. Further it even governs the Newton’s law of motion. One of the advantages of classical systems over solid state materials is its clear controllability. Here we investigate mechanical graphene, which is a spring-mass model with the honeycomb structure as a typical mechanical model with nontrivial topological phenomena. The vibration spectrum of mechanical graphene is characterized by Dirac cones serving as sources of topological nontriviality. We find that the spectrum has dramatic dependence on the spring tension at equilibrium as a natural control parameter, i.e., creation and annihilation of the Dirac particles are realized as the tension increases. Just by rotating the system, the manipulated Dirac particles lead to topological transition, i.e., a jump of the “Chern number” occurs associated with flipping of propagating direction of chiral edge modes. This is a bulk-edge correspondence governed by the Newton’s law. A simple observation that in-gap edge modes exist only at the fixed boundary, but not at the free one, is attributed to the symmetry protection of topological phases. PMID:26667580

Experimental observation of topological Fermi arcs in type-II Weyl semimetal MoTe2

NASA Astrophysics Data System (ADS)

Deng, Ke; Wan, Guoliang; Deng, Peng; Zhang, Kenan; Ding, Shijie; Wang, Eryin; Yan, Mingzhe; Huang, Huaqing; Zhang, Hongyun; Xu, Zhilin; Denlinger, Jonathan; Fedorov, Alexei; Yang, Haitao; Duan, Wenhui; Yao, Hong; Wu, Yang; Fan, Shoushan; Zhang, Haijun; Chen, Xi; Zhou, Shuyun

2016-12-01

Weyl semimetal is a new quantum state of matter hosting the condensed matter physics counterpart of the relativistic Weyl fermions originally introduced in high-energy physics. The Weyl semimetal phase realized in the TaAs class of materials features multiple Fermi arcs arising from topological surface states and exhibits novel quantum phenomena, such as a chiral anomaly-induced negative magnetoresistance and possibly emergent supersymmetry. Recently it was proposed theoretically that a new type (type-II) of Weyl fermion that arises due to the breaking of Lorentz invariance, which does not have a counterpart in high-energy physics, can emerge as topologically protected touching between electron and hole pockets. Here, we report direct experimental evidence of topological Fermi arcs in the predicted type-II Weyl semimetal MoTe2 (refs ,,). The topological surface states are confirmed by directly observing the surface states using bulk- and surface-sensitive angle-resolved photoemission spectroscopy, and the quasi-particle interference pattern between the putative topological Fermi arcs in scanning tunnelling microscopy. By establishing MoTe2 as an experimental realization of a type-II Weyl semimetal, our work opens up opportunities for probing the physical properties of this exciting new state.

Floquet topological phases in a spin-1 /2 double kicked rotor

NASA Astrophysics Data System (ADS)

Zhou, Longwen; Gong, Jiangbin

2018-06-01

The double kicked rotor model is a physically realizable extension of the paradigmatic kicked rotor model in the study of quantum chaos. Even before the concept of Floquet topological phases became widely known, the discovery of the Hofstadter butterfly spectrum in the double kicked rotor model [J. Wang and J. Gong, Phys. Rev. A 77, 031405 (2008), 10.1103/PhysRevA.77.031405] already suggested the importance of periodic driving to the generation of Floquet topological matter. In this work, we explore Floquet topological phases of a double kicked rotor with an extra spin-1 /2 degree of freedom. The latter has been experimentally engineered in a quantum kicked rotor recently by loading 87Rb condensates into a periodically pulsed optical lattice. Theoretically, we found that under the on-resonance condition, the spin-1 /2 double kicked rotor admits rich topological phases due to the interplay between its external and internal degrees of freedom. Each of these topological phases is characterized by a pair of winding numbers, whose combination predicts the number of topologically protected zero and π -quasienergy edge states in the system. Topological phases with arbitrarily large winding numbers can be easily found by tuning the kicking strength. We discuss an experimental proposal to realize this model in kicked 87Rb condensates, and suggest detecting its topological invariants by measuring the mean chiral displacement in momentum space.

Nobel Lecture: Topological quantum matter*

NASA Astrophysics Data System (ADS)

Haldane, F. Duncan M.

2017-10-01

Nobel Lecture, presented December 8, 2016, Aula Magna, Stockholm University. I will describe the history and background of three discoveries cited in this Nobel Prize: The "TKNN" topological formula for the integer quantum Hall effect found by David Thouless and collaborators, the Chern insulator or quantum anomalous Hall effect, and its role in the later discovery of time-reversal-invariant topological insulators, and the unexpected topological spin-liquid state of the spin-1 quantum antiferromagnetic chain, which provided an initial example of topological quantum matter. I will summarize how these early beginnings have led to the exciting, and currently extremely active, field of "topological matter."

Manipulating Topological Edge Spins in One-Dimensional Optical Lattice

NASA Astrophysics Data System (ADS)

Liu, Xiong-Jun; Liu, Zheng-Xin; Cheng, Meng

2013-03-01

We propose to observe and manipulate topological edge spins in 1D optical lattice based on currently available experimental platforms. Coupling the atomic spin states to a laser-induced periodic Zeeman field, the lattice system can be driven into a symmetry protected topological (SPT) phase, which belongs to the chiral unitary (AIII) class protected by particle number conservation and chiral symmetries. In free-fermion case the SPT phase is classified by a Z invariant which reduces to Z4 with interactions. The zero edge modes of the SPT phase are spin-polarized, with left and right edge spins polarized to opposite directions and forming a topological spin-qubit (TSQ). We demonstrate a novel scheme to manipulate the zero modes and realize single spin control in optical lattice. The manipulation of TSQs has potential applications to quantum computation. We acknowledge the support from JQI-NSF-PFC, Microsoft-Q, and DARPA- QuEST.

Single-electron induced surface plasmons on a topological nanoparticle

PubMed Central

Siroki, G.; Lee, D.K.K.; Haynes, P. D.; Giannini, V.

2016-01-01

It is rarely the case that a single electron affects the behaviour of several hundred thousands of atoms. Here we demonstrate a phenomenon where this happens. The key role is played by topological insulators—materials that have surface states protected by time-reversal symmetry. Such states are delocalized over the surface and are immune to its imperfections in contrast to ordinary insulators. For topological insulators, the effects of these surface states will be more strongly pronounced in the case of nanoparticles. Here we show that under the influence of light a single electron in a topologically protected surface state creates a surface charge density similar to a plasmon in a metallic nanoparticle. Such an electron can act as a screening layer, which suppresses absorption inside the particle. In addition, it can couple phonons and light, giving rise to a previously unreported topological particle polariton mode. These effects may be useful in the areas of plasmonics, cavity electrodynamics and quantum information. PMID:27491515

Experimental Realization of a Reflections-Free Compact Delay Line Based on a Photonic Topological Insulator

PubMed Central

Lai, Kueifu; Ma, Tsuhsuang; Bo, Xiao; Anlage, Steven; Shvets, Gennady

2016-01-01

Electromagnetic (EM) waves propagating through an inhomogeneous medium are generally scattered whenever the medium’s electromagnetic properties change on the scale of a single wavelength. This fundamental phenomenon constrains how optical structures are designed and interfaced with each other. Recent theoretical work indicates that electromagnetic structures collectively known as photonic topological insulators (PTIs) can be employed to overcome this fundamental limitation, thereby paving the way for ultra-compact photonic structures that no longer have to be wavelength-scale smooth. Here we present the first experimental demonstration of a photonic delay line based on topologically protected surface electromagnetic waves (TPSWs) between two PTIs which are the EM counterparts of the quantum spin-Hall topological insulators in condensed matter. Unlike conventional guided EM waves that do not benefit from topological protection, TPSWs are shown to experience multi-wavelength reflection-free time delays when detoured around sharply-curved paths, thus offering a unique paradigm for compact and efficient wave buffers and other devices. PMID:27345575

Non-Abelian fractional topological insulators in three spatial dimensions from coupled wires

NASA Astrophysics Data System (ADS)

Iadecola, Thomas; Neupert, Titus; Chamon, Claudio; Mudry, Christopher

The study of topological order in three spatial dimensions constitutes a major frontier in theoretical condensed matter physics. Recently, substantial progress has been made in constructing (3+1)-dimensional Abelian topological states of matter from arrays of coupled quantum wires. In this talk, I will illustrate how wire constructions based on non-Abelian bosonization can be used to build and characterize non-Abelian symmetry-enriched topological phases in three dimensions. In particular, I will describe a family of states of matter, constructed in this way, that constitute a natural non-Abelian generalization of strongly correlated three dimensional fractional topological insulators. These states of matter support strongly interacting symmetry-protected gapless surface states, and host non-Abelian pointlike and linelike excitations in the bulk.

A bilayer Double Semion model with symmetry-enriched topological order

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ortiz, L., E-mail: lauraort@ucm.es; Martin-Delgado, M.A.

2016-12-15

We construct a new model of two-dimensional quantum spin systems that combines intrinsic topological orders and a global symmetry called flavour symmetry. It is referred as the bilayer Doubled Semion model (bDS) and is an instance of symmetry-enriched topological order. A honeycomb bilayer lattice is introduced to combine a Double Semion Topological Order with a global spin–flavour symmetry to get the fractionalization of its quasiparticles. The bDS model exhibits non-trivial braiding self-statistics of excitations and its dual model constitutes a Symmetry-Protected Topological Order with novel edge states. This dual model gives rise to a bilayer Non-Trivial Paramagnet that is invariantmore » under the flavour symmetry and the well-known spin flip symmetry.« less

van der Waals heterostructures of germanene, stanene, and silicene with hexagonal boron nitride and their topological domain walls

NASA Astrophysics Data System (ADS)

Wang, Maoyuan; Liu, Liping; Liu, Cheng-Cheng; Yao, Yugui

2016-04-01

We investigate van der Waals (vdW) heterostructures made of germanene, stanene, or silicene with hexagonal boron nitride (h-BN). The intriguing topological properties of these buckled honeycomb materials can be maintained and further engineered in the heterostructures, where the competition between the substrate effect and external electric fields can be used to control the tunable topological phase transitions. Using such heterostructures as building blocks, various vdW topological domain walls (DW) are designed, along which there exist valley polarized quantum spin Hall edge states or valley-contrasting edge states which are protected by valley(spin)- resolved topological charges and can be tailored by the patterning of the heterojunctions and by external fields.

Simulation of Non-Abelian Braiding in Majorana Time Crystals

NASA Astrophysics Data System (ADS)

Bomantara, Raditya Weda; Gong, Jiangbin

2018-06-01

Discrete time crystals have attracted considerable theoretical and experimental studies but their potential applications have remained unexplored. A particular type of discrete time crystals, termed "Majorana time crystals," is found to emerge in a periodically driven superconducting wire accommodating two different species of topological edge modes. It is further shown that one can manipulate different Majorana edge modes separated in the time lattice, giving rise to an unforeseen scenario for topologically protected gate operations mimicking braiding. The proposed protocol can also generate a magic state that is important for universal quantum computation. This study thus advances the quantum control in discrete time crystals and reveals their great potential arising from their time-domain properties.

Quantum entanglement properties of geometrical and topological quantum gates

NASA Astrophysics Data System (ADS)

Sezer, Hasan Cavit; Duy, Hoang Ngoc; Heydari, Hoshang

2011-03-01

In this paper we will investigate the action of holonomic and topological quantum gates on different classes of four qubit states. In particular, we review the construction of holonomic quantum gate based on geometric phase and topological quantum gate based on braid group. Then, we investigate the entanglement properties of three different classes of four-qubit states based on geometric invariants. The result shows that entanglement properties of the two most generic classes of four-qubit states can be controlled by holonomic and topological quantum gate..

Detection of Zak phases and topological invariants in a chiral quantum walk of twisted photons.

PubMed

Cardano, Filippo; D'Errico, Alessio; Dauphin, Alexandre; Maffei, Maria; Piccirillo, Bruno; de Lisio, Corrado; De Filippis, Giulio; Cataudella, Vittorio; Santamato, Enrico; Marrucci, Lorenzo; Lewenstein, Maciej; Massignan, Pietro

2017-06-01

Topological insulators are fascinating states of matter exhibiting protected edge states and robust quantized features in their bulk. Here we propose and validate experimentally a method to detect topological properties in the bulk of one-dimensional chiral systems. We first introduce the mean chiral displacement, an observable that rapidly approaches a value proportional to the Zak phase during the free evolution of the system. Then we measure the Zak phase in a photonic quantum walk of twisted photons, by observing the mean chiral displacement in its bulk. Next, we measure the Zak phase in an alternative, inequivalent timeframe and combine the two windings to characterize the full phase diagram of this Floquet system. Finally, we prove the robustness of the measure by introducing dynamical disorder in the system. This detection method is extremely general and readily applicable to all present one-dimensional platforms simulating static or Floquet chiral systems.

Detection of Zak phases and topological invariants in a chiral quantum walk of twisted photons

PubMed Central

Cardano, Filippo; D’Errico, Alessio; Dauphin, Alexandre; Maffei, Maria; Piccirillo, Bruno; de Lisio, Corrado; De Filippis, Giulio; Cataudella, Vittorio; Santamato, Enrico; Marrucci, Lorenzo; Lewenstein, Maciej; Massignan, Pietro

2017-01-01

Topological insulators are fascinating states of matter exhibiting protected edge states and robust quantized features in their bulk. Here we propose and validate experimentally a method to detect topological properties in the bulk of one-dimensional chiral systems. We first introduce the mean chiral displacement, an observable that rapidly approaches a value proportional to the Zak phase during the free evolution of the system. Then we measure the Zak phase in a photonic quantum walk of twisted photons, by observing the mean chiral displacement in its bulk. Next, we measure the Zak phase in an alternative, inequivalent timeframe and combine the two windings to characterize the full phase diagram of this Floquet system. Finally, we prove the robustness of the measure by introducing dynamical disorder in the system. This detection method is extremely general and readily applicable to all present one-dimensional platforms simulating static or Floquet chiral systems. PMID:28569741

Experimental evidence of hourglass fermion in the candidate nonsymmorphic topological insulator KHgSb

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ma, Junzhang; Yi, Changjiang; Lv, Baiqing

Topological insulators (TIs) host novel states of quantum matter characterized by nontrivial conducting boundary states connecting valence and conduction bulk bands. All TIs discovered experimentally so far rely on either time-reversal or mirror crystal symmorphic symmetry to protect massless Dirac-like boundary states. Several materials were recently proposed to be TIs with nonsymmorphic symmetry, where a glide mirror protects exotic surface fermions with hourglass-shaped dispersion. However, an experimental confirmation of this new fermion is missing. Using angle-resolved photoemission spectroscopy, we provide experimental evidence of hourglass fermions on the (010) surface of crystalline KHgSb, whereas the (001) surface has no boundary state,more » in agreement with first-principles calculations. Our study will stimulate further research activities of topological properties of nonsymmorphic materials.« less

Experimental evidence of hourglass fermion in the candidate nonsymmorphic topological insulator KHgSb

DOE PAGES

Ma, Junzhang; Yi, Changjiang; Lv, Baiqing; ...

2017-05-05

Topological insulators (TIs) host novel states of quantum matter characterized by nontrivial conducting boundary states connecting valence and conduction bulk bands. All TIs discovered experimentally so far rely on either time-reversal or mirror crystal symmorphic symmetry to protect massless Dirac-like boundary states. Several materials were recently proposed to be TIs with nonsymmorphic symmetry, where a glide mirror protects exotic surface fermions with hourglass-shaped dispersion. However, an experimental confirmation of this new fermion is missing. Using angle-resolved photoemission spectroscopy, we provide experimental evidence of hourglass fermions on the (010) surface of crystalline KHgSb, whereas the (001) surface has no boundary state,more » in agreement with first-principles calculations. Our study will stimulate further research activities of topological properties of nonsymmorphic materials.« less

Topological Quantum Phase Transition and Local Topological Order in a Strongly Interacting Light-Matter System.

PubMed

Sarkar, Sujit

2017-05-12

An attempt is made to understand the topological quantum phase transition, emergence of relativistic modes and local topological order of light in a strongly interacting light-matter system. We study this system, in a one dimensional array of nonlinear cavities. Topological quantum phase transition occurs with massless excitation only for the finite detuning process. We present a few results based on the exact analytical calculations along with the physical explanations. We observe the emergence of massive Majorana fermion mode at the topological state, massless Majorana-Weyl fermion mode during the topological quantum phase transition and Dirac fermion mode for the non-topological state. Finally, we study the quantized Berry phase (topological order) and its connection to the topological number (winding number).

Observation of Topological Links Associated with Hopf Insulators in a Solid-State Quantum Simulator

NASA Astrophysics Data System (ADS)

Yuan, X.-X.; He, L.; Wang, S.-T.; Deng, D.-L.; Wang, F.; Lian, W.-Q.; Wang, X.; Zhang, C.-H.; Zhang, H.-L.; Chang, X.-Y.; Duan, L.-M.

2017-06-01

Hopf insulators are intriguing three-dimensional topological insulators characterized by an integer topological invariant. They originate from the mathematical theory of Hopf fibration and epitomize the deep connection between knot theory and topological phases of matter, which distinguishes them from other classes of topological insulators. Here, we implement a model Hamiltonian for Hopf insulators in a solid-state quantum simulator and report the first experimental observation of their topological properties, including fascinating topological links associated with the Hopf fibration and the integer-valued topological invariant obtained from a direct tomographic measurement. Our observation of topological links and Hopf fibration in a quantum simulator opens the door to probe rich topological properties of Hopf insulators in experiments. The quantum simulation and probing methods are also applicable to the study of other intricate three-dimensional topological model Hamiltonians.

Quasi-one-dimensional quantum anomalous Hall systems as new platforms for scalable topological quantum computation

NASA Astrophysics Data System (ADS)

Chen, Chui-Zhen; Xie, Ying-Ming; Liu, Jie; Lee, Patrick A.; Law, K. T.

2018-03-01

Quantum anomalous Hall insulator/superconductor heterostructures emerged as a competitive platform to realize topological superconductors with chiral Majorana edge states as shown in recent experiments [He et al. Science 357, 294 (2017), 10.1126/science.aag2792]. However, chiral Majorana modes, being extended, cannot be used for topological quantum computation. In this work, we show that quasi-one-dimensional quantum anomalous Hall structures exhibit a large topological regime (much larger than the two-dimensional case) which supports localized Majorana zero energy modes. The non-Abelian properties of a cross-shaped quantum anomalous Hall junction is shown explicitly by time-dependent calculations. We believe that the proposed quasi-one-dimensional quantum anomalous Hall structures can be easily fabricated for scalable topological quantum computation.

Emergent gauge fields and their nonperturbative effects in correlated electrons

NASA Astrophysics Data System (ADS)

Kim, Ki-Seok; Tanaka, Akihiro

2015-06-01

The history of modern condensed matter physics may be regarded as the competition and reconciliation between Stoner’s and Anderson’s physical pictures, where the former is based on momentum-space descriptions focusing on long wave-length fluctuations while the latter is based on real-space physics emphasizing emergent localized excitations. In particular, these two view points compete with each other in various nonperturbative phenomena, which range from the problem of high Tc superconductivity, quantum spin liquids in organic materials and frustrated spin systems, heavy-fermion quantum criticality, metal-insulator transitions in correlated electron systems such as doped silicons and two-dimensional electron systems, the fractional quantum Hall effect, to the recently discussed Fe-based superconductors. An approach to reconcile these competing frameworks is to introduce topologically nontrivial excitations into the Stoner’s description, which appear to be localized in either space or time and sometimes both, where scattering between itinerant electrons and topological excitations such as skyrmions, vortices, various forms of instantons, emergent magnetic monopoles, and etc. may catch nonperturbative local physics beyond the Stoner’s paradigm. In this review paper, we discuss nonperturbative effects of topological excitations on dynamics of correlated electrons. First, we focus on the problem of scattering between itinerant fermions and topological excitations in antiferromagnetic doped Mott insulators, expected to be relevant for the pseudogap phase of high Tc cuprates. We propose that nonperturbative effects of topological excitations can be incorporated within the perturbative framework, where an enhanced global symmetry with a topological term plays an essential role. In the second part, we go on to discuss the subject of symmetry protected topological states in a largely similar light. While we do not introduce itinerant fermions here, the nonperturbative dynamics of topological excitations is again seen to be crucial in classifying topologically nontrivial gapped systems. We point to some hidden links between several effective field theories with topological terms, starting with one-dimensional physics, and subsequently finding natural generalizations to higher dimensions.

Emergent Gauge Fields and Their Nonperturbative Effects in Correlated Electrons

NASA Astrophysics Data System (ADS)

Kim, Ki-Seok; Tanaka, Akihiro

The history of modern condensed matter physics may be regarded as the competition and reconciliation between Stoner's and Anderson's physical pictures, where the former is based on momentum-space descriptions focusing on long wave-length fluctuations while the latter is based on real-space physics emphasizing emergent localized excitations. In particular, these two view points compete with each other in various nonperturbative phenomena, which range from the problem of high Tc superconductivity, quantum spin liquids in organic materials and frustrated spin systems, heavy-fermion quantum criticality, metal-insulator transitions in correlated electron systems such as doped silicons and two-dimensional electron systems, the fractional quantum Hall effect, to the recently discussed Fe-based superconductors. An approach to reconcile these competing frameworks is to introduce topologically nontrivial excitations into the Stoner's description, which appear to be localized in either space or time and sometimes both, where scattering between itinerant electrons and topological excitations such as skyrmions, vortices, various forms of instantons, emergent magnetic monopoles, and etc. may catch nonperturbative local physics beyond the Stoner's paradigm. In this review article we discuss nonperturbative effects of topological excitations on dynamics of correlated electrons. First, we focus on the problem of scattering between itinerant fermions and topological excitations in antiferromagnetic doped Mott insulators, expected to be relevant for the pseudogap phase of high Tc cuprates. We propose that nonperturbative effects of topological excitations can be incorporated within the perturbative framework, where an enhanced global symmetry with a topological term plays an essential role. In the second part, we go on to discuss the subject of symmetry protected topological states in a largely similar light. While we do not introduce itinerant fermions here, the nonperturbative dynamics of topological excitations is again seen to be crucial in classifying topologically nontrivial gapped systems. We point to some hidden links between several effective field theories with topological terms, starting with one dimensional physics, and subsequently finding natural generalizations to higher dimensions.

Robust quantum network architectures and topologies for entanglement distribution

NASA Astrophysics Data System (ADS)

Das, Siddhartha; Khatri, Sumeet; Dowling, Jonathan P.

2018-01-01

Entanglement distribution is a prerequisite for several important quantum information processing and computing tasks, such as quantum teleportation, quantum key distribution, and distributed quantum computing. In this work, we focus on two-dimensional quantum networks based on optical quantum technologies using dual-rail photonic qubits for the building of a fail-safe quantum internet. We lay out a quantum network architecture for entanglement distribution between distant parties using a Bravais lattice topology, with the technological constraint that quantum repeaters equipped with quantum memories are not easily accessible. We provide a robust protocol for simultaneous entanglement distribution between two distant groups of parties on this network. We also discuss a memory-based quantum network architecture that can be implemented on networks with an arbitrary topology. We examine networks with bow-tie lattice and Archimedean lattice topologies and use percolation theory to quantify the robustness of the networks. In particular, we provide figures of merit on the loss parameter of the optical medium that depend only on the topology of the network and quantify the robustness of the network against intermittent photon loss and intermittent failure of nodes. These figures of merit can be used to compare the robustness of different network topologies in order to determine the best topology in a given real-world scenario, which is critical in the realization of the quantum internet.

New Forms of Matter in Optical Lattices

DTIC Science & Technology

2016-05-19

Daley, A. M. Läuchli, and P. Zoller Thermal vs. Entanglement Entropy: A Measurement Protocol for Fermionic Atoms with a Quantum Gas Microscope...J. A. Edge, E. Taylor, S. Zhang, S. Trotzky, J. H. Thywissen Transverse Demagnetization Dynamics of a Unitary Fermi Gas Science 344, 722 (2014...Jiang, J Ignacio Cirac, Peter Zoller, Mikhail D Lukin, "Topologically Protected Quantum State Transfer in a Chiral Spin Liquid , "Nature Communications

Tensor-entanglement-filtering renormalization approach and symmetry-protected topological order

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gu Zhengcheng; Wen Xiaogang

2009-10-15

We study the renormalization group flow of the Lagrangian for statistical and quantum systems by representing their path integral in terms of a tensor network. Using a tensor-entanglement-filtering renormalization approach that removes local entanglement and produces a coarse-grained lattice, we show that the resulting renormalization flow of the tensors in the tensor network has a nice fixed-point structure. The isolated fixed-point tensors T{sub inv} plus the symmetry group G{sub sym} of the tensors (i.e., the symmetry group of the Lagrangian) characterize various phases of the system. Such a characterization can describe both the symmetry breaking phases and topological phases, asmore » illustrated by two-dimensional (2D) statistical Ising model, 2D statistical loop-gas model, and 1+1D quantum spin-1/2 and spin-1 models. In particular, using such a (G{sub sym},T{sub inv}) characterization, we show that the Haldane phase for a spin-1 chain is a phase protected by the time-reversal, parity, and translation symmetries. Thus the Haldane phase is a symmetry-protected topological phase. The (G{sub sym},T{sub inv}) characterization is more general than the characterizations based on the boundary spins and string order parameters. The tensor renormalization approach also allows us to study continuous phase transitions between symmetry breaking phases and/or topological phases. The scaling dimensions and the central charges for the critical points that describe those continuous phase transitions can be calculated from the fixed-point tensors at those critical points.« less

Quantum Entanglement and the Topological Order of Fractional Hall States

NASA Astrophysics Data System (ADS)

Rezayi, Edward

2015-03-01

Fractional quantum Hall states or, more generally, topological phases of matter defy Landau classification based on order parameter and broken symmetry. Instead they have been characterized by their topological order. Quantum information concepts, such as quantum entanglement, appear to provide the most efficient method of detecting topological order solely from the knowledge of the ground state wave function. This talk will focus on real-space bi-partitioning of quantum Hall states and will present both exact diagonalization and quantum Monte Carlo studies of topological entanglement entropy in various geometries. Results on the torus for non-contractible cuts are quite rich and, through the use of minimum entropy states, yield the modular S-matrix and hence uniquely determine the topological order, as shown in recent literature. Concrete examples of minimum entropy states from known quantum Hall wave functions and their corresponding quantum numbers, used in exact diagonalizations, will be given. In collaboration with Clare Abreu and Raul Herrera. Supported by DOE Grant DE-SC0002140.

Topological quantum distillation.

PubMed

Bombin, H; Martin-Delgado, M A

2006-11-03

We construct a class of topological quantum codes to perform quantum entanglement distillation. These codes implement the whole Clifford group of unitary operations in a fully topological manner and without selective addressing of qubits. This allows us to extend their application also to quantum teleportation, dense coding, and computation with magic states.

Exponential protection of zero modes in Majorana islands.

PubMed

Albrecht, S M; Higginbotham, A P; Madsen, M; Kuemmeth, F; Jespersen, T S; Nygård, J; Krogstrup, P; Marcus, C M

2016-03-10

Majorana zero modes are quasiparticle excitations in condensed matter systems that have been proposed as building blocks of fault-tolerant quantum computers. They are expected to exhibit non-Abelian particle statistics, in contrast to the usual statistics of fermions and bosons, enabling quantum operations to be performed by braiding isolated modes around one another. Quantum braiding operations are topologically protected insofar as these modes are pinned near zero energy, with the departure from zero expected to be exponentially small as the modes become spatially separated. Following theoretical proposals, several experiments have identified signatures of Majorana modes in nanowires with proximity-induced superconductivity and atomic chains, with small amounts of mode splitting potentially explained by hybridization of Majorana modes. Here, we use Coulomb-blockade spectroscopy in an InAs nanowire segment with epitaxial aluminium, which forms a proximity-induced superconducting Coulomb island (a 'Majorana island') that is isolated from normal-metal leads by tunnel barriers, to measure the splitting of near-zero-energy Majorana modes. We observe exponential suppression of energy splitting with increasing wire length. For short devices of a few hundred nanometres, sub-gap state energies oscillate as the magnetic field is varied, as is expected for hybridized Majorana modes. Splitting decreases by a factor of about ten for each half a micrometre of increased wire length. For devices longer than about one micrometre, transport in strong magnetic fields occurs through a zero-energy state that is energetically isolated from a continuum, yielding uniformly spaced Coulomb-blockade conductance peaks, consistent with teleportation via Majorana modes. Our results help to explain the trivial-to-topological transition in finite systems and to quantify the scaling of topological protection with end-mode separation.

Quantum friction in two-dimensional topological materials

DOE Office of Scientific and Technical Information (OSTI.GOV)

Farias, M. Belén; Kort-Kamp, Wilton J. M.; Dalvit, Diego A. R.

In this paper, we develop the theory of quantum friction in two-dimensional topological materials. The quantum drag force on a metallic nanoparticle moving above such systems is sensitive to the nontrivial topology of their electronic phases, shows a novel distance scaling law, and can be manipulated through doping or via the application of external fields. We use the developed framework to investigate quantum friction due to the quantum Hall effect in magnetic field biased graphene, and to topological phase transitions in the graphene family materials. Finally, it is shown that topologically nontrivial states in two-dimensional materials enable an increase ofmore » two orders of magnitude in the quantum drag force with respect to conventional neutral graphene systems.« less

Quantum friction in two-dimensional topological materials

DOE PAGES

Farias, M. Belén; Kort-Kamp, Wilton J. M.; Dalvit, Diego A. R.

2018-04-24

In this paper, we develop the theory of quantum friction in two-dimensional topological materials. The quantum drag force on a metallic nanoparticle moving above such systems is sensitive to the nontrivial topology of their electronic phases, shows a novel distance scaling law, and can be manipulated through doping or via the application of external fields. We use the developed framework to investigate quantum friction due to the quantum Hall effect in magnetic field biased graphene, and to topological phase transitions in the graphene family materials. Finally, it is shown that topologically nontrivial states in two-dimensional materials enable an increase ofmore » two orders of magnitude in the quantum drag force with respect to conventional neutral graphene systems.« less

Statistical moments of quantum-walk dynamics reveal topological quantum transitions.

PubMed

Cardano, Filippo; Maffei, Maria; Massa, Francesco; Piccirillo, Bruno; de Lisio, Corrado; De Filippis, Giulio; Cataudella, Vittorio; Santamato, Enrico; Marrucci, Lorenzo

2016-04-22

Many phenomena in solid-state physics can be understood in terms of their topological properties. Recently, controlled protocols of quantum walk (QW) are proving to be effective simulators of such phenomena. Here we report the realization of a photonic QW showing both the trivial and the non-trivial topologies associated with chiral symmetry in one-dimensional (1D) periodic systems. We find that the probability distribution moments of the walker position after many steps can be used as direct indicators of the topological quantum transition: while varying a control parameter that defines the system phase, these moments exhibit a slope discontinuity at the transition point. Numerical simulations strongly support the conjecture that these features are general of 1D topological systems. Extending this approach to higher dimensions, different topological classes, and other typologies of quantum phases may offer general instruments for investigating and experimentally detecting quantum transitions in such complex systems.

Statistical moments of quantum-walk dynamics reveal topological quantum transitions

PubMed Central

Cardano, Filippo; Maffei, Maria; Massa, Francesco; Piccirillo, Bruno; de Lisio, Corrado; De Filippis, Giulio; Cataudella, Vittorio; Santamato, Enrico; Marrucci, Lorenzo

2016-01-01

Many phenomena in solid-state physics can be understood in terms of their topological properties. Recently, controlled protocols of quantum walk (QW) are proving to be effective simulators of such phenomena. Here we report the realization of a photonic QW showing both the trivial and the non-trivial topologies associated with chiral symmetry in one-dimensional (1D) periodic systems. We find that the probability distribution moments of the walker position after many steps can be used as direct indicators of the topological quantum transition: while varying a control parameter that defines the system phase, these moments exhibit a slope discontinuity at the transition point. Numerical simulations strongly support the conjecture that these features are general of 1D topological systems. Extending this approach to higher dimensions, different topological classes, and other typologies of quantum phases may offer general instruments for investigating and experimentally detecting quantum transitions in such complex systems. PMID:27102945

Phase transition and field effect topological quantum transistor made of monolayer MoS2

NASA Astrophysics Data System (ADS)

Simchi, H.; Simchi, M.; Fardmanesh, M.; Peeters, F. M.

2018-06-01

We study topological phase transitions and topological quantum field effect transistor in monolayer molybdenum disulfide (MoS2) using a two-band Hamiltonian model. Without considering the quadratic (q 2) diagonal term in the Hamiltonian, we show that the phase diagram includes quantum anomalous Hall effect, quantum spin Hall effect, and spin quantum anomalous Hall effect regions such that the topological Kirchhoff law is satisfied in the plane. By considering the q 2 diagonal term and including one valley, it is shown that MoS2 has a non-trivial topology, and the valley Chern number is non-zero for each spin. We show that the wave function is (is not) localized at the edges when the q 2 diagonal term is added (deleted) to (from) the spin-valley Dirac mass equation. We calculate the quantum conductance of zigzag MoS2 nanoribbons by using the nonequilibrium Green function method and show how this device works as a field effect topological quantum transistor.

Towards topological quantum computer

NASA Astrophysics Data System (ADS)

Melnikov, D.; Mironov, A.; Mironov, S.; Morozov, A.; Morozov, An.

2018-01-01

Quantum R-matrices, the entangling deformations of non-entangling (classical) permutations, provide a distinguished basis in the space of unitary evolutions and, consequently, a natural choice for a minimal set of basic operations (universal gates) for quantum computation. Yet they play a special role in group theory, integrable systems and modern theory of non-perturbative calculations in quantum field and string theory. Despite recent developments in those fields the idea of topological quantum computing and use of R-matrices, in particular, practically reduce to reinterpretation of standard sets of quantum gates, and subsequently algorithms, in terms of available topological ones. In this paper we summarize a modern view on quantum R-matrix calculus and propose to look at the R-matrices acting in the space of irreducible representations, which are unitary for the real-valued couplings in Chern-Simons theory, as the fundamental set of universal gates for topological quantum computer. Such an approach calls for a more thorough investigation of the relation between topological invariants of knots and quantum algorithms.

Nexus fermions in topological symmorphic crystalline metals

DOE PAGES

Chang, Guoqing; Xu, Su-Yang; Huang, Shin-Ming; ...

2017-05-10

Topological metals and semimetals (TMs) have recently drawn significant interest. These materials give rise to condensed matter realizations of many important concepts in high-energy physics, leading to wide-ranging protected properties in transport and spectroscopic experiments. It has been well-established that the known TMs can be classified by the dimensionality of the topologically protected band degeneracies. While Weyl and Dirac semimetals feature zero-dimensional points, the band crossing of nodal-line semimetals forms a one-dimensional closed loop. In this paper, we identify a TM that goes beyond the above paradigms. It shows an exotic configuration of degeneracies without a well-defined dimensionality. Specifically, itmore » consists of 0D nexus with triple-degeneracy that interconnects 1D lines with double-degeneracy. We show that, because of the novel form of band crossing, the new TM cannot be described by the established results that characterize the topology of the Dirac and Weyl nodes. Moreover, triply-degenerate nodes realize emergent fermionic quasiparticles not present in relativistic quantum field theory. We present materials candidates. Thus, our results open the door for realizing new topological phenomena and fermions including transport anomalies and spectroscopic responses in metallic crystals with nontrivial topology beyond the Weyl/Dirac paradigm.« less

Topology and Edge Modes in Quantum Critical Chains

NASA Astrophysics Data System (ADS)

Verresen, Ruben; Jones, Nick G.; Pollmann, Frank

2018-02-01

We show that topology can protect exponentially localized, zero energy edge modes at critical points between one-dimensional symmetry-protected topological phases. This is possible even without gapped degrees of freedom in the bulk—in contrast to recent work on edge modes in gapless chains. We present an intuitive picture for the existence of these edge modes in the case of noninteracting spinless fermions with time-reversal symmetry (BDI class of the tenfold way). The stability of this phenomenon relies on a topological invariant defined in terms of a complex function, counting its zeros and poles inside the unit circle. This invariant can prevent two models described by the same conformal field theory (CFT) from being smoothly connected. A full classification of critical phases in the noninteracting BDI class is obtained: Each phase is labeled by the central charge of the CFT, c ∈1/2 N , and the topological invariant, ω ∈Z . Moreover, c is determined by the difference in the number of edge modes between the phases neighboring the transition. Numerical simulations show that the topological edge modes of critical chains can be stable in the presence of interactions and disorder.

Floquet Symmetry-Protected Topological Phases in Cold-Atom Systems

NASA Astrophysics Data System (ADS)

Potirniche, I.-D.; Potter, A. C.; Schleier-Smith, M.; Vishwanath, A.; Yao, N. Y.

2017-09-01

We propose and analyze two distinct routes toward realizing interacting symmetry-protected topological (SPT) phases via periodic driving. First, we demonstrate that a driven transverse-field Ising model can be used to engineer complex interactions which enable the emulation of an equilibrium SPT phase. This phase remains stable only within a parametric time scale controlled by the driving frequency, beyond which its topological features break down. To overcome this issue, we consider an alternate route based upon realizing an intrinsically Floquet SPT phase that does not have any equilibrium analog. In both cases, we show that disorder, leading to many-body localization, prevents runaway heating and enables the observation of coherent quantum dynamics at high energy densities. Furthermore, we clarify the distinction between the equilibrium and Floquet SPT phases by identifying a unique micromotion-based entanglement spectrum signature of the latter. Finally, we propose a unifying implementation in a one-dimensional chain of Rydberg-dressed atoms and show that protected edge modes are observable on realistic experimental time scales.

Bifurcations of edge states—topologically protected and non-protected—in continuous 2D honeycomb structures

NASA Astrophysics Data System (ADS)

Fefferman, C. L.; Lee-Thorp, J. P.; Weinstein, M. I.

2016-03-01

Edge states are time-harmonic solutions to energy-conserving wave equations, which are propagating parallel to a line-defect or ‘edge’ and are localized transverse to it. This paper summarizes and extends the authors’ work on the bifurcation of topologically protected edge states in continuous two-dimensional (2D) honeycomb structures. We consider a family of Schrödinger Hamiltonians consisting of a bulk honeycomb potential and a perturbing edge potential. The edge potential interpolates between two different periodic structures via a domain wall. We begin by reviewing our recent bifurcation theory of edge states for continuous 2D honeycomb structures (http://arxiv.org/abs/1506.06111). The topologically protected edge state bifurcation is seeded by the zero-energy eigenstate of a one-dimensional Dirac operator. We contrast these protected bifurcations with (more common) non-protected bifurcations from spectral band edges, which are induced by bound states of an effective Schrödinger operator. Numerical simulations for honeycomb structures of varying contrasts and ‘rational edges’ (zigzag, armchair and others), support the following scenario: (a) for low contrast, under a sign condition on a distinguished Fourier coefficient of the bulk honeycomb potential, there exist topologically protected edge states localized transverse to zigzag edges. Otherwise, and for general edges, we expect long lived edge quasi-modes which slowly leak energy into the bulk. (b) For an arbitrary rational edge, there is a threshold in the medium-contrast (depending on the choice of edge) above which there exist topologically protected edge states. In the special case of the armchair edge, there are two families of protected edge states; for each parallel quasimomentum (the quantum number associated with translation invariance) there are edge states which propagate in opposite directions along the armchair edge.

Squeezing as a route to photonic analogues of topological superconductors

NASA Astrophysics Data System (ADS)

Houde, Martin; Peano, Vittorio; Brendel, Christian; Marquardt, Florian; Clerk, Aashish

There has been considerable recent interest in studying topological phases of photonic systems. In many cases the resulting system is described by a quadratic particle-conserving Hamiltonian which is directly equivalent to its fermionic counterpart. Here, we consider a class of photonic topological phases where this correspondence fails: photonic systems where particle-number non-conserving terms break time-reversal symmetry. We show that these phases support protected edge modes which facilitate chiral inelastic and elastic transport channels. We also discuss the possibility of quantum amplification using these edge states. Our system could be realized in a variety of systems, including nonlinear photonic crystals, superconducting circuits and optomechanical systems.

Topological order, entanglement, and quantum memory at finite temperature

NASA Astrophysics Data System (ADS)

Mazáč, Dalimil; Hamma, Alioscia

2012-09-01

We compute the topological entropy of the toric code models in arbitrary dimension at finite temperature. We find that the critical temperatures for the existence of full quantum (classical) topological entropy correspond to the confinement-deconfinement transitions in the corresponding Z2 gauge theories. This implies that the thermal stability of topological entropy corresponds to the stability of quantum (classical) memory. The implications for the understanding of ergodicity breaking in topological phases are discussed.

Topological Oxide Insulator in Cubic Perovskite Structure

PubMed Central

Jin, Hosub; Rhim, Sonny H.; Im, Jino; Freeman, Arthur J.

2013-01-01

The emergence of topologically protected conducting states with the chiral spin texture is the most prominent feature at the surface of topological insulators. On the application side, large band gap and high resistivity to distinguish surface from bulk degrees of freedom should be guaranteed for the full usage of the surface states. Here, we suggest that the oxide cubic perovskite YBiO3, more than just an oxide, defines itself as a new three-dimensional topological insulator exhibiting both a large bulk band gap and a high resistivity. Based on first-principles calculations varying the spin-orbit coupling strength, the non-trivial band topology of YBiO3 is investigated, where the spin-orbit coupling of the Bi 6p orbital plays a crucial role. Taking the exquisite synthesis techniques in oxide electronics into account, YBiO3 can also be used to provide various interface configurations hosting exotic topological phenomena combined with other quantum phases. PMID:23575973

Observation of topological states in an optical Raman lattice with ultracold fermions

NASA Astrophysics Data System (ADS)

Song, Bo; He, Chengdong; Zhang, Long; Poon, Ting Fung Jeffrey; Hajiyev, Elnur; Ren, Zejian; Seo, Bojeong; Zhang, Shanchao; Liu, Xiong-Jun; Jo, Gyu-Boong

2017-04-01

The spin-orbit coupling with cold atoms, especially in optical lattices, provides a versatile platform to investigate the intriguing topological matters. In this talk, we will present the realization of one-dimensional spin-dependent lattice dressed by the periodic Raman field. Ultracold 173Yb fermions loaded into an optical Raman lattice reveal non-trivial spin textures due to the band topology, by which we measured topological invariants and determined a topological phase transition. In addition, we explored the non-equilibrium quench dynamics between the topological and the trivial states by suddenly changing the band topology of the optical Raman lattice. The optical Raman lattice demonstrated here opens a new avenue to study the spin-orbit coupling physics and furthermore to realize novel quantum matters such as symmetry-protected topological states. Funded by Croucher Foundation and Research Grants Council (RGC) of Hong Kong (Project ECS26300014, GRF16300215, GRF16311516, and Croucher Innovation Grants); MOST (Grant No. 2016YFA0301604) and NSFC (No. 11574008).

Topological Quantum Information Processing Mediated Via Hybrid Topological Insulator Structures

DTIC Science & Technology

2013-11-13

manipulation, entanglement and detection ofMajorana fermions in diamond-topological insulator - superconductor heterojunctions. Furthennore, we propose to...the formation, manipulation, entanglement and detection of Majorana fermions in diamond-topological insulator - superconductor heterojunctions...Interactions between Superconductors and Topological Insulators Recent advances have revealed a new type of information processing, topological quantum

Controlling neutron orbital angular momentum

NASA Astrophysics Data System (ADS)

Clark, Charles W.; Barankov, Roman; Huber, Michael G.; Arif, Muhammad; Cory, David G.; Pushin, Dmitry A.

2015-09-01

The quantized orbital angular momentum (OAM) of photons offers an additional degree of freedom and topological protection from noise. Photonic OAM states have therefore been exploited in various applications ranging from studies of quantum entanglement and quantum information science to imaging. The OAM states of electron beams have been shown to be similarly useful, for example in rotating nanoparticles and determining the chirality of crystals. However, although neutrons--as massive, penetrating and neutral particles--are important in materials characterization, quantum information and studies of the foundations of quantum mechanics, OAM control of neutrons has yet to be achieved. Here, we demonstrate OAM control of neutrons using macroscopic spiral phase plates that apply a `twist' to an input neutron beam. The twisted neutron beams are analysed with neutron interferometry. Our techniques, applied to spatially incoherent beams, demonstrate both the addition of quantum angular momenta along the direction of propagation, effected by multiple spiral phase plates, and the conservation of topological charge with respect to uniform phase fluctuations. Neutron-based studies of quantum information science, the foundations of quantum mechanics, and scattering and imaging of magnetic, superconducting and chiral materials have until now been limited to three degrees of freedom: spin, path and energy. The optimization of OAM control, leading to well defined values of OAM, would provide an additional quantized degree of freedom for such studies.

Quantum phase transition and protected ideal transport in a Kondo chain

DOE PAGES

Tsvelik, A. M.; Yevtushenko, O. M.

2015-11-30

We study the low energy physics of a Kondo chain where electrons from a one-dimensional band interact with magnetic moments via an anisotropic exchange interaction. It is demonstrated that the anisotropy gives rise to two different phases which are separated by a quantum phase transition. In the phase with easy plane anisotropy, Z2 symmetry between sectors with different helicity of the electrons is broken. As a result, localization effects are suppressed and the dc transport acquires (partial) symmetry protection. This effect is similar to the protection of the edge transport in time-reversal invariant topological insulators. The phase with easy axismore » anisotropy corresponds to the Tomonaga-Luttinger liquid with a pronounced spin-charge separation. The slow charge density wave modes have no protection against localizatioin.« less

Topological order following a quantum quench

NASA Astrophysics Data System (ADS)

Tsomokos, Dimitris I.; Hamma, Alioscia; Zhang, Wen; Haas, Stephan; Fazio, Rosario

2009-12-01

We determine the conditions under which topological order survives a rapid quantum quench. Specifically, we consider the case where a quantum spin system is prepared in the ground state of the toric code model and, after the quench, it evolves with a Hamiltonian that does not support topological order. We provide analytical results supported by numerical evidence for a variety of quench Hamiltonians. The robustness of topological order under nonequilibrium situations is tested by studying the topological entropy and a dynamical measure, which makes use of the similarity between partial density matrices obtained from different topological sectors.

Continuity of the sequential product of sequential quantum effect algebras

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lei, Qiang, E-mail: leiqiang@hit.edu.cn; Su, Xiaochao, E-mail: hitswh@163.com; Wu, Junde, E-mail: wjd@zju.edu.cn

In order to study quantum measurement theory, sequential product defined by A∘B = A{sup 1/2}BA{sup 1/2} for any two quantum effects A, B has been introduced. Physically motivated conditions ask the sequential product to be continuous with respect to the strong operator topology. In this paper, we study the continuity problems of the sequential product A∘B = A{sup 1/2}BA{sup 1/2} with respect to other important topologies, such as norm topology, weak operator topology, order topology, and interval topology.

Room Temperature Quantum Spin Hall Insulator in Ethynyl-Derivative Functionalized Stanene Films

PubMed Central

Zhang, Run-wu; Zhang, Chang-wen; Ji, Wei-xiao; Li, Sheng-shi; Yan, Shi-shen; Hu, Shu-jun; Li, Ping; Wang, Pei-ji; Li, Feng

2016-01-01

Quantum spin Hall (QSH) insulators feature edge states that topologically protected from backscattering. However, the major obstacles to application for QSH effect are the lack of suitable QSH insulators with a large bulk gap. Based on first-principles calculations, we predict a class of large-gap QSH insulators in ethynyl-derivative functionalized stanene (SnC2X; X = H, F, Cl, Br, I), allowing for viable applications at room temperature. Noticeably, the SnC2Cl, SnC2Br, and SnC2I are QSH insulators with a bulk gap of ~0.2 eV, while the SnC2H and SnC2F can be transformed into QSH insulator under the tensile strains. A single pair of topologically protected helical edge states is established for the edge of these systems with the Dirac point locating at the bulk gap, and their QSH states are confirmed with topological invariant Z2 = 1. The films on BN substrate also maintain a nontrivial large-gap QSH effect, which harbors a Dirac cone lying within the band gap. These findings may shed new light in future design and fabrication of large-gap QSH insulators based on two-dimensional honeycomb lattices in spintronics. PMID:26728874

Dynamical generation of Floquet Majorana flat bands in s-wave superconductors

NASA Astrophysics Data System (ADS)

Poudel, A.; Ortiz, G.; Viola, L.

2015-04-01

We present quantum control techniques to engineer flat bands of symmetry-protected Majorana edge modes in s-wave superconductors. Specifically, we show how periodic control may be employed for designing time-independent effective Hamiltonians, which support Floquet Majorana flat bands, starting from equilibrium conditions that are either topologically trivial or only support a Majorana pair per edge. In the first approach, a suitable modulation of the chemical potential simultaneously induces Majorana flat bands and dynamically activates a pre-existing chiral symmetry which is responsible for their protection. In the second approach, the application of effective parity kicks dynamically generates a desired chiral symmetry by suppressing chirality-breaking terms in the static Hamiltonian. Our results demonstrate how the use of time-dependent control enlarges the range of possibilities for realizing gapless topological superconductivity, potentially enabling access to topological states of matter that have no known equilibrium counterpart.

Topological spinon bands and vison excitations in spin-orbit coupled quantum spin liquids

NASA Astrophysics Data System (ADS)

Sonnenschein, Jonas; Reuther, Johannes

2017-12-01

Spin liquids are exotic quantum states characterized by the existence of fractional and deconfined quasiparticle excitations, referred to as spinons and visons. Their fractional nature establishes topological properties such as a protected ground-state degeneracy. This work investigates spin-orbit coupled spin liquids where, additionally, topology enters via nontrivial band structures of the spinons. We revisit the Z2 spin-liquid phases that have recently been identified in a projective symmetry-group analysis on the square lattice when spin-rotation symmetry is maximally lifted [J. Reuther et al., Phys. Rev. B 90, 174417 (2014), 10.1103/PhysRevB.90.174417]. We find that in the case of nearest-neighbor couplings only, Z2 spin liquids on the square lattice always exhibit trivial spinon bands. Adding second-neighbor terms, the simplest projective symmetry-group solution closely resembles the Bernevig-Hughes-Zhang model for topological insulators. Assuming that the emergent gauge fields are static, we investigate vison excitations, which we confirm to be deconfined in all investigated spin phases. Particularly, if the spinon bands are topological, the spinons and visons form bound states consisting of several spinon-Majorana zero modes coupling to one vison. The existence of such zero modes follows from an exact mapping between these spin phases and topological p +i p superconductors with vortices. We propose experimental probes to detect such states in real materials.

Feasibility of self-correcting quantum memory and thermal stability of topological order

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yoshida, Beni, E-mail: rouge@mit.edu

2011-10-15

Recently, it has become apparent that the thermal stability of topologically ordered systems at finite temperature, as discussed in condensed matter physics, can be studied by addressing the feasibility of self-correcting quantum memory, as discussed in quantum information science. Here, with this correspondence in mind, we propose a model of quantum codes that may cover a large class of physically realizable quantum memory. The model is supported by a certain class of gapped spin Hamiltonians, called stabilizer Hamiltonians, with translation symmetries and a small number of ground states that does not grow with the system size. We show that themore » model does not work as self-correcting quantum memory due to a certain topological constraint on geometric shapes of its logical operators. This quantum coding theoretical result implies that systems covered or approximated by the model cannot have thermally stable topological order, meaning that systems cannot be stable against both thermal fluctuations and local perturbations simultaneously in two and three spatial dimensions. - Highlights: > We define a class of physically realizable quantum codes. > We determine their coding and physical properties completely. > We establish the connection between topological order and self-correcting memory. > We find they do not work as self-correcting quantum memory. > We find they do not have thermally stable topological order.« less

Deconfined quantum critical point on the triangular lattice

NASA Astrophysics Data System (ADS)

Jian, Chao-Ming; Thomson, Alex; Rasmussen, Alex; Bi, Zhen; Xu, Cenke

2018-05-01

In this work we propose a theory for the deconfined quantum critical point (DQCP) for spin-1/2 systems on a triangular lattice, which is a direct unfine-tuned quantum phase transition between the standard "√{3 }×√{3 } " noncollinear antiferromagnetic order (or the so-called 120∘ state) and the "√{12 }×√{12 } " valence solid bond (VBS) order, both of which are very standard ordered phases often observed in numerical simulations. This transition is beyond the standard Landau-Ginzburg paradigm and is also fundamentally different from the original DQCP theory on the square lattice due to the very different structures of both the magnetic and VBS order on frustrated lattices. We first propose a topological term in the effective-field theory that captures the "intertwinement" between the √{3 }×√{3 } antiferromagnetic order and the √{12 }×√{12 } VBS order. Then using a controlled renormalization-group calculation, we demonstrate that an unfine-tuned direct continuous DQCP exists between the two ordered phases mentioned above. This DQCP is described by the Nf=4 quantum electrodynamics (QED) with an emergent PSU(4)=SU(4)/Z4 symmetry only at the critical point. The aforementioned topological term is also naturally derived from the Nf=4 QED. We also point out that physics around this DQCP is analogous to the boundary of a 3 d bosonic symmetry- protected topological state with only on-site symmetries.

Adiabatic topological quantum computing

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cesare, Chris; Landahl, Andrew J.; Bacon, Dave

Topological quantum computing promises error-resistant quantum computation without active error correction. However, there is a worry that during the process of executing quantum gates by braiding anyons around each other, extra anyonic excitations will be created that will disorder the encoded quantum information. Here, we explore this question in detail by studying adiabatic code deformations on Hamiltonians based on topological codes, notably Kitaev’s surface codes and the more recently discovered color codes. We develop protocols that enable universal quantum computing by adiabatic evolution in a way that keeps the energy gap of the system constant with respect to the computationmore » size and introduces only simple local Hamiltonian interactions. This allows one to perform holonomic quantum computing with these topological quantum computing systems. The tools we develop allow one to go beyond numerical simulations and understand these processes analytically.« less

Adiabatic topological quantum computing

DOE PAGES

Cesare, Chris; Landahl, Andrew J.; Bacon, Dave; ...

2015-07-31

Topological quantum computing promises error-resistant quantum computation without active error correction. However, there is a worry that during the process of executing quantum gates by braiding anyons around each other, extra anyonic excitations will be created that will disorder the encoded quantum information. Here, we explore this question in detail by studying adiabatic code deformations on Hamiltonians based on topological codes, notably Kitaev’s surface codes and the more recently discovered color codes. We develop protocols that enable universal quantum computing by adiabatic evolution in a way that keeps the energy gap of the system constant with respect to the computationmore » size and introduces only simple local Hamiltonian interactions. This allows one to perform holonomic quantum computing with these topological quantum computing systems. The tools we develop allow one to go beyond numerical simulations and understand these processes analytically.« less

Strong and weak second-order topological insulators with hexagonal symmetry and ℤ3 index

NASA Astrophysics Data System (ADS)

Ezawa, Motohiko

2018-06-01

We propose second-order topological insulators (SOTIs) whose lattice structure has a hexagonal symmetry C6. We start with a three-dimensional weak topological insulator constructed on a stacked triangular lattice, which has only side topological surface states. We then introduce an additional mass term which gaps out the side surface states but preserves the hinge states. The resultant system is a three-dimensional SOTI. The bulk topological quantum number is shown to be the Z3 index protected by inversion time-reversal symmetry I T and rotoinversion symmetry I C6 . We obtain three phases: trivial, strong, and weak SOTI phases. We argue the origin of these two types of SOTIs. A hexagonal prism is a typical structure respecting these symmetries, where six topological hinge states emerge at the side. The building block is a hexagon in two dimensions, where topological corner states emerge at the six corners in the SOTI phase. Strong and weak SOTIs are obtained when the interlayer hopping interaction is strong and weak, respectively.

Topological Phases in Graphene Nanoribbons: Junction States, Spin Centers, and Quantum Spin Chains

NASA Astrophysics Data System (ADS)

Cao, Ting; Zhao, Fangzhou; Louie, Steven G.

2017-08-01

We show that semiconducting graphene nanoribbons (GNRs) of different width, edge, and end termination (synthesizable from molecular precursors with atomic precision) belong to different electronic topological classes. The topological phase of GNRs is protected by spatial symmetries and dictated by the terminating unit cell. We have derived explicit formulas for their topological invariants and shown that localized junction states developed between two GNRs of distinct topology may be tuned by lateral junction geometry. The topology of a GNR can be further modified by dopants, such as a periodic array of boron atoms. In a superlattice consisting of segments of doped and pristine GNRs, the junction states are stable spin centers, forming a Heisenberg antiferromagnetic spin 1 /2 chain with tunable exchange interaction. The discoveries here not only are of scientific interest for studies of quasi-one-dimensional systems, but also open a new path for design principles of future GNR-based devices through their topological characters.

Topological Phases in Graphene Nanoribbons: Junction States, Spin Centers, and Quantum Spin Chains.

PubMed

Cao, Ting; Zhao, Fangzhou; Louie, Steven G

2017-08-18

We show that semiconducting graphene nanoribbons (GNRs) of different width, edge, and end termination (synthesizable from molecular precursors with atomic precision) belong to different electronic topological classes. The topological phase of GNRs is protected by spatial symmetries and dictated by the terminating unit cell. We have derived explicit formulas for their topological invariants and shown that localized junction states developed between two GNRs of distinct topology may be tuned by lateral junction geometry. The topology of a GNR can be further modified by dopants, such as a periodic array of boron atoms. In a superlattice consisting of segments of doped and pristine GNRs, the junction states are stable spin centers, forming a Heisenberg antiferromagnetic spin 1/2 chain with tunable exchange interaction. The discoveries here not only are of scientific interest for studies of quasi-one-dimensional systems, but also open a new path for design principles of future GNR-based devices through their topological characters.

Zeeman effect of the topological surface states revealed by quantum oscillations up to 91 Tesla

DOE PAGES

Zhang, Zuocheng; Wei, Wei; Yang, Fangyuan; ...

2015-12-01

In this paper, we report quantum oscillation studies on the Bi 2Te 3-xS x topological insulator single crystals in pulsed magnetic fields up to 91 T. For the x = 0.4 sample with the lowest bulk carrier density, the surface and bulk quantum oscillations can be disentangled by combined Shubnikov–de Haas and de Hass–van Alphen oscillations, as well as quantum oscillations in nanometer-thick peeled crystals. At high magnetic fields beyond the bulk quantum limit, our results suggest that the zeroth Landau level of topological surface states is shifted due to the Zeeman effect. The g factor of the topological surfacemore » states is estimated to be between 1.8 and 4.5. Lastly, these observations shed new light on the quantum transport phenomena of topological insulators in ultrahigh magnetic fields.« less

Topological Quantum Information Processing Mediated Via Hybrid Topogical Insulator Structures

DTIC Science & Technology

2014-03-28

formation, manipulation, entanglement and detection of Majorana fermions in diamond-topological insulator - superconductor heterojunctions. Furthermore...between Superconductors and Topological Insulators Recent advances have revealed a new type of information processing, topological quantum...Topological Insulator - Superconductor Heterostructures," Physical Review B 84, 144507 (2011). 7 Hsiang-Hsuan Hung, Pouyan Ghaemi, Taylor L

Measurement and control of a Coulomb-blockaded parafermion box

NASA Astrophysics Data System (ADS)

Snizhko, Kyrylo; Egger, Reinhold; Gefen, Yuval

2018-02-01

Parafermionic zero modes are fractional topologically protected quasiparticles expected to arise in various platforms. We show that Coulomb charging effects define a parafermion box with unique access options via fractional edge states and/or quantum antidots. Basic protocols for the detection, manipulation, and control of parafermionic quantum states are formulated. With those tools, one may directly observe the dimension of the zero-mode Hilbert space, prove the degeneracy of this space, and perform on-demand digital operations satisfying a parafermionic algebra.

Quantum spin Hall state in monolayer 1T '-WTe 2

DOE PAGES

Tang, Shujie; Zhang, Chaofan; Wong, Dillon; ...

2017-06-26

A quantum spin Hall (QSH) insulator is a novel two-dimensional quantum state of matter that features quantized Hall conductance in the absence of a magnetic field, resulting from topologically protected dissipationless edge states that bridge the energy gap opened by band inversion and strong spin–orbit coupling. By investigating the electronic structure of epitaxially grown monolayer 1T '-WTe 2 using angle-resolved photoemission (ARPES) and first-principles calculations, we observe clear signatures of topological band inversion and bandgap opening, which are the hallmarks of a QSH state. Scanning tunnelling microscopy measurements further confirm the correct crystal structure and the existence of a bulkmore » bandgap, and provide evidence for a modified electronic structure near the edge that is consistent with the expectations for a QSH insulator. Our results establish monolayer 1T '-WTe 2 as a new class of QSH insulator with large band gap in a robust two-dimensional materials family of transition metal dichalcogenides (TMDCs).« less

Quantum spin Hall state in monolayer 1T '-WTe 2

DOE PAGES

Tang, Shujie; Zhang, Chaofan; Wong, Dillon; ...

2017-06-26

A quantum spin Hall (QSH) insulator is a novel two-dimensional quantum state of matter that features quantized Hall conductance in the absence of a magnetic field, resulting from topologically protected dissipationless edge states that bridge the energy gap opened by band inversion and strong spin–orbit coupling. By investigating the electronic structure of epitaxially grown monolayer 1T '-WTe 2 using angle-resolved photoemission (ARPES) and first-principles calculations, we observe clear signatures of topological band inversion and bandgap opening, which are the hallmarks of a QSH state. Scanning tunnelling microscopy measurements further confirm the correct crystal structure and the existence of a bulkmore » bandgap, and provide evidence for a modified electronic structure near the edge that is consistent with the expectations for a QSH insulator. Finally, our results establish monolayer 1T '-WTe 2 as a new class of QSH insulator with large band gap in a robust two-dimensional materials family of transition metal dichalcogenides (TMDCs).« less

Observation of topological valley transport of sound in sonic crystals

NASA Astrophysics Data System (ADS)

Lu, Jiuyang; Qiu, Chunyin; Ye, Liping; Fan, Xiying; Ke, Manzhu; Zhang, Fan; Liu, Zhengyou

2017-04-01

The concept of valley pseudospin, labelling quantum states of energy extrema in momentum space, is attracting attention because of its potential as a new type of information carrier. Compared with the non-topological bulk valley transport, realized soon after predictions, topological valley transport in domain walls is extremely challenging owing to the inter-valley scattering inevitably induced by atomic-scale imperfections--but an electronic signature was recently observed in bilayer graphene. Here, we report the experimental observation of topological valley transport of sound in sonic crystals. The macroscopic nature of sonic crystals permits a flexible and accurate design of domain walls. In addition to a direct visualization of the valley-selective edge modes through spatial scanning of the sound field, reflection immunity is observed in sharply curved interfaces. The topologically protected interface transport of sound, strikingly different from that in traditional sound waveguides, may serve as the basis for designing devices with unconventional functions.

Tunneling topological vacua via extended operators: (Spin-)TQFT spectra and boundary deconfinement in various dimensions

NASA Astrophysics Data System (ADS)

Wang, Juven; Ohmori, Kantaro; Putrov, Pavel; Zheng, Yunqin; Wan, Zheyan; Guo, Meng; Lin, Hai; Gao, Peng; Yau, Shing-Tung

2018-05-01

Distinct quantum vacua of topologically ordered states can be tunneled into each other via extended operators. The possible applications include condensed matter and quantum cosmology. We present a straightforward approach to calculate the partition function on various manifolds and ground state degeneracy (GSD), mainly based on continuum/cochain topological quantum field theories (TQFTs), in any dimension. This information can be related to the counting of extended operators of bosonic/fermionic TQFTs. On the lattice scale, anyonic particles/strings live at the ends of line/surface operators. Certain systems in different dimensions are related to each other through dimensional reduction schemes, analogous to (de)categorification. Examples include spin TQFTs derived from gauging the interacting fermionic symmetry-protected topological states (with fermion parity {Z}_2^f) of symmetry groups {Z}_4× {Z}_2 and ({Z}_4)^2 in 3+1D, also {Z}_2 and ({Z}_2)^2 in 2+1D. Gauging the last three cases begets non-Abelian spin TQFTs (fermionic topological order). We consider situations where a TQFT lives on (1) a closed spacetime or (2) a spacetime with a boundary, such that the bulk and boundary are fully gapped and short- or long-range entangled (SRE/LRE). Anyonic excitations can be deconfined on the boundary. We introduce new exotic topological interfaces on which neither particle nor string excitations alone condense, but only fuzzy-composite objects of extended operators can end (e.g., a string-like composite object formed by a set of particles can end on a special 2+1D boundary of 3+1D bulk). We explore the relations between group extension constructions and partially breaking constructions (e.g., 0-form/higher-form/"composite" breaking) of topological boundaries, after gauging. We comment on the implications of entanglement entropy for some such LRE systems.

Topological states of condensed matter

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Jing; Zhang, Shou-Cheng

Topological states of quantum matter have been investigated intensively in recent years in materials science and condensed matter physics. The field developed explosively largely because of the precise theoretical predictions, well-controlled materials processing, and novel characterization techniques. In this Perspective, we review recent progress in topological insulators, the quantum anomalous Hall effect, chiral topological superconductors, helical topological superconductors and Weyl semimetals.

Topological states of condensed matter

DOE PAGES

Wang, Jing; Zhang, Shou-Cheng

2017-10-25

Topological states of quantum matter have been investigated intensively in recent years in materials science and condensed matter physics. The field developed explosively largely because of the precise theoretical predictions, well-controlled materials processing, and novel characterization techniques. In this Perspective, we review recent progress in topological insulators, the quantum anomalous Hall effect, chiral topological superconductors, helical topological superconductors and Weyl semimetals.

Space-time topology and quantum gravity.

NASA Astrophysics Data System (ADS)

Friedman, J. L.

Characteristic features are discussed of a theory of quantum gravity that allows space-time with a non-Euclidean topology. The review begins with a summary of the manifolds that can occur as classical vacuum space-times and as space-times with positive energy. Local structures with non-Euclidean topology - topological geons - collapse, and one may conjecture that in asymptotically flat space-times non-Euclidean topology is hiden from view. In the quantum theory, large diffeos can act nontrivially on the space of states, leading to state vectors that transform as representations of the corresponding symmetry group π0(Diff). In particular, in a quantum theory that, at energies E < EPlanck, is a theory of the metric alone, there appear to be ground states with half-integral spin, and in higher-dimensional gravity, with the kinematical quantum numbers of fundamental fermions.

When quantum optics meets topology

NASA Astrophysics Data System (ADS)

Amo, Alberto

2018-02-01

Routing photons at the micrometer scale remains one of the greatest challenges of integrated quantum optics. The main difficulty is the scattering losses at bends and splitters in the photonic circuit. Current approaches imply elaborate designs, quite sensitive to fabrication details (1). Inspired by the physics underlying the one-way transport of electrons in topological insulators, on page 666 of this issue, Barik et al. (2) report a topological photonic crystal in which single photons are emitted and routed through bends with negligible loss. The marriage between quantum optics and topology promises new opportunities for compact quantum optics gating and manipulation.

A Design Method for Topologically Insulating Metamaterials

NASA Astrophysics Data System (ADS)

Matlack, Kathryn; Serra-Garcia, Marc; Palermo, Antonio; Huber, Sebastian; Daraio, Chiara

Topological insulators are a unique class of electronic materials that exhibit protected edge states that are insulating in the bulk, and immune to back-scattering and defects. Discrete models, such as mass-spring systems, provide a means to translate these properties, based on the quantum hall spin effect, to the mechanical domain. This talk will present how to engineer a 2D mechanical metamaterial that supports topologically-protected and defect-immune edge states, directly from the mass-spring model of a topological insulator. The design method uses combinatorial searches plus gradient-based optimizations to determine the configuration of the metamaterials building blocks that leads to the global behavior specified by the target mass-spring model. We use metamaterials with weakly coupled unit cells to isolate the dynamics within our frequency range of interest and to enable a systematic design process. This approach can generally be applied to implement behaviors of a discrete model directly in mechanical, acoustic, or photonic metamaterials within the weak-coupling regime. This work was partially supported by the ETH Postdoctoral Fellowship, and by the Swiss National Science Foundation.

Symmetry-protected topological phases of one-dimensional interacting fermions with spin-charge separation

NASA Astrophysics Data System (ADS)

Montorsi, Arianna; Dolcini, Fabrizio; Iotti, Rita C.; Rossi, Fausto

2017-06-01

The low energy behavior of a huge variety of one-dimensional interacting spinful fermionic systems exhibits spin-charge separation, described in the continuum limit by two sine-Gordon models decoupled in the charge and spin channels. Interaction is known to induce, besides the gapless Luttinger liquid phase, eight possible gapped phases, among which are the Mott, Haldane, charge-/spin-density, and bond-ordered wave insulators, and the Luther Emery liquid. Here we prove that some of these physically distinct phases have nontrivial topological properties, notably the presence of degenerate protected edge modes with fractionalized charge/spin. Moreover, we show that the eight gapped phases are in one-to-one correspondence with the symmetry-protected topological (SPT) phases classified by group cohomology theory in the presence of particle-hole symmetry P. The latter result is also exploited to characterize SPT phases by measurable nonlocal order parameters which follow the system evolution to the quantum phase transition. The implications on the appearance of exotic orders in the class of microscopic Hubbard Hamiltonians, possibly without P symmetry at higher energies, are discussed.

Electronic properties of novel topological quantum materials studied by angle-resolved photoemission spectroscopy (ARPES)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wu, Yun

The discovery of quantum Hall e ect has motivated the use of topology instead of broken symmetry to classify the states of matter. Quantum spin Hall e ect has been proposed to have a separation of spin currents as an analogue of the charge currents separation in quantum Hall e ect, leading us to the era of topological insulators. Three-dimensional analogue of the Dirac state in graphene has brought us the three-dimensional Dirac states. Materials with three-dimensional Dirac states could potentially be the parent compounds for Weyl semimetals and topological insulators when time-reversal or space inversion symmetry is broken. Inmore » addition to the single Dirac point linking the two dispersion cones in the Dirac/Weyl semimetals, Dirac points can form a line in the momentum space, resulting in a topological node line semimetal. These fascinating novel topological quantum materials could provide us platforms for studying the relativistic physics in condensed matter systems and potentially lead to design of new electronic devices that run faster and consume less power than traditional, silicon based transistors. In this thesis, we present the electronic properties of novel topological quantum materials studied by angle-resolved photoemission spectroscopy (ARPES).« less

Topological phononic states of underwater sound based on coupled ring resonators

DOE Office of Scientific and Technical Information (OSTI.GOV)

He, Cheng; Li, Zheng; Ni, Xu

We report a design of topological phononic states for underwater sound using arrays of acoustic coupled ring resonators. In each individual ring resonator, two degenerate acoustic modes, corresponding to clockwise and counter-clockwise propagation, are treated as opposite pseudospins. The gapless edge states arise in the bandgap resulting in protected pseudospin-dependent sound transportation, which is a phononic analogue of the quantum spin Hall effect. We also investigate the robustness of the topological sound state, suggesting that the observed pseudospin-dependent sound transportation remains unless the introduced defects facilitate coupling between the clockwise and counter-clockwise modes (in other words, the original mode degeneracymore » is broken). The topological engineering of sound transportation will certainly promise unique design for next generation of acoustic devices in sound guiding and switching, especially for underwater acoustic devices.« less

Observation of unusual topological surface states in half-Heusler compounds LnPtBi (Ln=Lu, Y)

DOE PAGES

Liu, Z. K.; Yang, L. X.; Wu, S. -C.; ...

2016-09-27

Topological quantum materials represent a new class of matter with both exotic physical phenomena and novel application potentials. Many Heusler compounds, which exhibit rich emergent properties such as unusual magnetism, superconductivity and heavy fermion behaviour, have been predicted to host non-trivial topological electronic structures. The coexistence of topological order and other unusual properties makes Heusler materials ideal platform to search for new topological quantum phases (such as quantum anomalous Hall insulator and topological superconductor). By carrying out angle-resolved photoemission spectroscopy and ab initio calculations on rare-earth half-Heusler compounds LnPtBi (Ln=Lu, Y), we directly observe the unusual topological surface states onmore » these materials, establishing them as first members with non-trivial topological electronic structure in this class of materials. Moreover, as LnPtBi compounds are non-centrosymmetric superconductors, our discovery further highlights them as promising candidates of topological superconductors.« less

Observation of unusual topological surface states in half-Heusler compounds LnPtBi (Ln=Lu, Y)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Z. K.; Yang, L. X.; Wu, S. -C.

Topological quantum materials represent a new class of matter with both exotic physical phenomena and novel application potentials. Many Heusler compounds, which exhibit rich emergent properties such as unusual magnetism, superconductivity and heavy fermion behaviour, have been predicted to host non-trivial topological electronic structures. The coexistence of topological order and other unusual properties makes Heusler materials ideal platform to search for new topological quantum phases (such as quantum anomalous Hall insulator and topological superconductor). By carrying out angle-resolved photoemission spectroscopy and ab initio calculations on rare-earth half-Heusler compounds LnPtBi (Ln=Lu, Y), we directly observe the unusual topological surface states onmore » these materials, establishing them as first members with non-trivial topological electronic structure in this class of materials. Moreover, as LnPtBi compounds are non-centrosymmetric superconductors, our discovery further highlights them as promising candidates of topological superconductors.« less

Rényi entropies and topological quantum numbers in 2D gapped Dirac materials

NASA Astrophysics Data System (ADS)

Bolívar, Juan Carlos; Romera, Elvira

2017-05-01

New topological quantum numbers are introduced by analyzing complexity measures and relative Rényi entropies in silicene in the presence of perpendicular electric and magnetic fields. These topological quantum numbers characterize the topological insulator and band insulator phases in silicene. In addition, we have found that, these information measures reach extremum values at the charge neutrality points. These results are valid for other 2D gapped Dirac materials analogous to silicene with a buckled honeycomb structure and a significant spin-orbit coupling.

Magnetic quantum phase transition in Cr-doped Bi 2(Se xTe 1-x) 3 driven by the Stark effect

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Zuocheng; Feng, Xiao; Wang, Jing

The interplay between magnetism and topology, as exemplified in the magnetic skyrmion systems, has emerged as a rich playground for finding novel quantum phenomena and applications in future information technology. Magnetic topological insulators (TI) have attracted much recent attention, especially after the experimental realization of quantum anomalous Hall effect. Future applications of magnetic TI hinge on the accurate manipulation of magnetism and topology by external perturbations, preferably with a gate electric field. In this work, we investigate the magneto transport properties of Cr doped Bi 2(Se xTe 1-x) 3 TI across the topological quantum critical point (QCP). We find thatmore » the external gate voltage has negligible effect on the magnetic order for samples far away from the topological QCP. However, for the sample near the QCP, we observe a ferromagnetic (FM) to paramagnetic (PM) phase transition driven by the gate electric field. Theoretical calculations show that a perpendicular electric field causes a shift of electronic energy levels due to the Stark effect, which induces a topological quantum phase transition and consequently a magnetic phase transition. Finally, the in situ electrical control of the topological and magnetic properties of TI shed important new lights on future topological electronic or spintronic device applications.« less

Magnetic quantum phase transition in Cr-doped Bi 2(Se xTe 1-x) 3 driven by the Stark effect

DOE PAGES

Zhang, Zuocheng; Feng, Xiao; Wang, Jing; ...

2017-08-07

The interplay between magnetism and topology, as exemplified in the magnetic skyrmion systems, has emerged as a rich playground for finding novel quantum phenomena and applications in future information technology. Magnetic topological insulators (TI) have attracted much recent attention, especially after the experimental realization of quantum anomalous Hall effect. Future applications of magnetic TI hinge on the accurate manipulation of magnetism and topology by external perturbations, preferably with a gate electric field. In this work, we investigate the magneto transport properties of Cr doped Bi 2(Se xTe 1-x) 3 TI across the topological quantum critical point (QCP). We find thatmore » the external gate voltage has negligible effect on the magnetic order for samples far away from the topological QCP. However, for the sample near the QCP, we observe a ferromagnetic (FM) to paramagnetic (PM) phase transition driven by the gate electric field. Theoretical calculations show that a perpendicular electric field causes a shift of electronic energy levels due to the Stark effect, which induces a topological quantum phase transition and consequently a magnetic phase transition. Finally, the in situ electrical control of the topological and magnetic properties of TI shed important new lights on future topological electronic or spintronic device applications.« less

Physical realization of topological quantum walks on IBM-Q and beyond

NASA Astrophysics Data System (ADS)

Balu, Radhakrishnan; Castillo, Daniel; Siopsis, George

2018-07-01

We discuss an efficient physical realization of topological quantum walks on a one-dimensional finite lattice with periodic boundary conditions (circle). The N-point lattice is realized with {log}}2N qubits, and the quantum circuit utilizes a number of quantum gates that are polynomial in the number of qubits. In a certain scaling limit, we show that a large number of steps are implemented with a number of quantum gates which are independent of the number of steps. We ran the quantum algorithm on the IBM-Q five-qubit quantum computer, thus experimentally demonstrating topological features, such as boundary bound states, on a one-dimensional lattice with N = 4 points.

Extended Quantum Field Theory, Index Theory, and the Parity Anomaly

NASA Astrophysics Data System (ADS)

Müller, Lukas; Szabo, Richard J.

2018-06-01

We use techniques from functorial quantum field theory to provide a geometric description of the parity anomaly in fermionic systems coupled to background gauge and gravitational fields on odd-dimensional spacetimes. We give an explicit construction of a geometric cobordism bicategory which incorporates general background fields in a stack, and together with the theory of symmetric monoidal bicategories we use it to provide the concrete forms of invertible extended quantum field theories which capture anomalies in both the path integral and Hamiltonian frameworks. Specialising this situation by using the extension of the Atiyah-Patodi-Singer index theorem to manifolds with corners due to Loya and Melrose, we obtain a new Hamiltonian perspective on the parity anomaly. We compute explicitly the 2-cocycle of the projective representation of the gauge symmetry on the quantum state space, which is defined in a parity-symmetric way by suitably augmenting the standard chiral fermionic Fock spaces with Lagrangian subspaces of zero modes of the Dirac Hamiltonian that naturally appear in the index theorem. We describe the significance of our constructions for the bulk-boundary correspondence in a large class of time-reversal invariant gauge-gravity symmetry-protected topological phases of quantum matter with gapless charged boundary fermions, including the standard topological insulator in 3 + 1 dimensions.

Quantum glassiness in strongly correlated clean systems: an example of topological overprotection.

PubMed

Chamon, Claudio

2005-02-04

This Letter presents solvable examples of quantum many-body Hamiltonians of systems that are unable to reach their ground states as the environment temperature is lowered to absolute zero. These examples, three-dimensional generalizations of quantum Hamiltonians proposed for topological quantum computing, (1) have no quenched disorder, (2) have solely local interactions, (3) have an exactly solvable spectrum, (4) have topologically ordered ground states, and (5) have slow dynamical relaxation rates akin to those of strong structural glasses.

Quantum Glassiness in Strongly Correlated Clean Systems: An Example of Topological Overprotection

NASA Astrophysics Data System (ADS)

Chamon, Claudio

2005-01-01

This Letter presents solvable examples of quantum many-body Hamiltonians of systems that are unable to reach their ground states as the environment temperature is lowered to absolute zero. These examples, three-dimensional generalizations of quantum Hamiltonians proposed for topological quantum computing, (1)have no quenched disorder, (2)have solely local interactions, (3)have an exactly solvable spectrum, (4)have topologically ordered ground states, and (5)have slow dynamical relaxation rates akin to those of strong structural glasses.

Bosonic anomalies, induced fractional quantum numbers, and degenerate zero modes: The anomalous edge physics of symmetry-protected topological states

NASA Astrophysics Data System (ADS)

Wang, Juven C.; Santos, Luiz H.; Wen, Xiao-Gang

2015-05-01

The boundary of symmetry-protected topological states (SPTs) can harbor new quantum anomaly phenomena. In this work, we characterize the bosonic anomalies introduced by the 1+1D non-onsite-symmetric gapless edge modes of (2+1)D bulk bosonic SPTs with a generic finite Abelian group symmetry (isomorphic to G =∏iZNi=ZN1×ZN2×ZN3×⋯ ). We demonstrate that some classes of SPTs (termed "Type II") trap fractional quantum numbers (such as fractional ZN charges) at the 0D kink of the symmetry-breaking domain walls, while some classes of SPTs (termed "Type III") have degenerate zero energy modes (carrying the projective representation protected by the unbroken part of the symmetry), either near the 0D kink of a symmetry-breaking domain wall, or on a symmetry-preserving 1D system dimensionally reduced from a thin 2D tube with a monodromy defect 1D line embedded. More generally, the energy spectrum and conformal dimensions of gapless edge modes under an external gauge flux insertion (or twisted by a branch cut, i.e., a monodromy defect line) through the 1D ring can distinguish many SPT classes. We provide a manifest correspondence from the physical phenomena, the induced fractional quantum number, and the zero energy mode degeneracy to the mathematical concept of cocycles that appears in the group cohomology classification of SPTs, thus achieving a concrete physical materialization of the cocycles. The aforementioned edge properties are formulated in terms of a long wavelength continuum field theory involving scalar chiral bosons, as well as in terms of matrix product operators and discrete quantum lattice models. Our lattice approach yields a regularization with anomalous non-onsite symmetry for the field theory description. We also formulate some bosonic anomalies in terms of the Goldstone-Wilczek formula.

Infinite family of three-dimensional Floquet topological paramagnets

NASA Astrophysics Data System (ADS)

Potter, Andrew C.; Vishwanath, Ashvin; Fidkowski, Lukasz

2018-06-01

We uncover an infinite family of time-reversal symmetric 3 d interacting topological insulators of bosons or spins, in time-periodically driven systems, which we term Floquet topological paramagnets (FTPMs). These FTPM phases exhibit intrinsically dynamical properties that could not occur in thermal equilibrium and are governed by an infinite set of Z2-valued topological invariants, one for each prime number. The topological invariants are physically characterized by surface magnetic domain walls that act as unidirectional quantum channels, transferring quantized packets of information during each driving period. We construct exactly solvable models realizing each of these phases, and discuss the anomalous dynamics of their topologically protected surface states. Unlike previous encountered examples of Floquet SPT phases, these 3 d FTPMs are not captured by group cohomology methods and cannot be obtained from equilibrium classifications simply by treating the discrete time translation as an ordinary symmetry. The simplest such FTPM phase can feature anomalous Z2 (toric code) surface topological order, in which the gauge electric and magnetic excitations are exchanged in each Floquet period, which cannot occur in a pure 2 d system without breaking time reversal symmetry.

Machine learning Z2 quantum spin liquids with quasiparticle statistics

NASA Astrophysics Data System (ADS)

Zhang, Yi; Melko, Roger G.; Kim, Eun-Ah

2017-12-01

After decades of progress and effort, obtaining a phase diagram for a strongly correlated topological system still remains a challenge. Although in principle one could turn to Wilson loops and long-range entanglement, evaluating these nonlocal observables at many points in phase space can be prohibitively costly. With growing excitement over topological quantum computation comes the need for an efficient approach for obtaining topological phase diagrams. Here we turn to machine learning using quantum loop topography (QLT), a notion we have recently introduced. Specifically, we propose a construction of QLT that is sensitive to quasiparticle statistics. We then use mutual statistics between the spinons and visons to detect a Z2 quantum spin liquid in a multiparameter phase space. We successfully obtain the quantum phase boundary between the topological and trivial phases using a simple feed-forward neural network. Furthermore, we demonstrate advantages of our approach for the evaluation of phase diagrams relating to speed and storage. Such statistics-based machine learning of topological phases opens new efficient routes to studying topological phase diagrams in strongly correlated systems.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Zuocheng; Wei, Wei; Yang, Fangyuan

In this paper, we report quantum oscillation studies on the Bi 2Te 3-xS x topological insulator single crystals in pulsed magnetic fields up to 91 T. For the x = 0.4 sample with the lowest bulk carrier density, the surface and bulk quantum oscillations can be disentangled by combined Shubnikov–de Haas and de Hass–van Alphen oscillations, as well as quantum oscillations in nanometer-thick peeled crystals. At high magnetic fields beyond the bulk quantum limit, our results suggest that the zeroth Landau level of topological surface states is shifted due to the Zeeman effect. The g factor of the topological surfacemore » states is estimated to be between 1.8 and 4.5. Lastly, these observations shed new light on the quantum transport phenomena of topological insulators in ultrahigh magnetic fields.« less

Quantum order, entanglement and localization in many-body systems

NASA Astrophysics Data System (ADS)

Khemani, Vedika

The interplay of disorder and interactions can have remarkable effects on the physics of quantum systems. A striking example is provided by the long conjectured--and recently confirmed--phenomenon of many-body localization. Many-body localized (MBL) phases violate foundational assumptions about ergodicity and thermalization in interacting systems, and represent a new frontier for non-equilibrium quantum statistical mechanics. We start with a study of the dynamical response of MBL phases to time-dependent perturbations. We find that that an asymptotically slow, local perturbation induces a highly non-local response, a surprising result for a localized insulator. A complementary calculation in the linear-response regime elucidates the structure of many-body resonances contributing to the dynamics of this phase. We then turn to a study of quantum order in MBL systems. It was shown that localization can allow novel high-temperature phases and phase transitions that are disallowed in equilibrium. We extend this idea of "localization protected order'' to the case of symmetry-protected topological phases and to the elucidation of phase structure in periodically driven Floquet systems. We show that Floquet systems can display nontrivial phases, some of which show a novel form of correlated spatiotemporal order and are absolutely stable to all generic perturbations. The next part of the thesis addresses the role of quantum entanglement, broadly speaking. Remarkably, it was shown that even highly-excited MBL eigenstates have low area-law entanglement. We exploit this feature to develop tensor-network based algorithms for efficiently computing and representing highly-excited MBL eigenstates. We then switch gears from disordered, localized systems and examine the entanglement Hamiltonian and its low energy spectrum from a statistical mechanical lens, particularly focusing on issues of universality and thermalization. We close with two miscellaneous results on topologically ordered phases. The first studies the nonequilibrium "Kibble-Zurek'' dynamics resulting from driving a system through a phase transition from a topologically ordered phase to a trivial one at a finite rate. The second shows that the four-state Potts model on the pyrochlore lattice exhibits a "Coulomb Phase'' characterized by three emergent gauge fields.

Optical Manipulation and Detection of Emergent Phenomena in Topological Insulators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gedik, Nuh

The three-dimensional topological insulator (TI) is a new quantum phase of matter that exhibits quantum-Hall-like properties, even in the absence of an external magnetic field. These materials are insulators in the bulk but have a topologically protected conducting state at the surface. Charge carriers on these surface states behave like a two-dimensional gas of massless helical Dirac fermions for which the spin is ideally locked perpendicular to the momentum. The purpose of this project is to probe the unique collective electronic behaviors of topological insulators by developing and using advanced time resolved spectroscopic techniques with state-of-the-art temporal and spatial resolutions.more » The nature of these materials requires development of specialized ultrafast techniques (such as time resolved ARPES that also has spin detection capability, ultrafast electron diffraction that has sub-100 fs time resolution and THz magneto-spectroscopy). The focus of this report is to detail our achievements in terms of establishing state of the art experimental facilities. Below, we will describe achievements under this award for the entire duration of five years. We will focus on detailing the development of ultrafast technqiues here. The details of the science that was done with these technqiues can be found in the publications referencing this grant.« less

Topologies on quantum topoi induced by quantization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nakayama, Kunji

2013-07-15

In the present paper, we consider effects of quantization in a topos approach of quantum theory. A quantum system is assumed to be coded in a quantum topos, by which we mean the topos of presheaves on the context category of commutative subalgebras of a von Neumann algebra of bounded operators on a Hilbert space. A classical system is modeled by a Lie algebra of classical observables. It is shown that a quantization map from the classical observables to self-adjoint operators on the Hilbert space naturally induces geometric morphisms from presheaf topoi related to the classical system to the quantummore » topos. By means of the geometric morphisms, we give Lawvere-Tierney topologies on the quantum topos (and their equivalent Grothendieck topologies on the context category). We show that, among them, there exists a canonical one which we call a quantization topology. We furthermore give an explicit expression of a sheafification functor associated with the quantization topology.« less

Gapless Andreev bound states in the quantum spin Hall insulator HgTe.

PubMed

Bocquillon, Erwann; Deacon, Russell S; Wiedenmann, Jonas; Leubner, Philipp; Klapwijk, Teunis M; Brüne, Christoph; Ishibashi, Koji; Buhmann, Hartmut; Molenkamp, Laurens W

2017-02-01

In recent years, Majorana physics has attracted considerable attention because of exotic new phenomena and its prospects for fault-tolerant topological quantum computation. To this end, one needs to engineer the interplay between superconductivity and electronic properties in a topological insulator, but experimental work remains scarce and ambiguous. Here, we report experimental evidence for topological superconductivity induced in a HgTe quantum well, a 2D topological insulator that exhibits the quantum spin Hall (QSH) effect. The a.c. Josephson effect demonstrates that the supercurrent has a 4π periodicity in the superconducting phase difference, as indicated by a doubling of the voltage step for multiple Shapiro steps. In addition, this response like that of a superconducting quantum interference device to a perpendicular magnetic field shows that the 4π-periodic supercurrent originates from states located on the edges of the junction. Both features appear strongest towards the QSH regime, and thus provide evidence for induced topological superconductivity in the QSH edge states.

Exploring 4D quantum Hall physics with a 2D topological charge pump

NASA Astrophysics Data System (ADS)

Lohse, Michael; Schweizer, Christian; Price, Hannah M.; Zilberberg, Oded; Bloch, Immanuel

2018-01-01

The discovery of topological states of matter has greatly improved our understanding of phase transitions in physical systems. Instead of being described by local order parameters, topological phases are described by global topological invariants and are therefore robust against perturbations. A prominent example is the two-dimensional (2D) integer quantum Hall effect: it is characterized by the first Chern number, which manifests in the quantized Hall response that is induced by an external electric field. Generalizing the quantum Hall effect to four-dimensional (4D) systems leads to the appearance of an additional quantized Hall response, but one that is nonlinear and described by a 4D topological invariant—the second Chern number. Here we report the observation of a bulk response with intrinsic 4D topology and demonstrate its quantization by measuring the associated second Chern number. By implementing a 2D topological charge pump using ultracold bosonic atoms in an angled optical superlattice, we realize a dynamical version of the 4D integer quantum Hall effect. Using a small cloud of atoms as a local probe, we fully characterize the nonlinear response of the system via in situ imaging and site-resolved band mapping. Our findings pave the way to experimentally probing higher-dimensional quantum Hall systems, in which additional strongly correlated topological phases, exotic collective excitations and boundary phenomena such as isolated Weyl fermions are predicted.

Exploring 4D quantum Hall physics with a 2D topological charge pump.

PubMed

Lohse, Michael; Schweizer, Christian; Price, Hannah M; Zilberberg, Oded; Bloch, Immanuel

2018-01-03

The discovery of topological states of matter has greatly improved our understanding of phase transitions in physical systems. Instead of being described by local order parameters, topological phases are described by global topological invariants and are therefore robust against perturbations. A prominent example is the two-dimensional (2D) integer quantum Hall effect: it is characterized by the first Chern number, which manifests in the quantized Hall response that is induced by an external electric field. Generalizing the quantum Hall effect to four-dimensional (4D) systems leads to the appearance of an additional quantized Hall response, but one that is nonlinear and described by a 4D topological invariant-the second Chern number. Here we report the observation of a bulk response with intrinsic 4D topology and demonstrate its quantization by measuring the associated second Chern number. By implementing a 2D topological charge pump using ultracold bosonic atoms in an angled optical superlattice, we realize a dynamical version of the 4D integer quantum Hall effect. Using a small cloud of atoms as a local probe, we fully characterize the nonlinear response of the system via in situ imaging and site-resolved band mapping. Our findings pave the way to experimentally probing higher-dimensional quantum Hall systems, in which additional strongly correlated topological phases, exotic collective excitations and boundary phenomena such as isolated Weyl fermions are predicted.

3D Quantum Hall Effect of Fermi Arc in Topological Semimetals

NASA Astrophysics Data System (ADS)

Wang, C. M.; Sun, Hai-Peng; Lu, Hai-Zhou; Xie, X. C.

2017-09-01

The quantum Hall effect is usually observed in 2D systems. We show that the Fermi arcs can give rise to a distinctive 3D quantum Hall effect in topological semimetals. Because of the topological constraint, the Fermi arc at a single surface has an open Fermi surface, which cannot host the quantum Hall effect. Via a "wormhole" tunneling assisted by the Weyl nodes, the Fermi arcs at opposite surfaces can form a complete Fermi loop and support the quantum Hall effect. The edge states of the Fermi arcs show a unique 3D distribution, giving an example of (d -2 )-dimensional boundary states. This is distinctly different from the surface-state quantum Hall effect from a single surface of topological insulator. As the Fermi energy sweeps through the Weyl nodes, the sheet Hall conductivity evolves from the 1 /B dependence to quantized plateaus at the Weyl nodes. This behavior can be realized by tuning gate voltages in a slab of topological semimetal, such as the TaAs family, Cd3 As2 , or Na3Bi . This work will be instructive not only for searching transport signatures of the Fermi arcs but also for exploring novel electron gases in other topological phases of matter.

Topological transport in Dirac nodal-line semimetals

NASA Astrophysics Data System (ADS)

Rui, W. B.; Zhao, Y. X.; Schnyder, Andreas P.

2018-04-01

Topological nodal-line semimetals are characterized by one-dimensional Dirac nodal rings that are protected by the combined symmetry of inversion P and time-reversal T . The stability of these Dirac rings is guaranteed by a quantized ±π Berry phase and their low-energy physics is described by a one-parameter family of (2+1)-dimensional quantum field theories exhibiting the parity anomaly. Here we study the Berry-phase supported topological transport of P T -invariant nodal-line semimetals. We find that small inversion breaking allows for an electric-field-induced anomalous transverse current, whose universal component originates from the parity anomaly. Due to this Hall-like current, carriers at opposite sides of the Dirac nodal ring flow to opposite surfaces when an electric field is applied. To detect the topological currents, we propose a dumbbell device, which uses surface states to filter charges based on their momenta. Suggestions for experiments and device applications are discussed.

Thermalization of topological entropy after a quantum quench

NASA Astrophysics Data System (ADS)

Zeng, Yu; Hamma, Alioscia; Fan, Heng

2016-09-01

Topologically ordered quantum phases are robust in the sense that perturbations in the Hamiltonian of the system will not change the topological nature of the ground-state wave function. However, in order to exploit topological order for applications such as self-correcting quantum memories and information processing, these states need to be also robust both dynamically and at finite temperature in the presence of an environment. It is well known that systems like the toric code in two spatial dimensions are fragile in temperature. In this paper, we show a completely analytic treatment of the toric code away from equilibrium, after a quantum quench of the system Hamiltonian. We show that, despite being subject to unitary evolution (and at zero temperature), the long-time behavior of the topological entropy is thermal, therefore vanishing. If the quench preserves a local gauge structure, there is a residual long-lived topological entropy. This also is the thermal behavior in presence of such gauge constraints. The result is obtained by studying the time evolution of the topological 2-Rényi entropy in a fully analytical, exact way.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Zuocheng; Feng, Xiao; Wang, Jing

The interplay between magnetism and topology, as exemplified in the magnetic skyrmion systems, has emerged as a rich playground for finding novel quantum phenomena and applications in future information technology. Magnetic topological insulators (TI) have attracted much recent attention, especially after the experimental realization of quantum anomalous Hall effect. Future applications of magnetic TI hinge on the accurate manipulation of magnetism and topology by external perturbations, preferably with a gate electric field. In this work, we investigate the magneto transport properties of Cr doped Bi 2(Se xTe 1-x) 3 TI across the topological quantum critical point (QCP). We find thatmore » the external gate voltage has negligible effect on the magnetic order for samples far away from the topological QCP. However, for the sample near the QCP, we observe a ferromagnetic (FM) to paramagnetic (PM) phase transition driven by the gate electric field. Theoretical calculations show that a perpendicular electric field causes a shift of electronic energy levels due to the Stark effect, which induces a topological quantum phase transition and consequently a magnetic phase transition. Finally, the in situ electrical control of the topological and magnetic properties of TI shed important new lights on future topological electronic or spintronic device applications.« less

Non-Hermitian bidirectional robust transport

NASA Astrophysics Data System (ADS)

Longhi, Stefano

2017-01-01

Transport of quantum or classical waves in open systems is known to be strongly affected by non-Hermitian terms that arise from an effective description of system-environment interaction. A simple and paradigmatic example of non-Hermitian transport, originally introduced by Hatano and Nelson two decades ago [N. Hatano and D. R. Nelson, Phys. Rev. Lett. 77, 570 (1996), 10.1103/PhysRevLett.77.570], is the hopping dynamics of a quantum particle on a one-dimensional tight-binding lattice in the presence of an imaginary vectorial potential. The imaginary gauge field can prevent Anderson localization via non-Hermitian delocalization, opening up a mobility region and realizing robust transport immune to disorder and backscattering. Like for robust transport of topologically protected edge states in quantum Hall and topological insulator systems, non-Hermitian robust transport in the Hatano-Nelson model is unidirectional. However, there is not any physical impediment to observe robust bidirectional non-Hermitian transport. Here it is shown that in a quasi-one-dimensional zigzag lattice, with non-Hermitian (imaginary) hopping amplitudes and a synthetic gauge field, robust transport immune to backscattering can occur bidirectionally along the lattice.

Two-dimensional topological insulators with large bulk energy gap

NASA Astrophysics Data System (ADS)

Yang, Z. Q.; Jia, Jin-Feng; Qian, Dong

2016-11-01

Two-dimensional (2D) topological insulators (TIs, or quantum spin Hall insulators) are special insulators that possess bulk 2D electronic energy gap and time-reversal symmetry protected one-dimensional (1D) edge state. Carriers in the edge state have the property of spin-momentum locking, enabling dissipation-free conduction along the 1D edge. The existence of 2D TIs was confirmed by experiments in semiconductor quantum wells. However, the 2D bulk gaps in those quantum wells are extremely small, greatly limiting potential application in future electronics and spintronics. Despite this limitation, 2D TIs with a large bulk gap attracted plenty of interest. In this paper, recent progress in searching for TIs with a large bulk gap is reviewed briefly. We start by introducing some theoretical predictions of these new materials and then discuss some recent important achievements in crystal growth and characterization. Project supported by the National Natural Science Foundation of China (Grant Nos. U1632272, 11574201, and 11521404). D. Q. acknowledges support from the Changjiang Scholars Program, China and the Program for Professor of Special Appointment (Eastern Scholar), China.

Photoinduced topological phase transition and spin polarization in a two-dimensional topological insulator

NASA Astrophysics Data System (ADS)

Chen, M. N.; Su, W.; Deng, M. X.; Ruan, Jiawei; Luo, W.; Shao, D. X.; Sheng, L.; Xing, D. Y.

2016-11-01

A great deal of attention has been paid to the topological phases engineered by photonics over the past few years. Here, we propose a topological quantum phase transition to a quantum anomalous Hall (QAH) phase induced by off-resonant circularly polarized light in a two-dimensional system that is initially in a quantum spin Hall phase or a trivial insulator phase. This provides an alternative method to realize the QAH effect, other than magnetic doping. The circularly polarized light effectively creates a Zeeman exchange field and a renormalized Dirac mass, which are tunable by varying the intensity of the light and drive the quantum phase transition. Both the transverse and longitudinal Hall conductivities are studied, and the former is consistent with the topological phase transition when the Fermi level lies in the band gap. A highly controllable spin-polarized longitudinal electrical current can be generated when the Fermi level is in the conduction band, which may be useful for designing topological spintronics.

Tunable Acoustic Valley-Hall Edge States in Reconfigurable Phononic Elastic Waveguides

NASA Astrophysics Data System (ADS)

Liu, Ting-Wei; Semperlotti, Fabio

2018-01-01

We investigate the occurrence of acoustic topological edge states in a 2D phononic elastic waveguide due to a phenomenon that is the acoustic analog of the quantum valley Hall effect. We show that a topological transition takes place between two lattices having broken space-inversion symmetry due to the application of a tunable strain field. This condition leads to the formation of gapless edge states at the domain walls, as further illustrated by the analysis of the bulk-edge correspondence and of the associated topological invariants. Interestingly, topological edge states can also be triggered at the boundary of a single domain, when boundary conditions are properly selected. We also show that the static modulation of the strain field allows us to tune the response of the material between the different supported edge states. Although time-reversal symmetry is still intact in this material system, the edge states are topologically protected when intervalley mixing is either weak or negligible. This characteristic enables selective valley injection, which is achieved via synchronized source strategy.

Real-space mapping of topological invariants using artificial neural networks

NASA Astrophysics Data System (ADS)

Carvalho, D.; García-Martínez, N. A.; Lado, J. L.; Fernández-Rossier, J.

2018-03-01

Topological invariants allow one to characterize Hamiltonians, predicting the existence of topologically protected in-gap modes. Those invariants can be computed by tracing the evolution of the occupied wave functions under twisted boundary conditions. However, those procedures do not allow one to calculate a topological invariant by evaluating the system locally, and thus require information about the wave functions in the whole system. Here we show that artificial neural networks can be trained to identify the topological order by evaluating a local projection of the density matrix. We demonstrate this for two different models, a one-dimensional topological superconductor and a two-dimensional quantum anomalous Hall state, both with spatially modulated parameters. Our neural network correctly identifies the different topological domains in real space, predicting the location of in-gap states. By combining a neural network with a calculation of the electronic states that uses the kernel polynomial method, we show that the local evaluation of the invariant can be carried out by evaluating a local quantity, in particular for systems without translational symmetry consisting of tens of thousands of atoms. Our results show that supervised learning is an efficient methodology to characterize the local topology of a system.

Emergent functions of quantum materials

NASA Astrophysics Data System (ADS)

Tokura, Yoshinori; Kawasaki, Masashi; Nagaosa, Naoto

2017-11-01

Materials can harbour quantum many-body systems, most typically in the form of strongly correlated electrons in solids, that lead to novel and remarkable functions thanks to emergence--collective behaviours that arise from strong interactions among the elements. These include the Mott transition, high-temperature superconductivity, topological superconductivity, colossal magnetoresistance, giant magnetoelectric effect, and topological insulators. These phenomena will probably be crucial for developing the next-generation quantum technologies that will meet the urgent technological demands for achieving a sustainable and safe society. Dissipationless electronics using topological currents and quantum spins, energy harvesting such as photovoltaics and thermoelectrics, and secure quantum computing and communication are the three major fields of applications working towards this goal. Here, we review the basic principles and the current status of the emergent phenomena and functions in materials from the viewpoint of strong correlation and topology.

Quantum oscillation evidence for a topological semimetal phase in ZrSnTe

NASA Astrophysics Data System (ADS)

Hu, Jin; Zhu, Yanglin; Gui, Xin; Graf, David; Tang, Zhijie; Xie, Weiwei; Mao, Zhiqiang

2018-04-01

The layered WHM-type (W =Zr /Hf /La , H =Si /Ge /Sn /Sb , M =S /Se /Te ) materials represent a large family of topological semimetals, which provides an excellent platform to study the evolution of topological semimetal state with the fine tuning of spin-orbit coupling and structural dimensionality for various combinations of W , H , and M elements. In this work, through high field de Haas-van Alphen (dHvA) quantum oscillation studies, we have found evidence for the predicted topological nontrivial bands in ZrSnTe. Furthermore, from the angular dependence of quantum oscillation frequency, we have revealed the three-dimensional Fermi surface topologies of this layered material owing to strong interlayer coupling.

Revealing topological Dirac fermions at the surface of strained HgTe thin films via quantum Hall transport spectroscopy

NASA Astrophysics Data System (ADS)

Thomas, C.; Crauste, O.; Haas, B.; Jouneau, P.-H.; Bäuerle, C.; Lévy, L. P.; Orignac, E.; Carpentier, D.; Ballet, P.; Meunier, T.

2017-12-01

We demonstrate evidences of electronic transport via topological Dirac surface states in a thin film of strained HgTe. At high perpendicular magnetic fields, we show that the electron transport reaches the quantum Hall regime with vanishing resistance. Furthermore, quantum Hall transport spectroscopy reveals energy splittings of relativistic Landau levels specific to coupled Dirac surface states. This study provides insights in the quantum Hall effect of topological insulator (TI) slabs, in the crossover regime between two- and three-dimensional TIs, and in the relevance of thin TI films to explore circuit functionalities in spintronics and quantum nanoelectronics.

Observation of a well-defined hybridization gap and in-gap states on the SmB6 (001) surface

NASA Astrophysics Data System (ADS)

Sun, Zhixiang; Maldonado, Ana; Paz, Wendel S.; Inosov, Dmytro S.; Schnyder, Andreas P.; Palacios, J. J.; Shitsevalova, Natalya Yu.; Filipov, Vladimir B.; Wahl, Peter

2018-06-01

The rise of topology in condensed-matter physics has generated strong interest in identifying novel quantum materials in which topological protection is driven by electronic correlations. Samarium hexaboride is a Kondo insulator for which it has been proposed that a band inversion between 5 d and 4 f bands gives rise to topologically protected surface states. However, unambiguous proof of the existence and topological nature of these surface states is still missing, and its low-energy electronic structure is still not fully established. Here we present a study of samarium hexaboride by ultralow-temperature scanning tunneling microscopy and spectroscopy. We obtain clear atomically resolved topographic images of the sample surface. Our tunneling spectra reveal signatures of a hybridization gap with a size of about 8 meV and with a reduction of the differential conductance inside the gap by almost half, and surprisingly, several strong resonances below the Fermi level. The spatial variations of the energy of the resonances point toward a microscopic variation of the electronic states by the different surface terminations. High-resolution tunneling spectra acquired at 100 mK reveal a splitting of the Kondo resonance, possibly due to the crystal electric field.

Quantum phase transitions driven by rhombic-type single-ion anisotropy in the S =1 Haldane chain

NASA Astrophysics Data System (ADS)

Tzeng, Yu-Chin; Onishi, Hiroaki; Okubo, Tsuyoshi; Kao, Ying-Jer

2017-08-01

The spin-1 Haldane chain is an example of the symmetry-protected-topological (SPT) phase in one dimension. Experimental realization of the spin chain materials usually involves both the uniaxial-type, D (Sz)2 , and the rhombic-type, E [(Sx)2-(Sy)2] , single-ion anisotropies. Here, we provide a precise ground-state phase diagram for a spin-1 Haldane chain with these single-ion anisotropies. Using quantum numbers, we find that the Z2 symmetry breaking phase can be characterized by double degeneracy in the entanglement spectrum. Topological quantum phase transitions take place on particular paths in the phase diagram, from the Haldane phase to the large-Ex, large-Ey, or large-D phases. The topological critical points are determined by the level spectroscopy method with a newly developed parity technique in the density matrix renormalization group [Phys. Rev. B 86, 024403 (2012), 10.1103/PhysRevB.86.024403], and the Haldane-large-D critical point is obtained with an unprecedented precision, (D/J ) c=0.9684713 (1 ) . Close to this critical point, a small rhombic single-ion anisotropy |E |/J ≪1 can destroy the Haldane phase and bring the system into a y -Néel phase. We propose that the compound [Ni (HF2) (3-Clpy ) 4] BF4 is a candidate system to search for the y -Néel phase.

Interface engineering of quantum Hall effects in digital transition metal oxide heterostructures.

PubMed

Xiao, Di; Zhu, Wenguang; Ran, Ying; Nagaosa, Naoto; Okamoto, Satoshi

2011-12-20

Topological insulators are characterized by a non-trivial band topology driven by the spin-orbit coupling. To fully explore the fundamental science and application of topological insulators, material realization is indispensable. Here we predict, based on tight-binding modelling and first-principles calculations, that bilayers of perovskite-type transition-metal oxides grown along the [111] crystallographic axis are potential candidates for two-dimensional topological insulators. The topological band structure of these materials can be fine-tuned by changing dopant ions, substrates and external gate voltages. We predict that LaAuO(3) bilayers have a topologically non-trivial energy gap of about 0.15 eV, which is sufficiently large to realize the quantum spin Hall effect at room temperature. Intriguing phenomena, such as fractional quantum Hall effect, associated with the nearly flat topologically non-trivial bands found in e(g) systems are also discussed.

Quantization of geometric phase with integer and fractional topological characterization in a quantum Ising chain with long-range interaction.

PubMed

Sarkar, Sujit

2018-04-12

An attempt is made to study and understand the behavior of quantization of geometric phase of a quantum Ising chain with long range interaction. We show the existence of integer and fractional topological characterization for this model Hamiltonian with different quantization condition and also the different quantized value of geometric phase. The quantum critical lines behave differently from the perspective of topological characterization. The results of duality and its relation to the topological quantization is presented here. The symmetry study for this model Hamiltonian is also presented. Our results indicate that the Zak phase is not the proper physical parameter to describe the topological characterization of system with long range interaction. We also present quite a few exact solutions with physical explanation. Finally we present the relation between duality, symmetry and topological characterization. Our work provides a new perspective on topological quantization.

Quantum phase transition between cluster and antiferromagnetic states

NASA Astrophysics Data System (ADS)

Son, W.; Amico, L.; Fazio, R.; Hamma, A.; Pascazio, S.; Vedral, V.

2011-09-01

We study a Hamiltonian system describing a three-spin-1/2 cluster-like interaction competing with an Ising-like exchange. We show that the ground state in the cluster phase possesses symmetry protected topological order. A continuous quantum phase transition occurs as result of the competition between the cluster and Ising terms. At the critical point the Hamiltonian is self-dual. The geometric entanglement is also studied and used to investigate the quantum phase transition. Our findings in one dimension corroborate the analysis of the two-dimensional generalization of the system, indicating, at a mean-field level, the presence of a direct transition between an antiferromagnetic and a valence bond solid ground state.

Topology versus Anderson localization: Nonperturbative solutions in one dimension

NASA Astrophysics Data System (ADS)

Altland, Alexander; Bagrets, Dmitry; Kamenev, Alex

2015-02-01

We present an analytic theory of quantum criticality in quasi-one-dimensional topological Anderson insulators. We describe these systems in terms of two parameters (g ,χ ) representing localization and topological properties, respectively. Certain critical values of χ (half-integer for Z classes, or zero for Z2 classes) define phase boundaries between distinct topological sectors. Upon increasing system size, the two parameters exhibit flow similar to the celebrated two-parameter flow of the integer quantum Hall insulator. However, unlike the quantum Hall system, an exact analytical description of the entire phase diagram can be given in terms of the transfer-matrix solution of corresponding supersymmetric nonlinear sigma models. In Z2 classes we uncover a hidden supersymmetry, present at the quantum critical point.

Two-spectral Yang-Baxter operators in topological quantum computation

NASA Astrophysics Data System (ADS)

Sanchez, William F.

2011-05-01

One of the current trends in quantum computing is the application of algebraic topological methods in the design of new algorithms and quantum computers, giving rise to topological quantum computing. One of the tools used in it is the Yang-Baxter equation whose solutions are interpreted as universal quantum gates. Lately, more general Yang-Baxter equations have been investigated, making progress as two-spectral equations and Yang-Baxter systems. This paper intends to apply these new findings to the field of topological quantum computation, more specifically, the proposition of the two-spectral Yang-Baxter operators as universal quantum gates for 2 qubits and 2 qutrits systems, obtaining 4x4 and 9x9 matrices respectively, and further elaboration of the corresponding Hamiltonian by the use of computer algebra software Mathematica® and its Qucalc package. In addition, possible physical systems to which the Yang-Baxter operators obtained can be applied are considered. In the present work it is demonstrated the utility of the Yang-Baxter equation to generate universal quantum gates and the power of computer algebra to design them; it is expected that these mathematical studies contribute to the further development of quantum computers

Quantum anomalous Hall Majorana platform

NASA Astrophysics Data System (ADS)

Zeng, Yongxin; Lei, Chao; Chaudhary, Gaurav; MacDonald, Allan H.

2018-02-01

We show that quasi-one-dimensional quantum wires can be written onto the surface of magnetic topological insulator (MTI) thin films by gate arrays. When the MTI is in a quantum anomalous Hall state, MTI/superconductor quantum wires have especially broad stability regions for both topological and nontopological states, facilitating creation and manipulation of Majorana particles on the MTI surface.

Transport properties of Dirac fermions in two dimensions

NASA Astrophysics Data System (ADS)

DaSilva, Ashley M.

The Dirac equation in particle physics is used to describe spin 1/2 fermions (such as electrons) moving at relativistic speeds. In condensed matter physics, this is usually not relevant, since particles in matter move slowly compared to the speed of light. However, recent progress has revealed two-dimensional realizations of Dirac fermions in condensed matter systems with zero mass and a redefined "speed of light." One of these systems, graphene, has been studied theoretically for decades as a building block of graphite. The other, the topological insulator, is quite new; this state of matter was predicted less than 10 years ago. Graphene was first isolated in 2004, and since then there has been an explosion of graphene research in the physics community. Much of the recent excitement has to do with the potential applications of graphene in devices. In this dissertation, I will discuss two problems related to graphene devices, and in particular how to use the strong interaction of graphene with its surroundings as an asset. I will show that a Boltzmann transport theory with all scattering mechanisms describes the current vs voltage of a graphene sheet extremely well using no adjustable parameters. One crucial element of this model is the transfer of energy from electrons directly to the substrate via scattering with optical phonons at the interface. The interaction is due to an electric field that is set up by these optical phonons, which is so strongly interacting in part due to the two dimensionality of the graphene. I will also discuss the adsorption of He atoms on a graphene sheet. This causes a change in the graphene conductivity which is large enough to be measurable. Work in this direction could provide a route to graphene sensors. The topological insulator is a recently predicted state of matter which is nominally an insulator but has metallic surface states which are topologically protected. This topological protection arises from the symmetry of the system, which requires a two-fold degeneracy at any time reversal symmetric momentum, and a band inversion, which provides a swapping of the conduction and valance band at a surface. These two conditions imply that an odd number of states will cross the gap even in the presence of disorder (as long as that disorder is time reversal symmetric). This manifests as a Dirac cone at the surface of insulators such as Bi2Se3 and Bi2Te 3. To be a true topological insulator, one must have a bulk insulator; experimentally however, most samples are bulk conductors. While rapid improvement is being made through techniques such as doping, one of the goals of the research presented in this thesis is to work towards a transport signal which is unique to the surface state even in the presence of a conducting bulk. In this direction, quantum corrections to the magnetoresistance have been shown to fail, as both bulk and surface have similar experimental signals. However work in this dissertation shows that we can still gain some insight by modeling the experimental data with the theory of quantum corrections. I will show evidence that electron-electron interactions are necessary to understand the low temperature conductivity of Bi2Se3 thin films. One unambiguous transport signal is the quantum Hall response; the energy of Dirac fermions in a strong magnetic field is quite different than their parabolic counterparts. Given this, a question that arises is the nature of the fractional quantum Hall effect in topological insulator surface states. I will predict the conditions under which the fractional quantum Hall effect is stable. Finally, one of the reasons topological insulators have gained so much enthusiasm is the potential application to topological quantum computation. This may be made possible if the theoretical predictions of particles called Majorana fermions could be realized experimentally. I discuss evidence that two necessary (although not sufficient) conditions are met: topological insulators can be made superconducting and there is evidence for the formation of vortices in such superconducting topological insulators.

Robust interface between flying and topological qubits

PubMed Central

Xue, Zheng-Yuan; Gong, Ming; Liu, Jia; Hu, Yong; Zhu, Shi-Liang; Wang, Z. D.

2015-01-01

Hybrid architectures, consisting of conventional and topological qubits, have recently attracted much attention due to their capability in consolidating robustness of topological qubits and universality of conventional qubits. However, these two kinds of qubits are normally constructed in significantly different energy scales, and thus the energy mismatch is a major obstacle for their coupling, which can support the exchange of quantum information between them. Here we propose a microwave photonic quantum bus for a strong direct coupling between the topological and conventional qubits, where the energy mismatch is compensated by an external driving field. In the framework of tight-binding simulation and perturbation approach, we show that the energy splitting of Majorana fermions in a finite length nanowire, which we use to define topological qubits, is still robust against local perturbations due to the topology of the system. Therefore, the present scheme realizes a rather robust interface between the flying and topological qubits. Finally, we demonstrate that this quantum bus can also be used to generate multipartitie entangled states with the topological qubits. PMID:26216201

Surface field theories of point group symmetry protected topological phases

NASA Astrophysics Data System (ADS)

Huang, Sheng-Jie; Hermele, Michael

2018-02-01

We identify field theories that describe the surfaces of three-dimensional bosonic point group symmetry protected topological (pgSPT) phases. The anomalous nature of the surface field theories is revealed via a dimensional reduction argument. Specifically, we study three different surface field theories. The first field theory is quantum electrodynamics in three space-time dimensions (QED3) with four flavors of fermions. We show this theory can describe the surfaces of a majority of bosonic pgSPT phases protected by a single mirror reflection, or by Cn v point group symmetry for n =2 ,3 ,4 ,6 . The second field theory is a variant of QED3 with charge-1 and charge-3 Dirac fermions. This field theory can describe the surface of a reflection symmetric pgSPT phase built by placing an E8 state on the mirror plane. The third field theory is an O (4 ) nonlinear sigma model with a topological theta term at θ =π , or, equivalently, a noncompact CP1 model. Using a coupled wire construction, we show this is a surface theory for bosonic pgSPT phases with U (1 ) ×Z2P symmetry. For the latter two field theories, we discuss the connection to gapped surfaces with topological order. Moreover, we conjecture that the latter two field theories can describe surfaces of more general bosonic pgSPT phases with Cn v point group symmetry.

Optical Radiation from Integer Quantum Hall States in Dirac Materials

NASA Astrophysics Data System (ADS)

Gullans, Michael; Taylor, Jacob; Ghaemi, Pouyan; Hafezi, Mohammad

Quantum Hall systems exhibit topologically protected edge states, which can have a macroscopic spatial extent. Such edge states provide a unique opportunity to study a quantum emitter whose size far exceeds the wavelength of emitted light. To better understand this limit, we theoretically characterize the optical radiation from integer quantum Hall states in two-dimensional Dirac materials. We show that the scattered light from the bulk reflects the spatial profile of the wavefunctions, enabling spatial imaging of the disorder landscape. We find that the radiation from the edge states are characterized by the presence of large multipole moments in the far-field. This multipole radiation arises from the transfer of angular momentum from the electrons into the scattered light, enabling the generation of coherent light with high orbital angular momentum.

Bending strain engineering in quantum spin hall system for controlling spin currents

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huang, Bing; Jin, Kyung-Hwan; Cui, Bin

Quantum spin Hall system can exhibit exotic spin transport phenomena, mediated by its topological edge states. The concept of bending strain engineering to tune the spin transport properties of a quantum spin Hall system is demonstrated. Here, we show that bending strain can be used to control the spin orientation of counter-propagating edge states of a quantum spin system to generate a non-zero spin current. This physics mechanism can be applied to effectively tune the spin current and pure spin current decoupled from charge current in a quantum spin Hall system by control of its bending curvature. Moreover, the curvedmore » quantum spin Hall system can be achieved by the concept of topological nanomechanical architecture in a controllable way, as demonstrated by the material example of Bi/Cl/Si(111) nanofilm. This concept of bending strain engineering of spins via topological nanomechanical architecture affords a promising route towards the realization of topological nano-mechanospintronics.« less

Bending strain engineering in quantum spin hall system for controlling spin currents

DOE PAGES

Huang, Bing; Jin, Kyung-Hwan; Cui, Bin; ...

2017-06-16

Quantum spin Hall system can exhibit exotic spin transport phenomena, mediated by its topological edge states. The concept of bending strain engineering to tune the spin transport properties of a quantum spin Hall system is demonstrated. Here, we show that bending strain can be used to control the spin orientation of counter-propagating edge states of a quantum spin system to generate a non-zero spin current. This physics mechanism can be applied to effectively tune the spin current and pure spin current decoupled from charge current in a quantum spin Hall system by control of its bending curvature. Moreover, the curvedmore » quantum spin Hall system can be achieved by the concept of topological nanomechanical architecture in a controllable way, as demonstrated by the material example of Bi/Cl/Si(111) nanofilm. This concept of bending strain engineering of spins via topological nanomechanical architecture affords a promising route towards the realization of topological nano-mechanospintronics.« less

Towards Holography via Quantum Source-Channel Codes.

PubMed

Pastawski, Fernando; Eisert, Jens; Wilming, Henrik

2017-07-14

While originally motivated by quantum computation, quantum error correction (QEC) is currently providing valuable insights into many-body quantum physics, such as topological phases of matter. Furthermore, mounting evidence originating from holography research (AdS/CFT) indicates that QEC should also be pertinent for conformal field theories. With this motivation in mind, we introduce quantum source-channel codes, which combine features of lossy compression and approximate quantum error correction, both of which are predicted in holography. Through a recent construction for approximate recovery maps, we derive guarantees on its erasure decoding performance from calculations of an entropic quantity called conditional mutual information. As an example, we consider Gibbs states of the transverse field Ising model at criticality and provide evidence that they exhibit nontrivial protection from local erasure. This gives rise to the first concrete interpretation of a bona fide conformal field theory as a quantum error correcting code. We argue that quantum source-channel codes are of independent interest beyond holography.

Towards Holography via Quantum Source-Channel Codes

NASA Astrophysics Data System (ADS)

Pastawski, Fernando; Eisert, Jens; Wilming, Henrik

2017-07-01

While originally motivated by quantum computation, quantum error correction (QEC) is currently providing valuable insights into many-body quantum physics, such as topological phases of matter. Furthermore, mounting evidence originating from holography research (AdS/CFT) indicates that QEC should also be pertinent for conformal field theories. With this motivation in mind, we introduce quantum source-channel codes, which combine features of lossy compression and approximate quantum error correction, both of which are predicted in holography. Through a recent construction for approximate recovery maps, we derive guarantees on its erasure decoding performance from calculations of an entropic quantity called conditional mutual information. As an example, we consider Gibbs states of the transverse field Ising model at criticality and provide evidence that they exhibit nontrivial protection from local erasure. This gives rise to the first concrete interpretation of a bona fide conformal field theory as a quantum error correcting code. We argue that quantum source-channel codes are of independent interest beyond holography.

Topological Quantum Phase Transition in Synthetic Non-Abelian Gauge Potential: Gauge Invariance and Experimental Detections

PubMed Central

Sun, Fadi; Yu, Xiao-Lu; Ye, Jinwu; Fan, Heng; Liu, Wu-Ming

2013-01-01

The method of synthetic gauge potentials opens up a new avenue for our understanding and discovering novel quantum states of matter. We investigate the topological quantum phase transition of Fermi gases trapped in a honeycomb lattice in the presence of a synthetic non-Abelian gauge potential. We develop a systematic fermionic effective field theory to describe a topological quantum phase transition tuned by the non-Abelian gauge potential and explore its various important experimental consequences. Numerical calculations on lattice scales are performed to compare with the results achieved by the fermionic effective field theory. Several possible experimental detection methods of topological quantum phase transition are proposed. In contrast to condensed matter experiments where only gauge invariant quantities can be measured, both gauge invariant and non-gauge invariant quantities can be measured by experimentally generating various non-Abelian gauges corresponding to the same set of Wilson loops. PMID:23846153

Quantum transport of two-species Dirac fermions in dual-gated three-dimensional topological insulators

DOE PAGES

Xu, Yang; Miotkowski, Ireneusz; Chen, Yong P.

2016-05-04

Topological insulators are a novel class of quantum matter with a gapped insulating bulk, yet gapless spin-helical Dirac fermion conducting surface states. Here, we report local and non-local electrical and magneto transport measurements in dual-gated BiSbTeSe 2 thin film topological insulator devices, with conduction dominated by the spatially separated top and bottom surfaces, each hosting a single species of Dirac fermions with independent gate control over the carrier type and density. We observe many intriguing quantum transport phenomena in such a fully tunable two-species topological Dirac gas, including a zero-magnetic-field minimum conductivity close to twice the conductance quantum at themore » double Dirac point, a series of ambipolar two-component half-integer Dirac quantum Hall states and an electron-hole total filling factor zero state (with a zero-Hall plateau), exhibiting dissipationless (chiral) and dissipative (non-chiral) edge conduction, respectively. As a result, such a system paves the way to explore rich physics, ranging from topological magnetoelectric effects to exciton condensation.« less

Physics of Majorana modes in interacting helical liquid.

PubMed

Sarkar, Sujit

2016-07-27

As an attempt to understand and search for the existence of Majorana zero mode, we study the topological quantum phase transition and also the nature of this transition in helical liquid system, which appears in different physical systems. We present Majorana-Ising transition along with the phase boundary in the presence of interaction. We show the appearance of Majorana mode under the renormalization of the parameters of the system and also the topological protection of it. We present the length scale dependent condition for the appearance of Majorana edge state and also the absence of edge state for a certain regime of parameter space.

Quantum error suppression with commuting Hamiltonians: two local is too local.

PubMed

Marvian, Iman; Lidar, Daniel A

2014-12-31

We consider error suppression schemes in which quantum information is encoded into the ground subspace of a Hamiltonian comprising a sum of commuting terms. Since such Hamiltonians are gapped, they are considered natural candidates for protection of quantum information and topological or adiabatic quantum computation. However, we prove that they cannot be used to this end in the two-local case. By making the favorable assumption that the gap is infinite, we show that single-site perturbations can generate a degeneracy splitting in the ground subspace of this type of Hamiltonian which is of the same order as the magnitude of the perturbation, and is independent of the number of interacting sites and their Hilbert space dimensions, just as in the absence of the protecting Hamiltonian. This splitting results in decoherence of the ground subspace, and we demonstrate that for natural noise models the coherence time is proportional to the inverse of the degeneracy splitting. Our proof involves a new version of the no-hiding theorem which shows that quantum information cannot be approximately hidden in the correlations between two quantum systems. The main reason that two-local commuting Hamiltonians cannot be used for quantum error suppression is that their ground subspaces have only short-range (two-body) entanglement.

Geometry, topology, and response in condensed matter systems

NASA Astrophysics Data System (ADS)

Varjas, Daniel

Topological order provides a new paradigm to view phases of matter. Unlike conventional symmetry breaking order, these states are not distinguished by different patterns of symmetry breaking, instead by their intricate mathematical structure, topology. By the bulk-boundary correspondence, the nontrivial topology of the bulk results in robust gapless excitations on symmetry preserving surfaces. We utilize both of these views to study topological phases together with the analysis of their quantized physical responses to perturbations. First we study the edge excitations of strongly interacting abelian fractional quantum Hall liquids on an infinite strip geometry. We use the infinite density matrix renormalization group method to numerically measure edge exponents in model systems, including subleading orders. Using analytic methods we derive a generalized Luttinger's theorem that relates momenta of edge excitations. Next we consider topological crystalline insulators protected by space group symmetry. After reviewing the general formalism, we present results about the quantization of the magnetoelectric response protected by orientation-reversing space group symmetries. We construct and analyze insulating and superconducting tight-binding models with glide symmetry in three dimensions to illustrate the general result. Following this, we derive constraints on weak indices of three dimensional topological insulators imposed by space group symmetries. We focus on spin-orbit coupled insulators with and without time reversal invariance and consider both symmorphic and nonsymmorphic symmetries. Finally, we calculate the response of metals and generalize the notion of the magnetoelectric effect to noninteracting gapless systems. We use semiclassical dynamics to study the magnetopiezoelectric effect, the current response to elastic strain in static external magnetic fields.

Simulating a topological transition in a superconducting phase qubit by fast adiabatic trajectories

NASA Astrophysics Data System (ADS)

Wang, Tenghui; Zhang, Zhenxing; Xiang, Liang; Gong, Zhihao; Wu, Jianlan; Yin, Yi

2018-04-01

The significance of topological phases has been widely recognized in the community of condensed matter physics. The well controllable quantum systems provide an artificial platform to probe and engineer various topological phases. The adiabatic trajectory of a quantum state describes the change of the bulk Bloch eigenstates with the momentum, and this adiabatic simulation method is however practically limited due to quantum dissipation. Here we apply the "shortcut to adiabaticity" (STA) protocol to realize fast adiabatic evolutions in the system of a superconducting phase qubit. The resulting fast adiabatic trajectories illustrate the change of the bulk Bloch eigenstates in the Su-Schrieffer-Heeger (SSH) model. A sharp transition is experimentally determined for the topological invariant of a winding number. Our experiment helps identify the topological Chern number of a two-dimensional toy model, suggesting the applicability of the fast adiabatic simulation method for topological systems.

Quantum Field Theory Approach to Condensed Matter Physics

NASA Astrophysics Data System (ADS)

Marino, Eduardo C.

2017-09-01

Preface; Part I. Condensed Matter Physics: 1. Independent electrons and static crystals; 2. Vibrating crystals; 3. Interacting electrons; 4. Interactions in action; Part II. Quantum Field Theory: 5. Functional formulation of quantum field theory; 6. Quantum fields in action; 7. Symmetries: explicit or secret; 8. Classical topological excitations; 9. Quantum topological excitations; 10. Duality, bosonization and generalized statistics; 11. Statistical transmutation; 12. Pseudo quantum electrodynamics; Part III. Quantum Field Theory Approach to Condensed Matter Systems: 13. Quantum field theory methods in condensed matter; 14. Metals, Fermi liquids, Mott and Anderson insulators; 15. The dynamics of polarons; 16. Polyacetylene; 17. The Kondo effect; 18. Quantum magnets in 1D: Fermionization, bosonization, Coulomb gases and 'all that'; 19. Quantum magnets in 2D: nonlinear sigma model, CP1 and 'all that'; 20. The spin-fermion system: a quantum field theory approach; 21. The spin glass; 22. Quantum field theory approach to superfluidity; 23. Quantum field theory approach to superconductivity; 24. The cuprate high-temperature superconductors; 25. The pnictides: iron based superconductors; 26. The quantum Hall effect; 27. Graphene; 28. Silicene and transition metal dichalcogenides; 29. Topological insulators; 30. Non-abelian statistics and quantum computation; References; Index.

Experimental observation of anomalous topological edge modes in a slowly driven photonic lattice

PubMed Central

Mukherjee, Sebabrata; Spracklen, Alexander; Valiente, Manuel; Andersson, Erika; Öhberg, Patrik; Goldman, Nathan; Thomson, Robert R.

2017-01-01

Topological quantum matter can be realized by subjecting engineered systems to time-periodic modulations. In analogy with static systems, periodically driven quantum matter can be topologically classified by topological invariants, whose non-zero value guarantees the presence of robust edge modes. In the high-frequency limit of the drive, topology is described by standard topological invariants, such as Chern numbers. Away from this limit, these topological numbers become irrelevant, and novel topological invariants must be introduced to capture topological edge transport. The corresponding edge modes were coined anomalous topological edge modes, to highlight their intriguing origin. Here we demonstrate the experimental observation of these topological edge modes in a 2D photonic lattice, where these propagating edge states are shown to coexist with a quasi-localized bulk. Our work opens an exciting route for the exploration of topological physics in time-modulated systems operating away from the high-frequency regime. PMID:28051060

Quantum glassiness in clean strongly correlated systems: an example of topological overprotection

NASA Astrophysics Data System (ADS)

Chamon, Claudio

2005-03-01

Describing matter at near absolute zero temperature requires understanding a system's quantum ground state and the low energy excitations around it, the quasiparticles, which are thermally populated by the system's contact to a heat bath. However, this paradigm breaks down if thermal equilibration is obstructed. I present solvable examples of quantum many-body Hamiltonians of systems that are unable to reach their ground states as the environment temperature is lowered to absolute zero. These examples, three dimensional generalizations of quantum Hamiltonians proposed for topological quantum computing, 1) have no quenched disorder, 2) have solely local interactions, 3) have an exactly solvable spectrum, 4) have topologically ordered ground states, and 5) have slow dynamical relaxation rates akin to those of strong structural glasses.

Dissolution of topological Fermi arcs in a dirty Weyl semimetal

NASA Astrophysics Data System (ADS)

Slager, Robert-Jan; Juričić, Vladimir; Roy, Bitan

2017-11-01

Weyl semimetals (WSMs) have recently attracted a great deal of attention as they provide a condensed matter realization of chiral anomaly, feature topologically protected Fermi arc surface states, and sustain sharp chiral Weyl quasiparticles up to a critical disorder at which a continuous quantum phase transition (QPT) drives the system into a metallic phase. We here numerically demonstrate that with increasing strength of disorder, the Fermi arc gradually loses its sharpness, and close to the WSM-metal QPT it completely dissolves into the metallic bath of the bulk. The predicted topological nature of the WSM-metal QPT and the resulting bulk-boundary correspondence across this transition can be directly observed in angle-resolved photoemission spectroscopy (ARPES) and Fourier transformed scanning tunneling microscopy (STM) measurements by following the continuous deformation of the Fermi arcs with increasing disorder in recently discovered Weyl materials.

Towards scalable quantum communication and computation: Novel approaches and realizations

NASA Astrophysics Data System (ADS)

Jiang, Liang

Quantum information science involves exploration of fundamental laws of quantum mechanics for information processing tasks. This thesis presents several new approaches towards scalable quantum information processing. First, we consider a hybrid approach to scalable quantum computation, based on an optically connected network of few-qubit quantum registers. Specifically, we develop a novel scheme for scalable quantum computation that is robust against various imperfections. To justify that nitrogen-vacancy (NV) color centers in diamond can be a promising realization of the few-qubit quantum register, we show how to isolate a few proximal nuclear spins from the rest of the environment and use them for the quantum register. We also demonstrate experimentally that the nuclear spin coherence is only weakly perturbed under optical illumination, which allows us to implement quantum logical operations that use the nuclear spins to assist the repetitive-readout of the electronic spin. Using this technique, we demonstrate more than two-fold improvement in signal-to-noise ratio. Apart from direct application to enhance the sensitivity of the NV-based nano-magnetometer, this experiment represents an important step towards the realization of robust quantum information processors using electronic and nuclear spin qubits. We then study realizations of quantum repeaters for long distance quantum communication. Specifically, we develop an efficient scheme for quantum repeaters based on atomic ensembles. We use dynamic programming to optimize various quantum repeater protocols. In addition, we propose a new protocol of quantum repeater with encoding, which efficiently uses local resources (about 100 qubits) to identify and correct errors, to achieve fast one-way quantum communication over long distances. Finally, we explore quantum systems with topological order. Such systems can exhibit remarkable phenomena such as quasiparticles with anyonic statistics and have been proposed as candidates for naturally error-free quantum computation. We propose a scheme to unambiguously detect the anyonic statistics in spin lattice realizations using ultra-cold atoms in an optical lattice. We show how to reliably read and write topologically protected quantum memory using an atomic or photonic qubit.

Fermionic topological quantum states as tensor networks

NASA Astrophysics Data System (ADS)

Wille, C.; Buerschaper, O.; Eisert, J.

2017-06-01

Tensor network states, and in particular projected entangled pair states, play an important role in the description of strongly correlated quantum lattice systems. They do not only serve as variational states in numerical simulation methods, but also provide a framework for classifying phases of quantum matter and capture notions of topological order in a stringent and rigorous language. The rapid development in this field for spin models and bosonic systems has not yet been mirrored by an analogous development for fermionic models. In this work, we introduce a tensor network formalism capable of capturing notions of topological order for quantum systems with fermionic components. At the heart of the formalism are axioms of fermionic matrix-product operator injectivity, stable under concatenation. Building upon that, we formulate a Grassmann number tensor network ansatz for the ground state of fermionic twisted quantum double models. A specific focus is put on the paradigmatic example of the fermionic toric code. This work shows that the program of describing topologically ordered systems using tensor networks carries over to fermionic models.

Proximate Kitaev quantum spin liquid behaviour in a honeycomb magnet

DOE PAGES

Banerjee, A.; Bridges, C. A.; Yan, J. -Q.; ...

2016-04-04

Quantum spin liquids (QSLs) are topological states of matter exhibiting remarkable properties such as the capacity to protect quantum information from decoherence. While their featureless ground states have precluded their straightforward experimental identification, excited states are more revealing and particularly interesting due to the emergence of fundamentally new excitations such as Majorana Fermions. Ideal probes of these excitations are inelastic neutron scattering experiments. We report these here for a ruthenium-based material α-RuCl 3, continuing a major search (so far concentrated on iridium materials inimical to neutron probes) for realizations of the celebrated Kitaev honeycomb topological QSL. Our measurements confirm themore » requisite strong spin-orbit coupling and low-temperature magnetic order matching predictions proximate to the QSL. We find stacking faults, inherent to the highly 2D nature of the material, resolve an outstanding puzzle. Crucially, dynamical response measurements above interlayer energy scales are naturally accounted for in terms of deconfinement physics expected for QSLs. Comparing these with recent dynamical calculations involving gauge flux excitations and Majorana fermions of the pure Kitaev model, we propose the excitation spectrum of α-RuCl 3 as prime candidate for realization of fractionalized Kitaev physics.« less

Excitations in the field-induced quantum spin liquid state of α-RuCl3

NASA Astrophysics Data System (ADS)

Banerjee, Arnab; Lampen-Kelley, Paula; Knolle, Johannes; Balz, Christian; Aczel, Adam Anthony; Winn, Barry; Liu, Yaohua; Pajerowski, Daniel; Yan, Jiaqiang; Bridges, Craig A.; Savici, Andrei T.; Chakoumakos, Bryan C.; Lumsden, Mark D.; Tennant, David Alan; Moessner, Roderich; Mandrus, David G.; Nagler, Stephen E.

2018-03-01

The celebrated Kitaev quantum spin liquid (QSL) is the paradigmatic example of a topological magnet with emergent excitations in the form of Majorana Fermions and gauge fluxes. Upon breaking of time-reversal symmetry, for example in an external magnetic field, these fractionalized quasiparticles acquire non-Abelian exchange statistics, an important ingredient for topologically protected quantum computing. Consequently, there has been enormous interest in exploring possible material realizations of Kitaev physics and several candidate materials have been put forward, recently including α-RuCl3. In the absence of a magnetic field this material orders at a finite temperature and exhibits low-energy spin wave excitations. However, at moderate energies, the spectrum is unconventional and the response shows evidence for fractional excitations. Here we use time-of-flight inelastic neutron scattering to show that the application of a sufficiently large magnetic field in the honeycomb plane suppresses the magnetic order and the spin waves, leaving a gapped continuum spectrum of magnetic excitations. Our comparisons of the scattering to the available calculations for a Kitaev QSL show that they are consistent with the magnetic field induced QSL phase.

Proximate Kitaev quantum spin liquid behaviour in a honeycomb magnet.

PubMed

Banerjee, A; Bridges, C A; Yan, J-Q; Aczel, A A; Li, L; Stone, M B; Granroth, G E; Lumsden, M D; Yiu, Y; Knolle, J; Bhattacharjee, S; Kovrizhin, D L; Moessner, R; Tennant, D A; Mandrus, D G; Nagler, S E

2016-07-01

Quantum spin liquids (QSLs) are topological states of matter exhibiting remarkable properties such as the capacity to protect quantum information from decoherence. Whereas their featureless ground states have precluded their straightforward experimental identification, excited states are more revealing and particularly interesting owing to the emergence of fundamentally new excitations such as Majorana fermions. Ideal probes of these excitations are inelastic neutron scattering experiments. These we report here for a ruthenium-based material, α-RuCl3, continuing a major search (so far concentrated on iridium materials) for realizations of the celebrated Kitaev honeycomb topological QSL. Our measurements confirm the requisite strong spin-orbit coupling and low-temperature magnetic order matching predictions proximate to the QSL. We find stacking faults, inherent to the highly two-dimensional nature of the material, resolve an outstanding puzzle. Crucially, dynamical response measurements above interlayer energy scales are naturally accounted for in terms of deconfinement physics expected for QSLs. Comparing these with recent dynamical calculations involving gauge flux excitations and Majorana fermions of the pure Kitaev model, we propose the excitation spectrum of α-RuCl3 as a prime candidate for fractionalized Kitaev physics.

Excitations in the field-induced quantum spin liquid state of α-RuCl 3

DOE PAGES

Banerjee, Arnab; Kelley, Paula J.; Knolle, Johannes; ...

2018-02-20

The celebrated Kitaev quantum spin liquid (QSL) is the paradigmatic example of a topological magnet with emergent excitations in the form of Majorana Fermions and gauge fluxes. Upon breaking of time-reversal symmetry, for example in an external magnetic field, these fractionalized quasiparticles acquire non-Abelian exchange statistics, an important ingredient for topologically protected quantum computing. Consequently, there has been enormous interest in exploring possible material realizations of Kitaev physics and several candidate materials have been put forward, recently including α-RuCl 3. In the absence of a magnetic field this material orders at a finite temperature and exhibits low-energy spin wave excitations.more » However, at moderate energies, the spectrum is unconventional and the response shows evidence for fractional excitations. Here in this paper, we use time-of-flight inelastic neutron scattering to show that the application of a sufficiently large magnetic field in the honeycomb plane suppresses the magnetic order and the spin waves, leaving a gapped continuum spectrum of magnetic excitations. Our comparisons of the scattering to the available calculations for a Kitaev QSL show that they are consistent with the magnetic field induced QSL phase.« less

Excitations in the field-induced quantum spin liquid state of α-RuCl 3

DOE Office of Scientific and Technical Information (OSTI.GOV)

Banerjee, Arnab; Kelley, Paula J.; Knolle, Johannes

The celebrated Kitaev quantum spin liquid (QSL) is the paradigmatic example of a topological magnet with emergent excitations in the form of Majorana Fermions and gauge fluxes. Upon breaking of time-reversal symmetry, for example in an external magnetic field, these fractionalized quasiparticles acquire non-Abelian exchange statistics, an important ingredient for topologically protected quantum computing. Consequently, there has been enormous interest in exploring possible material realizations of Kitaev physics and several candidate materials have been put forward, recently including α-RuCl 3. In the absence of a magnetic field this material orders at a finite temperature and exhibits low-energy spin wave excitations.more » However, at moderate energies, the spectrum is unconventional and the response shows evidence for fractional excitations. Here in this paper, we use time-of-flight inelastic neutron scattering to show that the application of a sufficiently large magnetic field in the honeycomb plane suppresses the magnetic order and the spin waves, leaving a gapped continuum spectrum of magnetic excitations. Our comparisons of the scattering to the available calculations for a Kitaev QSL show that they are consistent with the magnetic field induced QSL phase.« less

Proximate Kitaev quantum spin liquid behaviour in a honeycomb magnet

DOE Office of Scientific and Technical Information (OSTI.GOV)

Banerjee, A.; Bridges, C. A.; Yan, J. -Q.

Quantum spin liquids (QSLs) are topological states of matter exhibiting remarkable properties such as the capacity to protect quantum information from decoherence. While their featureless ground states have precluded their straightforward experimental identification, excited states are more revealing and particularly interesting due to the emergence of fundamentally new excitations such as Majorana Fermions. Ideal probes of these excitations are inelastic neutron scattering experiments. We report these here for a ruthenium-based material α-RuCl 3, continuing a major search (so far concentrated on iridium materials inimical to neutron probes) for realizations of the celebrated Kitaev honeycomb topological QSL. Our measurements confirm themore » requisite strong spin-orbit coupling and low-temperature magnetic order matching predictions proximate to the QSL. We find stacking faults, inherent to the highly 2D nature of the material, resolve an outstanding puzzle. Crucially, dynamical response measurements above interlayer energy scales are naturally accounted for in terms of deconfinement physics expected for QSLs. Comparing these with recent dynamical calculations involving gauge flux excitations and Majorana fermions of the pure Kitaev model, we propose the excitation spectrum of α-RuCl 3 as prime candidate for realization of fractionalized Kitaev physics.« less

Particle-hole symmetry, many-body localization, and topological edge modes

NASA Astrophysics Data System (ADS)

Vasseur, Romain; Friedman, Aaron J.; Parameswaran, S. A.; Potter, Andrew C.

We study the excited states of interacting fermions in one dimension with particle-hole symmetric disorder (equivalently, random-bond XXZ chains) using a combination of renormalization group methods and exact diagonalization. Absent interactions, the entire many-body spectrum exhibits infinite-randomness quantum critical behavior with highly degenerate excited states. We show that though interactions are an irrelevant perturbation in the ground state, they drastically affect the structure of excited states: even arbitrarily weak interactions split the degeneracies in favor of thermalization (weak disorder) or spontaneously broken particle-hole symmetry, driving the system into a many-body localized spin glass phase (strong disorder). In both cases, the quantum critical properties of the non-interacting model are destroyed, either by thermal decoherence or spontaneous symmetry breaking. This system then has the interesting and counterintuitive property that edges of the many-body spectrum are less localized than the center of the spectrum. We argue that our results rule out the existence of certain excited state symmetry-protected topological orders. Supported by the Gordon and Betty Moore Foundation's EPiQS Initiative (Grant GBMF4307 (ACP), the Quantum Materials Program at LBNL (RV), NSF Grant DMR-1455366 and UCOP Research Catalyst Award No. CA-15-327861 (SAP).

Orbital Magnetization of Quantum Spin Hall Insulator Nanoparticles.

PubMed

Potasz, P; Fernández-Rossier, J

2015-09-09

Both spin and orbital degrees of freedom contribute to the magnetic moment of isolated atoms. However, when inserted in crystals, atomic orbital moments are quenched because of the lack of rotational symmetry that protects them when isolated. Thus, the dominant contribution to the magnetization of magnetic materials comes from electronic spin. Here we show that nanoislands of quantum spin Hall insulators can host robust orbital edge magnetism whenever their highest occupied Kramers doublet is singly occupied, upgrading the spin edge current into a charge current. The resulting orbital magnetization scales linearly with size, outweighing the spin contribution for islands of a few nm in size. This linear scaling is specific of the Dirac edge states and very different from Schrodinger electrons in quantum rings. By modeling Bi(111) flakes, whose edge states have been recently observed, we show that orbital magnetization is robust with respect to disorder, thermal agitation, shape of the island, and crystallographic direction of the edges, reflecting its topological protection.

Pairing versus phase coherence of doped holes in distinct quantum spin backgrounds

NASA Astrophysics Data System (ADS)

Zhu, Zheng; Sheng, D. N.; Weng, Zheng-Yu

2018-03-01

We examine the pairing structure of holes injected into two distinct spin backgrounds: a short-range antiferromagnetic phase versus a symmetry protected topological phase. Based on density matrix renormalization group (DMRG) simulation, we find that although there is a strong binding between two holes in both phases, phase fluctuations can significantly influence the pair-pair correlation depending on the spin-spin correlation in the background. Here the phase fluctuation is identified as an intrinsic string operator nonlocally controlled by the spins. We show that while the pairing amplitude is generally large, the coherent Cooper pairing can be substantially weakened by the phase fluctuation in the symmetry-protected topological phase, in contrast to the short-range antiferromagnetic phase. It provides an example of a non-BCS mechanism for pairing, in which the paring phase coherence is determined by the underlying spin state self-consistently, bearing an interesting resemblance to the pseudogap physics in the cuprate.

Wave functions of symmetry-protected topological phases from conformal field theories

NASA Astrophysics Data System (ADS)

Scaffidi, Thomas; Ringel, Zohar

2016-03-01

We propose a method for analyzing two-dimensional symmetry-protected topological (SPT) wave functions using a correspondence with conformal field theories (CFTs) and integrable lattice models. This method generalizes the CFT approach for the fractional quantum Hall effect wherein the wave-function amplitude is written as a many-operator correlator in the CFT. Adopting a bottom-up approach, we start from various known microscopic wave functions of SPTs with discrete symmetries and show how the CFT description emerges at large scale, thereby revealing a deep connection between group cocycles and critical, sometimes integrable, models. We show that the CFT describing the bulk wave function is often also the one describing the entanglement spectrum, but not always. Using a plasma analogy, we also prove the existence of hidden quasi-long-range order for a large class of SPTs. Finally, we show how response to symmetry fluxes is easily described in terms of the CFT.

Superconducting topological surface states in the noncentrosymmetric bulk superconductor PbTaSe2.

PubMed

Guan, Syu-You; Chen, Peng-Jen; Chu, Ming-Wen; Sankar, Raman; Chou, Fangcheng; Jeng, Horng-Tay; Chang, Chia-Seng; Chuang, Tien-Ming

2016-11-01

The search for topological superconductors (TSCs) is one of the most urgent contemporary problems in condensed matter systems. TSCs are characterized by a full superconducting gap in the bulk and topologically protected gapless surface (or edge) states. Within each vortex core of TSCs, there exists the zero-energy Majorana bound states, which are predicted to exhibit non-Abelian statistics and to form the basis of the fault-tolerant quantum computation. To date, no stoichiometric bulk material exhibits the required topological surface states (TSSs) at the Fermi level ( E F ) combined with fully gapped bulk superconductivity. We report atomic-scale visualization of the TSSs of the noncentrosymmetric fully gapped superconductor PbTaSe 2 . Using quasi-particle scattering interference imaging, we find two TSSs with a Dirac point at E ≅ 1.0 eV, of which the inner TSS and the partial outer TSS cross E F , on the Pb-terminated surface of this fully gapped superconductor. This discovery reveals PbTaSe 2 as a promising candidate for TSC.

A bilayer Double Semion Model with Symmetry-Enriched Topological Order

NASA Astrophysics Data System (ADS)

Ortiz, Laura; Martin-Delgado, Miguel Angel

We construct a new model of two-dimensional quantum spin systems that combines intrinsic topological orders and a global symmetry called flavour symmetry. It is referred as the bilayer Doubled Semion model (bDS) and is an instance of symmetry-enriched topological order. A honeycomb bilayer lattice is introduced to combine a Double Semion Topolgical Order with a global spin-flavour symmetry to get the fractionalization of its quasiparticles. The bDS model exhibits non-trival braiding self-statistics of excitations and its dual model constitutes a Symmetry-Protected Topological Order with novel edge states. This dual model gives rise to a bilayer Non-Trivial Paramagnet that is invariant under the flavour symmetry and the well-known spin flip symmetry. We acknowledge financial support from the Spanish MINECO Grants FIS2012-33152, FIS2015-67411, and the CAM research consortium QUITEMAD+, Grant No. S2013/ICE-2801. The research of M.A.M.-D. has been supported in part by the U.S. Army Research Office throu.

Conformal field theory construction for non-Abelian hierarchy wave functions

NASA Astrophysics Data System (ADS)

Tournois, Yoran; Hermanns, Maria

2017-12-01

The fractional quantum Hall effect is the paradigmatic example of topologically ordered phases. One of its most fascinating aspects is the large variety of different topological orders that may be realized, in particular non-Abelian ones. Here we analyze a class of non-Abelian fractional quantum Hall model states which are generalizations of the Abelian Haldane-Halperin hierarchy. We derive their topological properties and show that the quasiparticles obey non-Abelian fusion rules of type su (q)k . For a subset of these states we are able to derive the conformal field theory description that makes the topological properties—in particular braiding—of the state manifest. The model states we study provide explicit wave functions for a large variety of interesting topological orders, which may be relevant for certain fractional quantum Hall states observed in the first excited Landau level.

Nodal Topological Phases in s-wave Superfluid of Ultracold Fermionic Gases

NASA Astrophysics Data System (ADS)

Huang, Bei-Bing; Yang, Xiao-Sen

2018-02-01

The gapless Weyl superfluid has been widely studied in the three-dimensional ultracold fermionic superfluid. In contrast to Weyl superfluid, there exists another kind of gapless superfluid with topologically protected nodal lines, which can be regarded as the superfluid counterpart of nodal line semimetal in the condensed matter physics, just as Weyl superfluid with Weyl semimetal. In this paper we study the ground states of the cold fermionic gases in cubic optical lattices with one-dimensional spin-orbit coupling and transverse Zeeman field and map out the topological phase diagram of the system. We demonstrate that in addition to a fully gapped topologically trivial phase, some different nodal line superfluid phases appear when the Zeeman field is adjusted. The presence of topologically stable nodal lines implies the dispersionless zero-energy flat band in a finite region of the surface Brillouin zone. Experimentally these nodal line superfluid states can be detected via the momentum-resolved radio-frequency spectroscopy. The nodal line topological superfluid provide fertile grounds for exploring exotic quantum matters in the context of ultracold atoms. Supported by National Natural Science Foundation of China under Grant Nos. 11547047 and 11504143

Quantized topological magnetoelectric effect of the zero-plateau quantum anomalous Hall state

DOE PAGES

Wang, Jing; Lian, Biao; Qi, Xiao-Liang; ...

2015-08-10

The topological magnetoelectric effect in a three-dimensional topological insulator is a novel phenomenon, where an electric field induces a magnetic field in the same direction, with a universal coefficient of proportionality quantized in units of $e²/2h$. Here in this paper, we propose that the topological magnetoelectric effect can be realized in the zero-plateau quantum anomalous Hall state of magnetic topological insulators or a ferromagnet-topological insulator heterostructure. The finite-size effect is also studied numerically, where the magnetoelectric coefficient is shown to converge to a quantized value when the thickness of the topological insulator film increases. We further propose a device setupmore » to eliminate nontopological contributions from the side surface.« less

String theory, gauge theory and quantum gravity. Proceedings. Trieste Spring School and Workshop on String Theory, Gauge Theory and Quantum Gravity, Trieste (Italy), 11 - 22 Apr 1994.

NASA Astrophysics Data System (ADS)

1995-04-01

The following topics were dealt with: string theory, gauge theory, quantum gravity, quantum geometry, black hole physics and information loss, second quantisation of the Wilson loop, 2D Yang-Mills theory, topological field theories, equivariant cohomology, superstring theory and fermion masses, supergravity, topological gravity, waves in string cosmology, superstring theories, 4D space-time.

Quantum gates by periodic driving

PubMed Central

Shi, Z. C.; Wang, W.; Yi, X. X.

2016-01-01

Topological quantum computation has been extensively studied in the past decades due to its robustness against decoherence. One way to realize the topological quantum computation is by adiabatic evolutions—it requires relatively long time to complete a gate, so the speed of quantum computation slows down. In this work, we present a method to realize single qubit quantum gates by periodic driving. Compared to adiabatic evolution, the single qubit gates can be realized at a fixed time much shorter than that by adiabatic evolution. The driving fields can be sinusoidal or square-well field. With the sinusoidal driving field, we derive an expression for the total operation time in the high-frequency limit, and an exact analytical expression for the evolution operator without any approximations is given for the square well driving. This study suggests that the period driving could provide us with a new direction in regulations of the operation time in topological quantum computation. PMID:26911900

Quantum gates by periodic driving.

PubMed

Shi, Z C; Wang, W; Yi, X X

2016-02-25

Topological quantum computation has been extensively studied in the past decades due to its robustness against decoherence. One way to realize the topological quantum computation is by adiabatic evolutions-it requires relatively long time to complete a gate, so the speed of quantum computation slows down. In this work, we present a method to realize single qubit quantum gates by periodic driving. Compared to adiabatic evolution, the single qubit gates can be realized at a fixed time much shorter than that by adiabatic evolution. The driving fields can be sinusoidal or square-well field. With the sinusoidal driving field, we derive an expression for the total operation time in the high-frequency limit, and an exact analytical expression for the evolution operator without any approximations is given for the square well driving. This study suggests that the period driving could provide us with a new direction in regulations of the operation time in topological quantum computation.

Quantum anomalous Hall effect in magnetic topological insulators

DOE PAGES

Wang, Jing; Lian, Biao; Zhang, Shou -Cheng

2015-08-25

The search for topologically non-trivial states of matter has become an important goal for condensed matter physics. Here, we give a theoretical introduction to the quantum anomalous Hall (QAH) effect based on magnetic topological insulators in two-dimensions (2D) and three-dimensions (3D). In 2D topological insulators, magnetic order breaks the symmetry between the counter-propagating helical edge states, and as a result, the quantum spin Hall effect can evolve into the QAH effect. In 3D, magnetic order opens up a gap for the topological surface states, and chiral edge state has been predicted to exist on the magnetic domain walls. We presentmore » the phase diagram in thin films of a magnetic topological insulator and review the basic mechanism of ferromagnetic order in magnetically doped topological insulators. We also review the recent experimental observation of the QAH effect. Furthermore, we discuss more recent theoretical work on the coexistence of the helical and chiral edge states, multi-channel chiral edge states, the theory of the plateau transition, and the thickness dependence in the QAH effect.« less

Design principles for HgTe based topological insulator devices

NASA Astrophysics Data System (ADS)

Sengupta, Parijat; Kubis, Tillmann; Tan, Yaohua; Povolotskyi, Michael; Klimeck, Gerhard

2013-07-01

The topological insulator properties of CdTe/HgTe/CdTe quantum wells are theoretically studied. The CdTe/HgTe/CdTe quantum well behaves as a topological insulator beyond a critical well width dimension. It is shown that if the barrier (CdTe) and well-region (HgTe) are altered by replacing them with the alloy CdxHg1-xTe of various stoichiometries, the critical width can be changed. The critical quantum well width is shown to depend on temperature, applied stress, growth directions, and external electric fields. Based on these results, a novel device concept is proposed that allows to switch between a normal semiconducting and topological insulator state through application of moderate external electric fields.

Two-component quantum Hall effects in topological flat bands

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zeng, Tian-Sheng; Zhu, Wei; Sheng, D. N.

2017-03-27

Here in this paper, we study quantum Hall states for two-component particles (hardcore bosons and fermions) loading in topological lattice models. By tuning the interplay of interspecies and intraspecies interactions, we demonstrate that two-component fractional quantum Hall states emerge at certain fractional filling factors ν = 1/2 for fermions (ν = 2/3 for bosons) in the lowest Chern band, classified by features from ground states including the unique Chern number matrix (inverse of the K matrix), the fractional charge and spin pumpings, and two parallel propagating edge modes. Moreover, we also apply our strategy to two-component fermions at integer fillingmore » factor ν = 2 , where a possible topological Neel antiferromagnetic phase is under intense debate very recently. For the typical π -flux checkerboard lattice, by tuning the onsite Hubbard repulsion, we establish a first-order phase transition directly from a two-component fermionic ν = 2 quantum Hall state at weak interaction to a topologically trivial antiferromagnetic insulator at strong interaction, and therefore exclude the possibility of an intermediate topological phase for our system.« less

Plasmon-Exciton Interactions Probed Using Spatial Coentrapment of Nanoparticles by Topological Singularities.

PubMed

Ackerman, Paul J; Mundoor, Haridas; Smalyukh, Ivan I; van de Lagemaat, Jao

2015-12-22

We study plasmon-exciton interaction by using topological singularities to spatially confine, selectively deliver, cotrap and optically probe colloidal semiconductor and plasmonic nanoparticles. The interaction is monitored in a single quantum system in the bulk of a liquid crystal medium where nanoparticles are manipulated and nanoconfined far from dielectric interfaces using laser tweezers and topological configurations containing singularities. When quantum dot-in-a-rod particles are spatially colocated with a plasmonic gold nanoburst particle in a topological singularity core, its fluorescence increases because blinking is significantly suppressed and the radiative decay rate increases by nearly an order of magnitude owing to the Purcell effect. We argue that the blinking suppression is the result of the radiative rate change that mitigates Auger recombination and quantum dot ionization, consequently reducing nonradiative recombination. Our work demonstrates that topological singularities are an effective platform for studying and controlling plasmon-exciton interactions.

Plasmon–Exciton Interactions Probed Using Spatial Coentrapment of Nanoparticles by Topological Singularities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ackerman, Paul J.; Mundoor, Haridas; Smalyukh, Ivan I.

2015-12-22

We study plasmon-exciton interaction by using topological singularities to spatially confine, selectively deliver, cotrap and optically probe colloidal semiconductor and plasmonic nanoparticles. The interaction is monitored in a single quantum system in the bulk of a liquid crystal medium where nanoparticles are manipulated and nanoconfined far from dielectric interfaces using laser tweezers and topological configurations containing singularities. When quantum dot-in-a-rod particles are spatially colocated with a plasmonic gold nanoburst particle in a topological singularity core, its fluorescence increases because blinking is significantly suppressed and the radiative decay rate increases by nearly an order of magnitude owing to the Purcell effect.more » We argue that the blinking suppression is the result of the radiative rate change that mitigates Auger recombination and quantum dot ionization, consequently reducing nonradiative recombination. Our work demonstrates that topological singularities are an effective platform for studying and controlling plasmon-exciton interactions.« less

On the role of self-adjointness in the continuum formulation of topological quantum phases

NASA Astrophysics Data System (ADS)

Tanhayi Ahari, Mostafa; Ortiz, Gerardo; Seradjeh, Babak

2016-11-01

Topological quantum phases of matter are characterized by an intimate relationship between the Hamiltonian dynamics away from the edges and the appearance of bound states localized at the edges of the system. Elucidating this correspondence in the continuum formulation of topological phases, even in the simplest case of a one-dimensional system, touches upon fundamental concepts and methods in quantum mechanics that are not commonly discussed in textbooks, in particular the self-adjoint extensions of a Hermitian operator. We show how such topological bound states can be derived in a prototypical one-dimensional system. Along the way, we provide a pedagogical exposition of the self-adjoint extension method as well as the role of symmetries in correctly formulating the continuum, field-theory description of topological matter with boundaries. Moreover, we show that self-adjoint extensions can be characterized generally in terms of a conserved local current associated with the self-adjoint operator.

Edge-mode superconductivity in a two-dimensional topological insulator.

PubMed

Pribiag, Vlad S; Beukman, Arjan J A; Qu, Fanming; Cassidy, Maja C; Charpentier, Christophe; Wegscheider, Werner; Kouwenhoven, Leo P

2015-07-01

Topological superconductivity is an exotic state of matter that supports Majorana zero-modes, which have been predicted to occur in the surface states of three-dimensional systems, in the edge states of two-dimensional systems, and in one-dimensional wires. Localized Majorana zero-modes obey non-Abelian exchange statistics, making them interesting building blocks for topological quantum computing. Here, we report superconductivity induced in the edge modes of semiconducting InAs/GaSb quantum wells, a two-dimensional topological insulator. Using superconducting quantum interference we demonstrate gate-tuning between edge-dominated and bulk-dominated regimes of superconducting transport. The edge-dominated regime arises only under conditions of high-bulk resistivity, which we associate with the two-dimensional topological phase. These experiments establish InAs/GaSb as a promising platform for the confinement of Majoranas into localized states, enabling future investigations of non-Abelian statistics.

Exotic topological density waves in cold atomic Rydberg-dressed fermions

PubMed Central

Li, Xiaopeng; Sarma, S Das

2015-01-01

Versatile controllability of interactions in ultracold atomic and molecular gases has now reached an era where quantum correlations and unconventional many-body phases can be studied with no corresponding analogues in solid-state systems. Recent experiments in Rydberg atomic gases have achieved exquisite control over non-local interactions, allowing novel quantum phases unreachable with the usual local interactions in atomic systems. Here we study Rydberg-dressed atomic fermions in a three-dimensional optical lattice predicting the existence of hitherto unheard-of exotic mixed topological density wave phases. By varying the spatial range of the non-local interaction, we find various chiral density waves with spontaneous time-reversal symmetry breaking, whose quasiparticles form three-dimensional quantum Hall and Weyl semimetal states. Remarkably, certain density waves even exhibit mixed topologies beyond the existing topological classification. Our results suggest gapless fermionic states could exhibit far richer topology than previously expected. PMID:25972134

Classifying the Quantum Phases of Matter

DTIC Science & Technology

2015-01-01

Kim related entanglement entropy to topological storage of quantum information [8]. Michalakis et al. showed that a particle-like excitation spectrum...Perturbative analysis of topological entanglement entropy from conditional independence, Phys. Rev. B 86, 254116 (2012), arXiv:1210.2360. [3] I. Kim...symmetries or long-range entanglement ), (2) elucidating the properties of three-dimensional quantum codes (in particular those which admit no string-like

Electronic properties of new topological quantum materials

NASA Astrophysics Data System (ADS)

Kaminski, Adam

Topological materials are characterized by the presence of nontrivial quantum electronic states, where often the electron spin is locked to its momentum. This opens up the possibility for developing new devices in which information is processed or stored by means of spin rather than charge. In this talk we will discuss the electronic properties of several of newly discovered topological quantum materials. In WTe2 we have observed a topological transition involving a change of the Fermi surface topology (known as a Lifshitz transition) driven by temperature. The strong temperature-dependence of the chemical potential that is at the heart of this phenomenon is also important for understanding the thermoelectric properties of such semimetals. Both WTe2 and MoTe2 were proposed to host type II Weyl semimetalic state. Indeed our data provides first experimental confirmation of such state in both of these materials. We will also present evidence for a new topological state in PtSn4 where pairs of extended Dirac node arcs rather are present rather than Dirac points, that is so far not understood theoretically. Our research opens up new directions on enhancing topological responsiveness of new quantum materials. This work was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Science and Engineering Division (ARPES measurements), Center for Emergent Materials, an NSF MRSEC, under Grant DMR-1420451 (theory and data anal.

Record surface state mobility and quantum Hall effect in topological insulator thin films via interface engineering

DOE PAGES

Koirala, Nikesh; Han, Myung -Geun; Brahlek, Matthew; ...

2015-11-19

Material defects remain as the main bottleneck to the progress of topological insulators (TIs). In particular, efforts to achieve thin TI samples with dominant surface transport have always led to increased defects and degraded mobilities, thus making it difficult to probe the quantum regime of the topological surface states. Here, by utilizing a novel buffer layer scheme composed of an In 2Se 3/(Bi 0.5In 0.5) 2Se 3 heterostructure, we introduce a quantum generation of Bi 2Se 3 films with an order of magnitude enhanced mobilities than before. Furthermore, this scheme has led to the first observation of the quantum Hallmore » effect in Bi 2Se 3.« less

Reconfigurable optical implementation of quantum complex networks

NASA Astrophysics Data System (ADS)

Nokkala, J.; Arzani, F.; Galve, F.; Zambrini, R.; Maniscalco, S.; Piilo, J.; Treps, N.; Parigi, V.

2018-05-01

Network theory has played a dominant role in understanding the structure of complex systems and their dynamics. Recently, quantum complex networks, i.e. collections of quantum systems arranged in a non-regular topology, have been theoretically explored leading to significant progress in a multitude of diverse contexts including, e.g., quantum transport, open quantum systems, quantum communication, extreme violation of local realism, and quantum gravity theories. Despite important progress in several quantum platforms, the implementation of complex networks with arbitrary topology in quantum experiments is still a demanding task, especially if we require both a significant size of the network and the capability of generating arbitrary topology—from regular to any kind of non-trivial structure—in a single setup. Here we propose an all optical and reconfigurable implementation of quantum complex networks. The experimental proposal is based on optical frequency combs, parametric processes, pulse shaping and multimode measurements allowing the arbitrary control of the number of the nodes (optical modes) and topology of the links (interactions between the modes) within the network. Moreover, we also show how to simulate quantum dynamics within the network combined with the ability to address its individual nodes. To demonstrate the versatility of these features, we discuss the implementation of two recently proposed probing techniques for quantum complex networks and structured environments.

Temperature-Induced Topological Phase Transition in HgTe Quantum Wells

NASA Astrophysics Data System (ADS)

Kadykov, A. M.; Krishtopenko, S. S.; Jouault, B.; Desrat, W.; Knap, W.; Ruffenach, S.; Consejo, C.; Torres, J.; Morozov, S. V.; Mikhailov, N. N.; Dvoretskii, S. A.; Teppe, F.

2018-02-01

We report a direct observation of temperature-induced topological phase transition between the trivial and topological insulator states in an HgTe quantum well. By using a gated Hall bar device, we measure and represent Landau levels in fan charts at different temperatures, and we follow the temperature evolution of a peculiar pair of "zero-mode" Landau levels, which split from the edge of electronlike and holelike subbands. Their crossing at a critical magnetic field Bc is a characteristic of inverted band structure in the quantum well. By measuring the temperature dependence of Bc, we directly extract the critical temperature Tc at which the bulk band gap vanishes and the topological phase transition occurs. Above this critical temperature, the opening of a trivial gap is clearly observed.

Topological Rényi Entropy after a Quantum Quench

NASA Astrophysics Data System (ADS)

Halász, Gábor B.; Hamma, Alioscia

2013-04-01

We present an analytical study on the resilience of topological order after a quantum quench. The system is initially prepared in the ground state of the toric-code model, and then quenched by switching on an external magnetic field. During the subsequent time evolution, the variation in topological order is detected via the topological Rényi entropy of order 2. We consider two different quenches: the first one has an exact solution, while the second one requires perturbation theory. In both cases, we find that the long-term time average of the topological Rényi entropy in the thermodynamic limit is the same as its initial value. Based on our results, we argue that topological order is resilient against a wide range of quenches.

Topological Rényi entropy after a quantum quench.

PubMed

Halász, Gábor B; Hamma, Alioscia

2013-04-26

We present an analytical study on the resilience of topological order after a quantum quench. The system is initially prepared in the ground state of the toric-code model, and then quenched by switching on an external magnetic field. During the subsequent time evolution, the variation in topological order is detected via the topological Rényi entropy of order 2. We consider two different quenches: the first one has an exact solution, while the second one requires perturbation theory. In both cases, we find that the long-term time average of the topological Rényi entropy in the thermodynamic limit is the same as its initial value. Based on our results, we argue that topological order is resilient against a wide range of quenches.

Zeeman-Field-Tuned Topological Phase Transitions in a Two-Dimensional Class-DIII Superconductor

PubMed Central

Deng, W. Y.; Geng, H.; Luo, W.; Sheng, L.; Xing, D. Y.

2016-01-01

We investigate the topological phase transitions in a two-dimensional time-reversal invariant topological superconductor in the presence of a Zeeman field. Based on the spin Chern number theory, we find that the system exhibits a number of topologically distinct phases with changing the out-of-plane component of the Zeeman field, including a quantum spin Hall-like phase, quantum anomalous Hall-like phases with total Chern number C = −2, −1, 1 and 2, and a topologically trivial superconductor phase. The BdG band gap closes at each boundary of the phase transitions. Furthermore, we demonstrate that the zero bias conductance provides clear transport signatures of the different topological phases, which are robust against symmetry-breaking perturbations. PMID:27148675

Multipartite Entanglement in Topological Quantum Phases.

PubMed

Pezzè, Luca; Gabbrielli, Marco; Lepori, Luca; Smerzi, Augusto

2017-12-22

We witness multipartite entanglement in the ground state of the Kitaev chain-a benchmark model of a one dimensional topological superconductor-also with variable-range pairing, using the quantum Fisher information. Phases having a finite winding number, for both short- and long-range pairing, are characterized by a power-law diverging finite-size scaling of multipartite entanglement. Moreover, the occurring quantum phase transitions are sharply marked by the divergence of the derivative of the quantum Fisher information, even in the absence of a closing energy gap.

Hidden order and flux attachment in symmetry-protected topological phases: A Laughlin-like approach

NASA Astrophysics Data System (ADS)

Ringel, Zohar; Simon, Steven H.

2015-05-01

Topological phases of matter are distinct from conventional ones by their lack of a local order parameter. Still in the quantum Hall effect, hidden order parameters exist and constitute the basis for the celebrated composite-particle approach. Whether similar hidden orders exist in 2D and 3D symmetry protected topological phases (SPTs) is a largely open question. Here, we introduce a new approach for generating SPT ground states, based on a generalization of the Laughlin wave function. This approach gives a simple and unifying picture of some classes of SPTs in 1D and 2D, and reveals their hidden order and flux attachment structures. For the 1D case, we derive exact relations between the wave functions obtained in this manner and group cohomology wave functions, as well as matrix product state classification. For the 2D Ising SPT, strong analytical and numerical evidence is given to show that the wave function obtained indeed describes the desired SPT. The Ising SPT then appears as a state with quasi-long-range order in composite degrees of freedom consisting of Ising-symmetry charges attached to Ising-symmetry fluxes.

Simulating quantum spin Hall effect in the topological Lieb lattice of a linear circuit network

NASA Astrophysics Data System (ADS)

Zhu, Weiwei; Hou, Shanshan; Long, Yang; Chen, Hong; Ren, Jie

2018-02-01

Inspired by the topological insulator circuit experimentally proposed by Jia Ningyuan et al. [Phys. Rev. X 5, 021031 (2015), 10.1103/PhysRevX.5.021031], we theoretically realize the topological Lieb lattice, a line-centered square lattice with rich topological properties, in a radio-frequency circuit. We design a specific capacitor-inductor connection to resemble the intrinsic spin-orbit coupling and construct the analog spin by mixing degrees of freedom of voltages. As such, we are able to simulate the quantum spin Hall effect in the topological Lieb lattice of linear circuits. We then investigate the spin-resolved topological edge mode and the topological phase transition of the band structure varied with capacitances. Finally, we discuss the extension of the π /2 phase change of hopping between sites to arbitrary phase values. Our results may find implications in engineering microwave topological metamaterials for signal transmission and energy harvesting.

Topological edge states and impurities: Manifestation in the local static and dynamical characteristics of dimerized quantum chains

NASA Astrophysics Data System (ADS)

Zvyagin, A. A.

2018-04-01

Based on the results of exact analytic calculations, we show that topological edge states and impurities in quantum dimerized chains manifest themselves in various local static and dynamical characteristics, which can be measured in experiments. In particular, topological edge states can be observed in the magnetic field behavior of the local magnetization or magnetic susceptibility of dimerized spin chains as jumps (for the magnetization) and features (for the static susceptibility) at zero field. In contrast, impurities reveal themselves in similar jumps and features, however, at nonzero values of the critical field. We also show that dynamical characteristics of dimerized quantum chains also manifest the features, related to the topological edge states and impurities. Those features, as a rule, can be seen more sharply than the manifestation of bulk extended states in, e.g., the dynamical local susceptibility. Such peculiarities can be observed in one-dimensional dimerized spin chains, e.g., in NMR experiments, or in various realizations of quantum dimerized chains in optical experiments.

Topological quantum computation of the Dold-Thom functor

NASA Astrophysics Data System (ADS)

Ospina, Juan

2014-05-01

A possible topological quantum computation of the Dold-Thom functor is presented. The method that will be used is the following: a) Certain 1+1-topological quantum field theories valued in symmetric bimonoidal categories are converted into stable homotopical data, using a machinery recently introduced by Elmendorf and Mandell; b) we exploit, in this framework, two recent results (independent of each other) on refinements of Khovanov homology: our refinement into a module over the connective k-theory spectrum and a stronger result by Lipshitz and Sarkar refining Khovanov homology into a stable homotopy type; c) starting from the Khovanov homotopy the Dold-Thom functor is constructed; d) the full construction is formulated as a topological quantum algorithm. It is conjectured that the Jones polynomial can be described as the analytical index of certain Dirac operator defined in the context of the Khovanov homotopy using the Dold-Thom functor. As a line for future research is interesting to study the corresponding supersymmetric model for which the Khovanov-Dirac operator plays the role of a supercharge.

Wigner flow reveals topological order in quantum phase space dynamics.

PubMed

Steuernagel, Ole; Kakofengitis, Dimitris; Ritter, Georg

2013-01-18

The behavior of classical mechanical systems is characterized by their phase portraits, the collections of their trajectories. Heisenberg's uncertainty principle precludes the existence of sharply defined trajectories, which is why traditionally only the time evolution of wave functions is studied in quantum dynamics. These studies are quite insensitive to the underlying structure of quantum phase space dynamics. We identify the flow that is the quantum analog of classical particle flow along phase portrait lines. It reveals hidden features of quantum dynamics and extra complexity. Being constrained by conserved flow winding numbers, it also reveals fundamental topological order in quantum dynamics that has so far gone unnoticed.

Quantum control of topological defects in magnetic systems

NASA Astrophysics Data System (ADS)

Takei, So; Mohseni, Masoud

2018-02-01

Energy-efficient classical information processing and storage based on topological defects in magnetic systems have been studied over the past decade. In this work, we introduce a class of macroscopic quantum devices in which a quantum state is stored in a topological defect of a magnetic insulator. We propose noninvasive methods to coherently control and read out the quantum state using ac magnetic fields and magnetic force microscopy, respectively. This macroscopic quantum spintronic device realizes the magnetic analog of the three-level rf-SQUID qubit and is built fully out of electrical insulators with no mobile electrons, thus eliminating decoherence due to the coupling of the quantum variable to an electronic continuum and energy dissipation due to Joule heating. For a domain wall size of 10-100 nm and reasonable material parameters, we estimate qubit operating temperatures in the range of 0.1-1 K, a decoherence time of about 0.01-1 μ s , and the number of Rabi flops within the coherence time scale in the range of 102-104 .

Synthetic electromagnetic knot in a three-dimensional skyrmion

PubMed Central

Lee, Wonjae; Gheorghe, Andrei H.; Tiurev, Konstantin; Ollikainen, Tuomas; Möttönen, Mikko; Hall, David S.

2018-01-01

Classical electromagnetism and quantum mechanics are both central to the modern understanding of the physical world and its ongoing technological development. Quantum simulations of electromagnetic forces have the potential to provide information about materials and systems that do not have conveniently solvable theoretical descriptions, such as those related to quantum Hall physics, or that have not been physically observed, such as magnetic monopoles. However, quantum simulations that simultaneously implement all of the principal features of classical electromagnetism have thus far proved elusive. We experimentally realize a simulation in which a charged quantum particle interacts with the knotted electromagnetic fields peculiar to a topological model of ball lightning. These phenomena are induced by precise spatiotemporal control of the spin field of an atomic Bose-Einstein condensate, simultaneously creating a Shankar skyrmion—a topological excitation that was theoretically predicted four decades ago but never before observed experimentally. Our results reveal the versatile capabilities of synthetic electromagnetism and provide the first experimental images of topological three-dimensional skyrmions in a quantum system. PMID:29511735

Z3 topological order in the face-centered-cubic quantum plaquette model

NASA Astrophysics Data System (ADS)

Devakul, Trithep

2018-04-01

We examine the topological order in the resonating singlet valence plaquette (RSVP) phase of the hard-core quantum plaquette model (QPM) on the face centered cubic (FCC) lattice. To do this, we construct a Rohksar-Kivelson type Hamiltonian of local plaquette resonances. This model is shown to exhibit a Z3 topological order, which we show by identifying a Z3 topological constant (which leads to a 33-fold topological ground state degeneracy on the 3-torus) and topological pointlike charge and looplike magnetic excitations which obey Z3 statistics. We also consider an exactly solvable generalization of this model, which makes the geometrical origin of the Z3 order explicitly clear. For other models and lattices, such generalizations produce a wide variety of topological phases, some of which are novel fracton phases.

Superconductivity bordering Rashba type topological transition

DOE PAGES

Jin, M. L.; Sun, F.; Xing, L. Y.; ...

2017-01-04

Strong spin orbital interaction (SOI) can induce unique quantum phenomena such as topological insulators, the Rashba effect, or p-wave superconductivity. Combining these three quantum phenomena into a single compound has important scientific implications. Here we report experimental observations of consecutive quantum phase transitions from a Rashba type topological trivial phase to topological insulator state then further proceeding to superconductivity in a SOI compound BiTeI tuned via pressures. The electrical resistivity measurement with V shape change signals the transition from a Rashba type topological trivial to a topological insulator phase at 2 GPa, which is caused by an energy gap closemore » then reopen with band inverse. Superconducting transition appears at 8 GPa with a critical temperature T C of 5.3 K. Structure refinements indicate that the consecutive phase transitions are correlated to the changes in the Bi–Te bond and bond angle as function of pressures. As a result, the Hall Effect measurements reveal an intimate relationship between superconductivity and the unusual change in carrier density that points to possible unconventional superconductivity.« less

Persistent Hall voltages across thin planar charged quantum rings on the surface of a topological insulator

NASA Astrophysics Data System (ADS)

Durganandini, P.

2015-03-01

We consider thin planar charged quantum rings on the surface of a three dimensional topological insulator coated with a thin ferromagnetic layer. We show theoretically, that when the ring is threaded by a magnetic field, then, due to the Aharanov-Bohm effect, there are not only the well known circulating persistent currents in the ring but also oscillating persistent Hall voltages across the thin ring. Such oscillating persistent Hall voltages arise due to the topological magneto-electric effect associated with the axion electrodynamics exhibited by the surface electronic states of the three dimensional topological insulator when time reversal symmetry is broken. We further generalize to the case of dipole currents and show that analogous Hall dipole voltages arise. We also discuss the robustness of the effect and suggest possible experimental realizations in quantum rings made of semiconductor heterostructures. Such experiments could also provide new ways of observing the predicted topological magneto-electric effect in three dimensional topological insulators with time reversal symmetry breaking. I thank BCUD, Pune University, Pune for financial support through research grant.

Topological nature of the node-arc semimetal PtSn4 probed by de Haas-van Alphen quantum oscillations

NASA Astrophysics Data System (ADS)

Wang, Y. J.; Liang, D. D.; Ge, M.; Yang, J.; Gong, J. X.; Luo, L.; Pi, L.; Zhu, W. K.; Zhang, C. J.; Zhang, Y. H.

2018-04-01

Dirac node arc semimetal state is a new topological quantum state which is proposed to exist in PtSn4 (Wu et al 2016 Dirac node arcs in PtSn4 Nat. Phys. 12 667–71). We present a systematic de Haas-van Alphen quantum oscillation study on this compound. Two intriguing oscillation branches, i.e. F 1 and F 2, are detected in the fast Fourier transformation spectra, both of which are characterized to possess tiny effective mass and ultrahigh quantum mobility. And the F 2 branch exhibits an angle-dependent nontrivial Berry phase. The features are consistent with the existence of the node arc semimetal state and shed new light on its complicated Fermi surfaces and topological nature.

Irreducible projective representations and their physical applications

NASA Astrophysics Data System (ADS)

Yang, Jian; Liu, Zheng-Xin

2018-01-01

An eigenfunction method is applied to reduce the regular projective representations (Reps) of finite groups to obtain their irreducible projective Reps. Anti-unitary groups are treated specially, where the decoupled factor systems and modified Schur’s lemma are introduced. We discuss the applications of irreducible Reps in many-body physics. It is shown that in symmetry protected topological phases, geometric defects or symmetry defects may carry projective Rep of the symmetry group; while in symmetry enriched topological phases, intrinsic excitations (such as spinons or visons) may carry projective Rep of the symmetry group. We also discuss the applications of projective Reps in problems related to spectrum degeneracy, such as in search of models without sign problem in quantum Monte Carlo simulations.

A novel artificial condensed matter lattice and a new platform for one-dimensional topological phases

DOE PAGES

Belopolski, Ilya; Xu, Su -Yang; Koirala, Nikesh; ...

2017-03-24

Engineered lattices in condensed matter physics, such as cold-atom optical lattices or photonic crystals, can have properties that are fundamentally different from those of naturally occurring electronic crystals. We report a novel type of artificial quantum matter lattice. Our lattice is a multilayer heterostructure built from alternating thin films of topological and trivial insulators. Each interface within the heterostructure hosts a set of topologically protected interface states, and by making the layers sufficiently thin, we demonstrate for the first time a hybridization of interface states across layers. In this way, our heterostructure forms an emergent atomic chain, where the interfacesmore » act as lattice sites and the interface states act as atomic orbitals, as seen from our measurements by angle-resolved photoemission spectroscopy. By changing the composition of the heterostructure, we can directly control hopping between lattice sites. We realize a topological and a trivial phase in our superlattice band structure. We argue that the superlattice may be characterized in a significant way by a one-dimensional topological invariant, closely related to the invariant of the Su-Schrieffer-Heeger model. Our topological insulator heterostructure demonstrates a novel experimental platform where we can engineer band structures by directly controlling how electrons hop between lattice sites.« less

A novel artificial condensed matter lattice and a new platform for one-dimensional topological phases

DOE Office of Scientific and Technical Information (OSTI.GOV)

Belopolski, Ilya; Xu, Su -Yang; Koirala, Nikesh

Engineered lattices in condensed matter physics, such as cold-atom optical lattices or photonic crystals, can have properties that are fundamentally different from those of naturally occurring electronic crystals. We report a novel type of artificial quantum matter lattice. Our lattice is a multilayer heterostructure built from alternating thin films of topological and trivial insulators. Each interface within the heterostructure hosts a set of topologically protected interface states, and by making the layers sufficiently thin, we demonstrate for the first time a hybridization of interface states across layers. In this way, our heterostructure forms an emergent atomic chain, where the interfacesmore » act as lattice sites and the interface states act as atomic orbitals, as seen from our measurements by angle-resolved photoemission spectroscopy. By changing the composition of the heterostructure, we can directly control hopping between lattice sites. We realize a topological and a trivial phase in our superlattice band structure. We argue that the superlattice may be characterized in a significant way by a one-dimensional topological invariant, closely related to the invariant of the Su-Schrieffer-Heeger model. Our topological insulator heterostructure demonstrates a novel experimental platform where we can engineer band structures by directly controlling how electrons hop between lattice sites.« less

Studying topology and dynamical phase transitions with ultracold quantum gases in optical lattices

NASA Astrophysics Data System (ADS)

Sengstock, Klaus

Topological properties lie at the heart of many fascinating phenomena in solid-state systems such as quantum Hall systems or Chern insulators. The topology of the bands can be captured by the distribution of Berry curvature, which describes the geometry of the eigenstates across the Brillouin zone. Using fermionic ultracold atoms in a hexagonal optical lattice, we engineered the Berry curvature of the Bloch bands using resonant driving and show a full momentum-resolved state tomography from which we obtain the Berry curvature and Chern number. Furthermore, we study the time-evolution of the many-body wavefunction after a sudden quench of the lattce parameters and observe the appearance, movement, and annihilation of vortices in reciprocal space. We identify their number as a dynamical topological order parameter, which suddenly changes its value at critical times. Our measurements constitute the first observation of a so called dynamical topological phase transition`, which we show to be a fruitful concept for the understanding of quantum dynamics far from equilibrium

Real-space imaging of a topologically protected edge state with ultracold atoms in an amplitude-chirped optical lattice

PubMed Central

Leder, Martin; Grossert, Christopher; Sitta, Lukas; Genske, Maximilian; Rosch, Achim; Weitz, Martin

2016-01-01

To describe a mobile defect in polyacetylene chains, Su, Schrieffer and Heeger formulated a model assuming two degenerate energy configurations that are characterized by two different topological phases. An immediate consequence was the emergence of a soliton-type edge state located at the boundary between two regions of different configurations. Besides giving first insights in the electrical properties of polyacetylene materials, interest in this effect also stems from its close connection to states with fractional charge from relativistic field theory. Here, using a one-dimensional optical lattice for cold rubidium atoms with a spatially chirped amplitude, we experimentally realize an interface between two spatial regions of different topological order in an atomic physics system. We directly observe atoms confined in the edge state at the intersection by optical real-space imaging and characterize the state as well as the size of the associated energy gap. Our findings hold prospects for the spectroscopy of surface states in topological matter and for the quantum simulation of interacting Dirac systems. PMID:27767054

Transport signatures of topology protected quantum criticality in Majorana islands

NASA Astrophysics Data System (ADS)

Papaj, Michal; Zhu, Zheng; Fu, Liang

Using numerical renormalization group we study a topological superconductor island coupled to three metallic leads in the vicinity of the charge degeneracy point. We show that the system flows to a non-Fermi liquid fixed point at low temperatures with fractional quantized DC conductance of 2 / 3e2 / h . Our proposal is experimentally feasible due to a much larger crossover temperature than in the previously studied cases and the robustness of the setup against the channel coupling anisotropy and charge degeneracy detuning. Including Majorana hybridization drives the system into a Fermi liquid phase at very low temperatures. The two proposed experimental signatures of multi-terminal electron teleportation include nonmonotonic temperature dependence of DC conductance and emergence of a plateau at 2 / 3e2 / h in tunnel coupling dependence of DC conductance. This work is funded by the DOE Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award de-sc0010526 (ZZ and LF) and the NSF STC ''Center for Integrated Quantum Materials'' under Cooperative Agreement No. DMR-1231319 (MP).

Graphene analogue in (111)-oriented BaBiO3 bilayer heterostructures for topological electronics.

PubMed

Kim, Rokyeon; Yu, Jaejun; Jin, Hosub

2018-01-11

Topological electronics is a new field that uses topological charges as current-carrying degrees of freedom. For topological electronics applications, systems should host topologically distinct phases to control the topological domain boundary through which the topological charges can flow. Due to their multiple Dirac cones and the π-Berry phase of each Dirac cone, graphene-like electronic structures constitute an ideal platform for topological electronics; graphene can provide various topological phases when incorporated with large spin-orbit coupling and mass-gap tunability via symmetry-breaking. Here, we propose that a (111)-oriented BaBiO 3 bilayer (BBL) sandwiched between large-gap perovskite oxides is a promising candidate for topological electronics by realizing a gap-tunable, and consequently a topology-tunable, graphene analogue. Depending on how neighboring perovskite spacers are chosen, the inversion symmetry of the BBL heterostructure can be either conserved or broken, leading to the quantum spin Hall (QSH) and quantum valley Hall (QVH) phases, respectively. BBL sandwiched by ferroelectric compounds enables switching of the QSH and QVH phases and generates the topological domain boundary. Given the abundant order parameters of the sandwiching oxides, the BBL can serve as versatile topological building blocks in oxide heterostructures.

Quantum Error Correction

NASA Astrophysics Data System (ADS)

Lidar, Daniel A.; Brun, Todd A.

2013-09-01

Prologue; Preface; Part I. Background: 1. Introduction to decoherence and noise in open quantum systems Daniel Lidar and Todd Brun; 2. Introduction to quantum error correction Dave Bacon; 3. Introduction to decoherence-free subspaces and noiseless subsystems Daniel Lidar; 4. Introduction to quantum dynamical decoupling Lorenza Viola; 5. Introduction to quantum fault tolerance Panos Aliferis; Part II. Generalized Approaches to Quantum Error Correction: 6. Operator quantum error correction David Kribs and David Poulin; 7. Entanglement-assisted quantum error-correcting codes Todd Brun and Min-Hsiu Hsieh; 8. Continuous-time quantum error correction Ognyan Oreshkov; Part III. Advanced Quantum Codes: 9. Quantum convolutional codes Mark Wilde; 10. Non-additive quantum codes Markus Grassl and Martin Rötteler; 11. Iterative quantum coding systems David Poulin; 12. Algebraic quantum coding theory Andreas Klappenecker; 13. Optimization-based quantum error correction Andrew Fletcher; Part IV. Advanced Dynamical Decoupling: 14. High order dynamical decoupling Zhen-Yu Wang and Ren-Bao Liu; 15. Combinatorial approaches to dynamical decoupling Martin Rötteler and Pawel Wocjan; Part V. Alternative Quantum Computation Approaches: 16. Holonomic quantum computation Paolo Zanardi; 17. Fault tolerance for holonomic quantum computation Ognyan Oreshkov, Todd Brun and Daniel Lidar; 18. Fault tolerant measurement-based quantum computing Debbie Leung; Part VI. Topological Methods: 19. Topological codes Héctor Bombín; 20. Fault tolerant topological cluster state quantum computing Austin Fowler and Kovid Goyal; Part VII. Applications and Implementations: 21. Experimental quantum error correction Dave Bacon; 22. Experimental dynamical decoupling Lorenza Viola; 23. Architectures Jacob Taylor; 24. Error correction in quantum communication Mark Wilde; Part VIII. Critical Evaluation of Fault Tolerance: 25. Hamiltonian methods in QEC and fault tolerance Eduardo Novais, Eduardo Mucciolo and Harold Baranger; 26. Critique of fault-tolerant quantum information processing Robert Alicki; References; Index.

Interferometric measurement method for Z2 invariants of time-reversal invariant topological insulators

NASA Astrophysics Data System (ADS)

Grusdt, Fabian; Abanin, Dmitry; Demler, Eugene

2013-05-01

Recently experiments with ultracold atoms started to explore topological phases in 1D optical lattices. While transport measurements are challenging in these systems, ways to directly measure topological quantum numbers using a combination of Bloch oscillations and Ramsey interferometry have been explored (Atala et al., arXiv:1212.0572). In this talk I will present ways to measure the Z2 topological quantum numbers of two and three dimensional time-reversal invariant (TR) topological insulators. In this case non-Abelian Bloch oscillations can be combined with Ramsey interferometry to map out the topological properties of a given band-structure. Our method is very general and works even in the presence of accidental degeneracies. The applicability of the scheme is discussed for different theoretically proposed implementations of TR topological insulators using ultracold atoms. F. G. is grateful to Harvard University for hospitality and acknowledges financial support from Graduate School Materials Science in Mainz (MAINZ).

Topological view of quantum tunneling coherent destruction

NASA Astrophysics Data System (ADS)

Bernardini, Alex E.; Chinaglia, Mariana

2017-08-01

Quantum tunneling of the ground and first excited states in a quantum superposition driven by a novel analytical configuration of a double-well (DW) potential is investigated. Symmetric and asymmetric potentials are considered as to support quantum mechanical zero mode and first excited state analytical solutions. Reporting about a symmetry breaking that supports the quantum conversion of a zero-mode stable vacuum into an unstable tachyonic quantum state, two inequivalent topological scenarios are supposed to drive stable tunneling and coherent tunneling destruction respectively. A complete prospect of the Wigner function dynamics, vector field fluxes and the time dependence of stagnation points is obtained for the analytical potentials that support stable and tachyonic modes.

Topological order and memory time in marginally-self-correcting quantum memory

NASA Astrophysics Data System (ADS)

Siva, Karthik; Yoshida, Beni

2017-03-01

We examine two proposals for marginally-self-correcting quantum memory: the cubic code by Haah and the welded code by Michnicki. In particular, we prove explicitly that they are absent of topological order above zero temperature, as their Gibbs ensembles can be prepared via a short-depth quantum circuit from classical ensembles. Our proof technique naturally gives rise to the notion of free energy associated with excitations. Further, we develop a framework for an ergodic decomposition of Davies generators in CSS codes which enables formal reduction to simpler classical memory problems. We then show that memory time in the welded code is doubly exponential in inverse temperature via the Peierls argument. These results introduce further connections between thermal topological order and self-correction from the viewpoint of free energy and quantum circuit depth.

General covariance, topological quantum field theories and fractional statistics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gamboa, J.

1992-01-20

Topological quantum field theories and fractional statistics are both defined in multiply connected manifolds. The authors study the relationship between both theories in 2 + 1 dimensions and the authors show that, due to the multiply-connected character of the manifold, the propagator for any quantum (field) theory always contains a first order pole that can be identified with a physical excitation with fractional spin. The article starts by reviewing the definition of general covariance in the Hamiltonian formalism, the gauge-fixing problem and the quantization following the lines of Batalin, Fradkin and Vilkovisky. The BRST-BFV quantization is reviewed in order tomore » understand the topological approach proposed here.« less

Wormholes, baby universes, and causality

NASA Astrophysics Data System (ADS)

Visser, Matt

1990-02-01

In this paper wormholes defined on a Minkowski signature manifold are considered, both at the classical and quantum levels. It is argued that causality in quantum gravity may best be imposed by restricting the functional integral to include only causal Lorentzian spacetimes. Subject to this assumption, one can put very tight constraints on the quantum behavior of wormholes, their cousins the baby universes, and topology-changing processes in general. Even though topology-changing processes are tightly constrained, this still allows very interesting geometrical (rather than topological) effects. In particular, the laboratory construction of baby universes is not prohibited provided that the ``umbilical cord'' is never cut. Methods for relaxing these causality constraints are also discussed.

Topological quantum pump in serpentine-shaped semiconducting narrow channels

NASA Astrophysics Data System (ADS)

Pandey, Sudhakar; Scopigno, Niccoló; Gentile, Paola; Cuoco, Mario; Ortix, Carmine

2018-06-01

We propose and analyze theoretically a one-dimensional solid-state electronic setup that operates as a topological charge pump in the complete absence of superimposed oscillating local voltages. The system consists of a semiconducting narrow channel with a strong Rashba spin-orbit interaction patterned in a mesoscale serpentine shape. A rotating planar magnetic field serves as the external ac perturbation, and cooperates with the Rashba spin-orbit interaction, which is modulated by the geometric curvature of the electronic channel to realize the topological pumping protocol, originally introduced by Thouless, in a different fashion. We expect the precise pumping of electric charges in our mesoscopic quantum device to be relevant for quantum metrology purposes.

Lattice-matched heterojunctions between topological and normal insulators: A first-principles study

NASA Astrophysics Data System (ADS)

Lee, Hyungjun; Yazyev, Oleg V.

2017-02-01

Gapless boundary modes at the interface between topologically distinct regions are one of the most salient manifestations of topology in physics. Metallic boundary states of time-reversal-invariant topological insulators (TIs), a realization of topological order in condensed matter, have been of much interest not only due to such a fundamental nature, but also due to their practical significance. These boundary states are immune to backscattering and localization owing to their topological origin, thereby opening up the possibility to tailor them for potential uses in spintronics and quantum computing. The heterojunction between a TI and a normal insulator (NI) is a representative playground for exploring such a topologically protected metallic boundary state and expected to constitute a building block for future electronic and spintronic solid-state devices based on TIs. Here, we report a first-principles study of two experimentally realized lattice-matched heterojunctions between TIs and NIs, Bi2Se3 (0001)/InP(111) and Bi2Te3 (0001)/BaF2(111). We evaluate the band offsets at these interfaces from many-body perturbation theory within the G W approximation as well as density-functional theory. Furthermore, we investigate the topological interface states, demonstrating that at these lattice-matched heterointerfaces, they are strictly localized and their helical spin textures are as well preserved as those at the vacuum-facing surfaces. These results taken together may help in designing devices relying on spin-helical metallic boundary states of TIs.

Effective field theories for topological insulators by functional bosonization

NASA Astrophysics Data System (ADS)

Chan, AtMa; Hughes, Taylor L.; Ryu, Shinsei; Fradkin, Eduardo

2013-02-01

Effective field theories that describe the dynamics of a conserved U(1) current in terms of “hydrodynamic” degrees of freedom of topological phases in condensed matter are discussed in general dimension D=d+1 using the functional bosonization technique. For noninteracting topological insulators (superconductors) with a conserved U(1) charge and characterized by an integer topological invariant [more specifically, they are topological insulators in the complex symmetry classes (class A and AIII), and in the “primary series” of topological insulators, in the eight real symmetry classes], we derive the BF-type topological field theories supplemented with the Chern-Simons (when D is odd) or the θ (when D is even) terms. For topological insulators characterized by a Z2 topological invariant (the first and second descendants of the primary series), their topological field theories are obtained by dimensional reduction. Building on this effective field theory description for noninteracting topological phases, we also discuss, following the spirit of the parton construction of the fractional quantum Hall effect by Block and Wen, the putative “fractional” topological insulators and their possible effective field theories, and use them to determine the physical properties of these nontrivial quantum phases.

A Study of Complex Deep Learning Networks on High Performance, Neuromorphic, and Quantum Computers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Potok, Thomas E; Schuman, Catherine D; Young, Steven R

Current Deep Learning models use highly optimized convolutional neural networks (CNN) trained on large graphical processing units (GPU)-based computers with a fairly simple layered network topology, i.e., highly connected layers, without intra-layer connections. Complex topologies have been proposed, but are intractable to train on current systems. Building the topologies of the deep learning network requires hand tuning, and implementing the network in hardware is expensive in both cost and power. In this paper, we evaluate deep learning models using three different computing architectures to address these problems: quantum computing to train complex topologies, high performance computing (HPC) to automatically determinemore » network topology, and neuromorphic computing for a low-power hardware implementation. Due to input size limitations of current quantum computers we use the MNIST dataset for our evaluation. The results show the possibility of using the three architectures in tandem to explore complex deep learning networks that are untrainable using a von Neumann architecture. We show that a quantum computer can find high quality values of intra-layer connections and weights, while yielding a tractable time result as the complexity of the network increases; a high performance computer can find optimal layer-based topologies; and a neuromorphic computer can represent the complex topology and weights derived from the other architectures in low power memristive hardware. This represents a new capability that is not feasible with current von Neumann architecture. It potentially enables the ability to solve very complicated problems unsolvable with current computing technologies.« less

Topological phase transitions and quantum Hall effect in the graphene family

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ledwith, Patrick John; Kort-Kamp, Wilton Junior de Melo; Dalvit, Diego Alejandro Roberto

Monolayer staggered materials of the graphene family present intrinsic spin-orbit coupling and can be driven through several topological phase transitions using external circularly polarized lasers and static electric or magnetic fields. We show how topological features arising from photoinduced phase transitions and the magnetic-field-induced quantum Hall effect coexist in these materials and simultaneously impact their Hall conductivity through their corresponding charge Chern numbers. We also show that the spectral response of the longitudinal conductivity contains signatures of the various phase-transition boundaries, that the transverse conductivity encodes information about the topology of the band structure, and that both present resonant peaksmore » which can be unequivocally associated with one of the four inequivalent Dirac cones present in these materials. As a result, this complex optoelectronic response can be probed with straightforward Faraday rotation experiments, allowing the study of the crossroads between quantum Hall physics, spintronics, and valleytronics.« less

Quantum simulation of 2D topological physics in a 1D array of optical cavities

PubMed Central

Luo, Xi-Wang; Zhou, Xingxiang; Li, Chuan-Feng; Xu, Jin-Shi; Guo, Guang-Can; Zhou, Zheng-Wei

2015-01-01

Orbital angular momentum of light is a fundamental optical degree of freedom characterized by unlimited number of available angular momentum states. Although this unique property has proved invaluable in diverse recent studies ranging from optical communication to quantum information, it has not been considered useful or even relevant for simulating nontrivial physics problems such as topological phenomena. Contrary to this misconception, we demonstrate the incredible value of orbital angular momentum of light for quantum simulation by showing theoretically how it allows to study a variety of important 2D topological physics in a 1D array of optical cavities. This application for orbital angular momentum of light not only reduces required physical resources but also increases feasible scale of simulation, and thus makes it possible to investigate important topics such as edge-state transport and topological phase transition in a small simulator ready for immediate experimental exploration. PMID:26145177

Adiabatic photo-steering theory in topological insulators.

PubMed

Inoue, Jun-Ichi

2014-12-01

Feasible external control of material properties is a crucial issue in condensed matter physics. A new approach to achieving this aim, named adiabatic photo-steering, is reviewed. The core principle of this scheme is that several material constants are effectively turned into externally tunable variables by irradiation of monochromatic laser light. Two-dimensional topological insulators are selected as the optimal systems that exhibit a prominent change in their properties following the application of this method. Two specific examples of photo-steered quantum phenomena, which reflect topological aspects of the electronic systems at hand, are presented. One is the integer quantum Hall effect described by the Haldane model, and the other is the quantum spin Hall effect described by the Kane-Mele model. The topological quantities associated with these phenomena are the conventional Chern number and spin Chern number, respectively. A recent interesting idea, time-reversal symmetry breaking via a temporary periodic external stimulation, is also discussed.

Adiabatic photo-steering theory in topological insulators

NASA Astrophysics Data System (ADS)

Inoue, Jun-ichi

2014-12-01

Feasible external control of material properties is a crucial issue in condensed matter physics. A new approach to achieving this aim, named adiabatic photo-steering, is reviewed. The core principle of this scheme is that several material constants are effectively turned into externally tunable variables by irradiation of monochromatic laser light. Two-dimensional topological insulators are selected as the optimal systems that exhibit a prominent change in their properties following the application of this method. Two specific examples of photo-steered quantum phenomena, which reflect topological aspects of the electronic systems at hand, are presented. One is the integer quantum Hall effect described by the Haldane model, and the other is the quantum spin Hall effect described by the Kane-Mele model. The topological quantities associated with these phenomena are the conventional Chern number and spin Chern number, respectively. A recent interesting idea, time-reversal symmetry breaking via a temporary periodic external stimulation, is also discussed.

Topological superfluids with finite-momentum pairing and Majorana fermions.

PubMed

Qu, Chunlei; Zheng, Zhen; Gong, Ming; Xu, Yong; Mao, Li; Zou, Xubo; Guo, Guangcan; Zhang, Chuanwei

2013-01-01

Majorana fermions (MFs), quantum particles that are their own antiparticles, are not only of fundamental importance in elementary particle physics and dark matter, but also building blocks for fault-tolerant quantum computation. Recently MFs have been intensively studied in solid state and cold atomic systems. These studies are generally based on superconducting pairing with zero total momentum. On the other hand, finite total momentum Cooper pairings, known as Fulde-Ferrell (FF) Larkin-Ovchinnikov (LO) states, were widely studied in many branches of physics. However, whether FF and LO superconductors can support MFs has not been explored. Here we show that MFs can exist in certain types of gapped FF states, yielding a new quantum matter: topological FF superfluids/superconductors. We demonstrate the existence of such topological FF superfluids and the associated MFs using spin-orbit-coupled degenerate Fermi gases and derive their parameter regions. The implementation of topological FF superconductors in semiconductor/superconductor heterostructures is also discussed.

Quantum simulation of 2D topological physics in a 1D array of optical cavities.

PubMed

Luo, Xi-Wang; Zhou, Xingxiang; Li, Chuan-Feng; Xu, Jin-Shi; Guo, Guang-Can; Zhou, Zheng-Wei

2015-07-06

Orbital angular momentum of light is a fundamental optical degree of freedom characterized by unlimited number of available angular momentum states. Although this unique property has proved invaluable in diverse recent studies ranging from optical communication to quantum information, it has not been considered useful or even relevant for simulating nontrivial physics problems such as topological phenomena. Contrary to this misconception, we demonstrate the incredible value of orbital angular momentum of light for quantum simulation by showing theoretically how it allows to study a variety of important 2D topological physics in a 1D array of optical cavities. This application for orbital angular momentum of light not only reduces required physical resources but also increases feasible scale of simulation, and thus makes it possible to investigate important topics such as edge-state transport and topological phase transition in a small simulator ready for immediate experimental exploration.

Topological phase transitions and quantum Hall effect in the graphene family

NASA Astrophysics Data System (ADS)

Ledwith, P.; Kort-Kamp, W. J. M.; Dalvit, D. A. R.

2018-04-01

Monolayer staggered materials of the graphene family present intrinsic spin-orbit coupling and can be driven through several topological phase transitions using external circularly polarized lasers and static electric or magnetic fields. We show how topological features arising from photoinduced phase transitions and the magnetic-field-induced quantum Hall effect coexist in these materials and simultaneously impact their Hall conductivity through their corresponding charge Chern numbers. We also show that the spectral response of the longitudinal conductivity contains signatures of the various phase-transition boundaries, that the transverse conductivity encodes information about the topology of the band structure, and that both present resonant peaks which can be unequivocally associated with one of the four inequivalent Dirac cones present in these materials. This complex optoelectronic response can be probed with straightforward Faraday rotation experiments, allowing the study of the crossroads between quantum Hall physics, spintronics, and valleytronics.

Topological phase transitions and quantum Hall effect in the graphene family

DOE PAGES

Ledwith, Patrick John; Kort-Kamp, Wilton Junior de Melo; Dalvit, Diego Alejandro Roberto

2018-04-15

Monolayer staggered materials of the graphene family present intrinsic spin-orbit coupling and can be driven through several topological phase transitions using external circularly polarized lasers and static electric or magnetic fields. We show how topological features arising from photoinduced phase transitions and the magnetic-field-induced quantum Hall effect coexist in these materials and simultaneously impact their Hall conductivity through their corresponding charge Chern numbers. We also show that the spectral response of the longitudinal conductivity contains signatures of the various phase-transition boundaries, that the transverse conductivity encodes information about the topology of the band structure, and that both present resonant peaksmore » which can be unequivocally associated with one of the four inequivalent Dirac cones present in these materials. As a result, this complex optoelectronic response can be probed with straightforward Faraday rotation experiments, allowing the study of the crossroads between quantum Hall physics, spintronics, and valleytronics.« less

Surface Majorana fermions and bulk collective modes in superfluid 3He-B

NASA Astrophysics Data System (ADS)

Park, YeJe; Chung, Suk Bum; Maciejko, Joseph

2015-02-01

The theoretical study of topological superfluids and superconductors has so far been carried out largely as a translation of the theory of noninteracting topological insulators into the superfluid language, whereby one replaces electrons by Bogoliubov quasiparticles and single-particle band Hamiltonians by Bogoliubov-de Gennes Hamiltonians. Band insulators and superfluids are, however, fundamentally different: While the former exist in the absence of interparticle interactions, the latter are broken symmetry states that owe their very existence to such interactions. In particular, unlike the static energy gap of a band insulator, the gap in a superfluid is due to a dynamical order parameter that is subject to both thermal and quantum fluctuations. In this work, we explore the consequences of bulk quantum fluctuations of the order parameter in the B phase of superfluid 3He on the topologically protected Majorana surface states. Neglecting the high-energy amplitude modes, we find that one of the three spin-orbit Goldstone modes in 3He-B couples to the surface Majorana fermions. This coupling in turn induces an effective short-range two-body interaction between the Majorana fermions, with coupling constant inversely proportional to the strength of the nuclear dipole-dipole interaction in bulk 3He. A mean-field theory suggests that the surface Majorana fermions in 3He-B may be in the vicinity of a metastable gapped time-reversal-symmetry-breaking phase.

Modelling of nanoscale quantum tunnelling structures using algebraic topology method

NASA Astrophysics Data System (ADS)

Sankaran, Krishnaswamy; Sairam, B.

2018-05-01

We have modelled nanoscale quantum tunnelling structures using Algebraic Topology Method (ATM). The accuracy of ATM is compared to the analytical solution derived based on the wave nature of tunnelling electrons. ATM provides a versatile, fast, and simple model to simulate complex structures. We are currently expanding the method for modelling electrodynamic systems.

Weakly-coupled quasi-1D helical modes in disordered 3D topological insulator quantum wires

NASA Astrophysics Data System (ADS)

Dufouleur, J.; Veyrat, L.; Dassonneville, B.; Xypakis, E.; Bardarson, J. H.; Nowka, C.; Hampel, S.; Schumann, J.; Eichler, B.; Schmidt, O. G.; Büchner, B.; Giraud, R.

2017-04-01

Disorder remains a key limitation in the search for robust signatures of topological superconductivity in condensed matter. Whereas clean semiconducting quantum wires gave promising results discussed in terms of Majorana bound states, disorder makes the interpretation more complex. Quantum wires of 3D topological insulators offer a serious alternative due to their perfectly-transmitted mode. An important aspect to consider is the mixing of quasi-1D surface modes due to the strong degree of disorder typical for such materials. Here, we reveal that the energy broadening γ of such modes is much smaller than their energy spacing Δ, an unusual result for highly-disordered mesoscopic nanostructures. This is evidenced by non-universal conductance fluctuations in highly-doped and disordered Bi2Se3 and Bi2Te3 nanowires. Theory shows that such a unique behavior is specific to spin-helical Dirac fermions with strong quantum confinement, which retain ballistic properties over an unusually large energy scale due to their spin texture. Our result confirms their potential to investigate topological superconductivity without ambiguity despite strong disorder.

Weakly-coupled quasi-1D helical modes in disordered 3D topological insulator quantum wires

PubMed Central

Dufouleur, J.; Veyrat, L.; Dassonneville, B.; Xypakis, E.; Bardarson, J. H.; Nowka, C.; Hampel, S.; Schumann, J.; Eichler, B.; Schmidt, O. G.; Büchner, B.; Giraud, R.

2017-01-01

Disorder remains a key limitation in the search for robust signatures of topological superconductivity in condensed matter. Whereas clean semiconducting quantum wires gave promising results discussed in terms of Majorana bound states, disorder makes the interpretation more complex. Quantum wires of 3D topological insulators offer a serious alternative due to their perfectly-transmitted mode. An important aspect to consider is the mixing of quasi-1D surface modes due to the strong degree of disorder typical for such materials. Here, we reveal that the energy broadening γ of such modes is much smaller than their energy spacing Δ, an unusual result for highly-disordered mesoscopic nanostructures. This is evidenced by non-universal conductance fluctuations in highly-doped and disordered Bi2Se3 and Bi2Te3 nanowires. Theory shows that such a unique behavior is specific to spin-helical Dirac fermions with strong quantum confinement, which retain ballistic properties over an unusually large energy scale due to their spin texture. Our result confirms their potential to investigate topological superconductivity without ambiguity despite strong disorder. PMID:28374744

Triangular Quantum Loop Topography for Machine Learning

NASA Astrophysics Data System (ADS)

Zhang, Yi; Kim, Eun-Ah

Despite rapidly growing interest in harnessing machine learning in the study of quantum many-body systems there has been little success in training neural networks to identify topological phases. The key challenge is in efficiently extracting essential information from the many-body Hamiltonian or wave function and turning the information into an image that can be fed into a neural network. When targeting topological phases, this task becomes particularly challenging as topological phases are defined in terms of non-local properties. Here we introduce triangular quantum loop (TQL) topography: a procedure of constructing a multi-dimensional image from the ''sample'' Hamiltonian or wave function using two-point functions that form triangles. Feeding the TQL topography to a fully-connected neural network with a single hidden layer, we demonstrate that the architecture can be effectively trained to distinguish Chern insulator and fractional Chern insulator from trivial insulators with high fidelity. Given the versatility of the TQL topography procedure that can handle different lattice geometries, disorder, interaction and even degeneracy our work paves the route towards powerful applications of machine learning in the study of topological quantum matters.

Weakly-coupled quasi-1D helical modes in disordered 3D topological insulator quantum wires.

PubMed

Dufouleur, J; Veyrat, L; Dassonneville, B; Xypakis, E; Bardarson, J H; Nowka, C; Hampel, S; Schumann, J; Eichler, B; Schmidt, O G; Büchner, B; Giraud, R

2017-04-04

Disorder remains a key limitation in the search for robust signatures of topological superconductivity in condensed matter. Whereas clean semiconducting quantum wires gave promising results discussed in terms of Majorana bound states, disorder makes the interpretation more complex. Quantum wires of 3D topological insulators offer a serious alternative due to their perfectly-transmitted mode. An important aspect to consider is the mixing of quasi-1D surface modes due to the strong degree of disorder typical for such materials. Here, we reveal that the energy broadening γ of such modes is much smaller than their energy spacing Δ, an unusual result for highly-disordered mesoscopic nanostructures. This is evidenced by non-universal conductance fluctuations in highly-doped and disordered Bi2Se3 and Bi 2 Te 3 nanowires. Theory shows that such a unique behavior is specific to spin-helical Dirac fermions with strong quantum confinement, which retain ballistic properties over an unusually large energy scale due to their spin texture. Our result confirms their potential to investigate topological superconductivity without ambiguity despite strong disorder.

Two-dimensional ferroelectric topological insulators in functionalized atomically thin bismuth layers

NASA Astrophysics Data System (ADS)

Kou, Liangzhi; Fu, Huixia; Ma, Yandong; Yan, Binghai; Liao, Ting; Du, Aijun; Chen, Changfeng

2018-02-01

We introduce a class of two-dimensional (2D) materials that possess coexisting ferroelectric and topologically insulating orders. Such ferroelectric topological insulators (FETIs) occur in noncentrosymmetric atomic layer structures with strong spin-orbit coupling (SOC). We showcase a prototype 2D FETI in an atomically thin bismuth layer functionalized by C H2OH , which exhibits a large ferroelectric polarization that is switchable by a ligand molecule rotation mechanism and a strong SOC that drives a band inversion leading to the topologically insulating state. An external electric field that switches the ferroelectric polarization also tunes the spin texture in the underlying atomic lattice. Moreover, the functionalized bismuth layer exhibits an additional quantum order driven by the valley splitting at the K and K' points in the Brillouin zone stemming from the symmetry breaking and strong SOC in the system, resulting in a remarkable state of matter with the simultaneous presence of the quantum spin Hall and quantum valley Hall effect. These phenomena are predicted to exist in other similarly constructed 2D FETIs, thereby offering a unique quantum material platform for discovering novel physics and exploring innovative applications.

Quantum algorithms for topological and geometric analysis of data

PubMed Central

Lloyd, Seth; Garnerone, Silvano; Zanardi, Paolo

2016-01-01

Extracting useful information from large data sets can be a daunting task. Topological methods for analysing data sets provide a powerful technique for extracting such information. Persistent homology is a sophisticated tool for identifying topological features and for determining how such features persist as the data is viewed at different scales. Here we present quantum machine learning algorithms for calculating Betti numbers—the numbers of connected components, holes and voids—in persistent homology, and for finding eigenvectors and eigenvalues of the combinatorial Laplacian. The algorithms provide an exponential speed-up over the best currently known classical algorithms for topological data analysis. PMID:26806491

Sensitivity of quantum walks to a boundary of two-dimensional lattices: approaches based on the CGMV method and topological phases

NASA Astrophysics Data System (ADS)

Endo, Takako; Konno, Norio; Obuse, Hideaki; Segawa, Etsuo

2017-11-01

In this paper, we treat quantum walks in a two-dimensional lattice with cutting edges along a straight boundary introduced by Asboth and Edge (2015 Phys. Rev. A 91 022324) in order to study one-dimensional edge states originating from topological phases of matter and to obtain collateral evidence of how a quantum walker reacts to the boundary. Firstly, we connect this model to the CMV matrix, which provides a 5-term recursion relation of the Laurent polynomial associated with spectral measure on the unit circle. Secondly, we explicitly derive the spectra of bulk and edge states of the quantum walk with the boundary using spectral analysis of the CMV matrix. Thirdly, while topological numbers of the model studied so far are well-defined only when gaps in the bulk spectrum exist, we find a new topological number defined only when there are no gaps in the bulk spectrum. We confirm that the existence of the spectrum for edge states derived from the CMV matrix is consistent with the prediction from a bulk-edge correspondence using topological numbers calculated in the cases where gaps in the bulk spectrum do or do not exist. Finally, we show how the edge states contribute to the asymptotic behavior of the quantum walk through limit theorems of the finding probability. Conversely, we also propose a differential equation using this limit distribution whose solution is the underlying edge state.

Magnetic quantum phase transition in Cr-doped Bi2(SexTe1-x)3 driven by the Stark effect

NASA Astrophysics Data System (ADS)

Zhang, Zuocheng; Feng, Xiao; Wang, Jing; Lian, Biao; Zhang, Jinsong; Chang, Cuizu; Guo, Minghua; Ou, Yunbo; Feng, Yang; Zhang, Shou-Cheng; He, Ke; Ma, Xucun; Xue, Qi-Kun; Wang, Yayu

2017-10-01

The recent experimental observation of the quantum anomalous Hall effect has cast significant attention on magnetic topological insulators. In these magnetic counterparts of conventional topological insulators such as Bi2Te3, a long-range ferromagnetic state can be established by chemical doping with transition-metal elements. However, a much richer electronic phase diagram can emerge and, in the specific case of Cr-doped Bi2(SexTe1-x)3, a magnetic quantum phase transition tuned by the actual chemical composition has been reported. From an application-oriented perspective, the relevance of these results hinges on the possibility to manipulate magnetism and electronic band topology by external perturbations such as an electric field generated by gate electrodes—similar to what has been achieved in conventional diluted magnetic semiconductors. Here, we investigate the magneto-transport properties of Cr-doped Bi2(SexTe1-x)3 with different compositions under the effect of a gate voltage. The electric field has a negligible effect on magnetic order for all investigated compositions, with the remarkable exception of the sample close to the topological quantum critical point, where the gate voltage reversibly drives a ferromagnetic-to-paramagnetic phase transition. Theoretical calculations show that a perpendicular electric field causes a shift in the electronic energy levels due to the Stark effect, which induces a topological quantum phase transition and, in turn, a magnetic phase transition.

Coherent inflationary dynamics for Bose-Einstein condensates crossing a quantum critical point

NASA Astrophysics Data System (ADS)

Feng, Lei; Clark, Logan W.; Gaj, Anita; Chin, Cheng

2018-03-01

Quantum phase transitions, transitions between many-body ground states, are of extensive interest in research ranging from condensed-matter physics to cosmology1-4. Key features of the phase transitions include a stage with rapidly growing new order, called inflation in cosmology5, followed by the formation of topological defects6-8. How inflation is initiated and evolves into topological defects remains a hot topic of debate. Ultracold atomic gas offers a pristine and tunable platform to investigate quantum critical dynamics9-21. We report the observation of coherent inflationary dynamics across a quantum critical point in driven Bose-Einstein condensates. The inflation manifests in the exponential growth of density waves and populations in well-resolved momentum states. After the inflation stage, extended coherent dynamics is evident in both real and momentum space. We present an intuitive description of the quantum critical dynamics in our system and demonstrate the essential role of phase fluctuations in the formation of topological defects.

Effects of Structural and Electronic Disorder in Topological Insulator Sb2Te3 Thin Films

NASA Astrophysics Data System (ADS)

Korzhovska, Inna

Topological quantum matter is a unique and potentially transformative protectorate against disorder-induced backscattering. The ultimate disorder limits to the topological state, however, are still not known - understanding these limits is critical to potential applications in the fields of spintronics and information processing. In topological insulators spin-orbit interaction and time-reversal-symmetry invariance guarantees - at least up to a certain disorder strength - that charge transport through 2D gapless Dirac surface states is robust against backscattering by non-magnetic disorder. Strong disorder may destroy topological protection and gap out Dirac surface states, although recent theories predict that under severe electronic disorder a quantized topological conductance might yet reemerge. Very strong electronic disorder, however, is not trivial to install and quantify, and topological matter under such conditions thus far has not been experimentally tested. This thesis addresses the behavior of three-dimensional (3D) topological insulator (TI) films in a wide range of structural and electronic disorder. We establish strong positional disorder in thin (20-50 nm) Sb2Te 3 films, free of extrinsic magnetic dopants. Sb 2Te3 is a known 2nd generation topological insulator in the low-disorder crystalline state. It is also a known phase-change material that undergoes insulator-to-metal transition with the concurrent orders of magnitude resistive drop, where a huge range of disorder could be controllably explored. In this work we show that even in the absence of magnetic dopants, disorder may induce spin correlations detrimental to the topological state. Chapter 1 contains a brief introduction to the topological matter and describes the role played by disorder. This is followed by theory considerations and a survey of prior experimental work. Next we describe the motivation for our experiments and explain the choice of the material. Chapter 2 describes deposition techniques used for material growth, including the parameters significance and effects on the material properties. Chapter 3 describes structural and electrical characterization techniques employed in the work. In Chapter 4-5 we discuss the experimental results. Sb2Te 3 films at extreme disorder, where spin correlations dominate the transport of charge, are discussed in Chapter 4. We employ transport measurements as our main tool to explore disorder-induced changes in the Sb2Te 3. In addition we directly detect disorder-induced spin response in thin Sb2Te3 films free of extrinsic magnetic dopants; it onsets at a surprisingly high temperature ( 200 K) and vanishes when disorder is reduced. Localized spins control the hopping (tunneling) transport through spin memory induced by the non-equilibrium charge currents. The observed spin-memory phenomenon emerges as negative magnetoresistance distinct from orbital quantum interference effects. The hopping mechanism and spin correlations dominate transport over an extensive disorder range. Spin correlations are eventually suppressed by the restoration of positional order in the (bulk) crystalline state, implying a disorder threshold to the topological state. As disorder is reduced the material undergoes structural and electronic transitions, which are discussed in Chapter 5. We obtain a number of characteristic attributes that change sharply at the structural and electronic transitions: localization length, dimensionality, and the nature of conductance. Structural transition is clearly seen in the changes in lattice vibrations tracked by Raman spectroscopy, which we use here as a metric of disorder. The significance of the disorder-induced localization transition is discussed. Next we investigate the effects of structural and electronic disorder on the bulk and surfaces in the crystalline state of Sb2Te3. The nontrivial topology of this strongly spin-orbit coupled material comes from the band inversion in the bulk. One of the key transport signatures of topological surfaces is weak antilocalization (WAL) correction to conductivity; it is associated with the topological pi Berry phase and should display a two-dimensional (2D) character. In our work, we establish the disorder level at which 2D WAL appears. The conduction at this threshold is one conduction quantum G0; it corresponds to the topological quantum channel. Finally, we summarize our key findings and discuss open questions and next steps toward the understanding of disorder-induced correlations in the spin and charge channels that can alter the emergent behaviors of the topological states.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tsvelik, A. M.; Yevtushenko, O. M.

We study the low energy physics of a Kondo chain where electrons from a one-dimensional band interact with magnetic moments via an anisotropic exchange interaction. It is demonstrated that the anisotropy gives rise to two different phases which are separated by a quantum phase transition. In the phase with easy plane anisotropy, Z2 symmetry between sectors with different helicity of the electrons is broken. As a result, localization effects are suppressed and the dc transport acquires (partial) symmetry protection. This effect is similar to the protection of the edge transport in time-reversal invariant topological insulators. The phase with easy axismore » anisotropy corresponds to the Tomonaga-Luttinger liquid with a pronounced spin-charge separation. The slow charge density wave modes have no protection against localizatioin.« less

Quadratic Fermi node in a 3D strongly correlated semimetal

PubMed Central

Kondo, Takeshi; Nakayama, M.; Chen, R.; Ishikawa, J. J.; Moon, E.-G.; Yamamoto, T.; Ota, Y.; Malaeb, W.; Kanai, H.; Nakashima, Y.; Ishida, Y.; Yoshida, R.; Yamamoto, H.; Matsunami, M.; Kimura, S.; Inami, N.; Ono, K.; Kumigashira, H.; Nakatsuji, S.; Balents, L.; Shin, S.

2015-01-01

Strong spin–orbit coupling fosters exotic electronic states such as topological insulators and superconductors, but the combination of strong spin–orbit and strong electron–electron interactions is just beginning to be understood. Central to this emerging area are the 5d transition metal iridium oxides. Here, in the pyrochlore iridate Pr2Ir2O7, we identify a non-trivial state with a single-point Fermi node protected by cubic and time-reversal symmetries, using a combination of angle-resolved photoemission spectroscopy and first-principles calculations. Owing to its quadratic dispersion, the unique coincidence of four degenerate states at the Fermi energy, and strong Coulomb interactions, non-Fermi liquid behaviour is predicted, for which we observe some evidence. Our discovery implies that Pr2Ir2O7 is a parent state that can be manipulated to produce other strongly correlated topological phases, such as topological Mott insulator, Weyl semimetal, and quantum spin and anomalous Hall states. PMID:26640114

Quadratic Fermi node in a 3D strongly correlated semimetal

DOE PAGES

Kondo, Takeshi; Nakayama, M.; Chen, R.; ...

2015-12-07

We report that strong spin–orbit coupling fosters exotic electronic states such as topological insulators and superconductors, but the combination of strong spin–orbit and strong electron–electron interactions is just beginning to be understood. Central to this emerging area are the 5d transition metal iridium oxides. Here, in the pyrochlore iridate Pr 2Ir 2O 7, we identify a non-trivial state with a single-point Fermi node protected by cubic and time-reversal symmetries, using a combination of angle-resolved photoemission spectroscopy and first-principles calculations. Owing to its quadratic dispersion, the unique coincidence of four degenerate states at the Fermi energy, and strong Coulomb interactions, non-Fermimore » liquid behaviour is predicted, for which we observe some evidence. Lastly, our discovery implies that Pr 2Ir 2O 7 is a parent state that can be manipulated to produce other strongly correlated topological phases, such as topological Mott insulator, Weyl semimetal, and quantum spin and anomalous Hall states.« less

Magnetic-flux-driven topological quantum phase transition and manipulation of perfect edge states in graphene tube.

PubMed

Lin, S; Zhang, G; Li, C; Song, Z

2016-08-24

We study the tight-binding model for a graphene tube with perimeter N threaded by a magnetic field. We show exactly that this model has different nontrivial topological phases as the flux changes. The winding number, as an indicator of topological quantum phase transition (QPT) fixes at N/3 if N/3 equals to its integer part [N/3], otherwise it jumps between [N/3] and [N/3] + 1 periodically as the flux varies a flux quantum. For an open tube with zigzag boundary condition, exact edge states are obtained. There exist two perfect midgap edge states, in which the particle is completely located at the boundary, even for a tube with finite length. The threading flux can be employed to control the quantum states: transferring the perfect edge state from one end to the other, or generating maximal entanglement between them.

Disorder-Enhanced Dielectric Response of Nanoscale and Mesoscopic Insulators

NASA Astrophysics Data System (ADS)

Onoda, Shigeki; Chern, Chyh-Hong; Murakami, Shuichi; Ogimoto, Yasushi; Nagaosa, Naoto

2006-12-01

Enhancement of the dielectric response of insulators by disorder is theoretically proposed, where the quantum interference of electronic waves through the nanoscale or mesoscopic system and its change due to external perturbations control the polarization. In the disordered case with all the states being localized, the resonant tunneling, which is topologically protected, plays a crucial role, and enhances the dielectric response by a factor 30 40 compared with the pure case. The realization of this idea with accessible materials or structures is also discussed.

Nature of Continuous Phase Transitions in Interacting Topological Insulators

DOE PAGES

Zeng, Tian-sheng; Zhu, Wei; Zhu, Jianxin; ...

2017-11-08

Here, we revisit the effects of the Hubbard repulsion on quantum spin Hall effects (QSHE) in two-dimensional quantum lattice models. We present both unbiased exact diagonalization and density-matrix renormalization group simulations with numerical evidence for a continuous quantum phase transition (CQPT) separating QSHE from the topologically trivial antiferromagnetic phase. Our numerical results suggest that the nature of CQPT exhibits distinct finite-size scaling behaviors, which may be consistent with either Ising or XY universality classes for different time-reversal symmetric QSHE systems.

Nature of Continuous Phase Transitions in Interacting Topological Insulators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zeng, Tian-sheng; Zhu, Wei; Zhu, Jianxin

Here, we revisit the effects of the Hubbard repulsion on quantum spin Hall effects (QSHE) in two-dimensional quantum lattice models. We present both unbiased exact diagonalization and density-matrix renormalization group simulations with numerical evidence for a continuous quantum phase transition (CQPT) separating QSHE from the topologically trivial antiferromagnetic phase. Our numerical results suggest that the nature of CQPT exhibits distinct finite-size scaling behaviors, which may be consistent with either Ising or XY universality classes for different time-reversal symmetric QSHE systems.

Oliver E. Buckley Condensed Matter Prize: Quantum-topological phases of matter

NASA Astrophysics Data System (ADS)

Wen, Xiao-Gang

For a long time, we thought that symmetry breaking patterns describe all phases and phase transitions. The featureless disordered liquids correspond to trivial phase. But in fact disordered liquids have very rich features, with amazing emergent phenomena, such as fractional quantum numbers, fractional and non-abelian statistics, perfect conducting boundary even in presence of magnetic impurities, etc. All those are due to many-body entanglement. In this talk, I will first discuss topological phases that have topological order (ie with long range entanglement). Then I will cover topological phases that have no topological order (ie with only short-range entanglement). I will stress on how to understand and describe many-body entanglement, which is a very new phenomenon. This research is supported by NSF Grant No. DMR-1506475.

Disorder-induced transitions in resonantly driven Floquet topological insulators

NASA Astrophysics Data System (ADS)

Titum, Paraj; Lindner, Netanel H.; Refael, Gil

2017-08-01

We investigate the effects of disorder in Floquet topological insulators (FTIs) occurring in semiconductor quantum wells. Such FTIs are induced by resonantly driving a transition between the valence and conduction bands. We show that when disorder is added, the topological nature of such FTIs persists as long as there is a mobility gap at the resonant quasienergy. For strong enough disorder, this gap closes and all the states become localized as the system undergoes a transition to a trivial insulator. Interestingly, the effects of disorder are not necessarily adverse: we show that in the same quantum well, disorder can also induce a transition from a trivial to a topological system, thereby establishing a Floquet topological Anderson insulator (FTAI). We identify the conditions on the driving field necessary for observing such a transition.

Amplitude-dependent topological edge states in nonlinear phononic lattices

NASA Astrophysics Data System (ADS)

Pal, Raj Kumar; Vila, Javier; Leamy, Michael; Ruzzene, Massimo

2018-03-01

This work investigates the effect of nonlinearities on topologically protected edge states in one- and two-dimensional phononic lattices. We first show that localized modes arise at the interface between two spring-mass chains that are inverted copies of each other. Explicit expressions derived for the frequencies of the localized modes guide the study of the effect of cubic nonlinearities on the resonant characteristics of the interface, which are shown to be described by a Duffing-like equation. Nonlinearities produce amplitude-dependent frequency shifts, which in the case of a softening nonlinearity cause the localized mode to migrate to the bulk spectrum. The case of a hexagonal lattice implementing a phononic analog of a crystal exhibiting the quantum spin Hall effect is also investigated in the presence of weakly nonlinear cubic springs. An asymptotic analysis provides estimates of the amplitude dependence of the localized modes, while numerical simulations illustrate how the lattice response transitions from bulk-to-edge mode-dominated by varying the excitation amplitude. In contrast with the interface mode of the first example studies, this occurs both for hardening and softening springs. The results of this study provide a theoretical framework for the investigation of nonlinear effects that induce and control topologically protected wave modes through nonlinear interactions and amplitude tuning.

Janus and Huygens Dipoles: Near-Field Directionality Beyond Spin-Momentum Locking.

PubMed

Picardi, Michela F; Zayats, Anatoly V; Rodríguez-Fortuño, Francisco J

2018-03-16

Unidirectional scattering from circularly polarized dipoles has been demonstrated in near-field optics, where the quantum spin-Hall effect of light translates into spin-momentum locking. By considering the whole electromagnetic field, instead of its spin component alone, near-field directionality can be achieved beyond spin-momentum locking. This unveils the existence of the Janus dipole, with side-dependent topologically protected coupling to waveguides, and reveals the near-field directionality of Huygens dipoles, generalizing Kerker's condition. Circular dipoles, together with Huygens and Janus sources, form the complete set of all possible directional dipolar sources in the far- and near-field. This allows the designing of directional emission, scattering, and waveguiding, fundamental for quantum optical technology, integrated nanophotonics, and new metasurface designs.

Janus and Huygens Dipoles: Near-Field Directionality Beyond Spin-Momentum Locking

NASA Astrophysics Data System (ADS)

Picardi, Michela F.; Zayats, Anatoly V.; Rodríguez-Fortuño, Francisco J.

2018-03-01

Unidirectional scattering from circularly polarized dipoles has been demonstrated in near-field optics, where the quantum spin-Hall effect of light translates into spin-momentum locking. By considering the whole electromagnetic field, instead of its spin component alone, near-field directionality can be achieved beyond spin-momentum locking. This unveils the existence of the Janus dipole, with side-dependent topologically protected coupling to waveguides, and reveals the near-field directionality of Huygens dipoles, generalizing Kerker's condition. Circular dipoles, together with Huygens and Janus sources, form the complete set of all possible directional dipolar sources in the far- and near-field. This allows the designing of directional emission, scattering, and waveguiding, fundamental for quantum optical technology, integrated nanophotonics, and new metasurface designs.

Hamiltonian quantum simulation with bounded-strength controls

NASA Astrophysics Data System (ADS)

Bookatz, Adam D.; Wocjan, Pawel; Viola, Lorenza

2014-04-01

We propose dynamical control schemes for Hamiltonian simulation in many-body quantum systems that avoid instantaneous control operations and rely solely on realistic bounded-strength control Hamiltonians. Each simulation protocol consists of periodic repetitions of a basic control block, constructed as a modification of an ‘Eulerian decoupling cycle,’ that would otherwise implement a trivial (zero) target Hamiltonian. For an open quantum system coupled to an uncontrollable environment, our approach may be employed to engineer an effective evolution that simulates a target Hamiltonian on the system while suppressing unwanted decoherence to the leading order, thereby allowing for dynamically corrected simulation. We present illustrative applications to both closed- and open-system simulation settings, with emphasis on simulation of non-local (two-body) Hamiltonians using only local (one-body) controls. In particular, we provide simulation schemes applicable to Heisenberg-coupled spin chains exposed to general linear decoherence, and show how to simulate Kitaev's honeycomb lattice Hamiltonian starting from Ising-coupled qubits, as potentially relevant to the dynamical generation of a topologically protected quantum memory. Additional implications for quantum information processing are discussed.

Photonic topological boundary pumping as a probe of 4D quantum Hall physics

NASA Astrophysics Data System (ADS)

Zilberberg, Oded; Huang, Sheng; Guglielmon, Jonathan; Wang, Mohan; Chen, Kevin P.; Kraus, Yaacov E.; Rechtsman, Mikael C.

2018-01-01

When a two-dimensional (2D) electron gas is placed in a perpendicular magnetic field, its in-plane transverse conductance becomes quantized; this is known as the quantum Hall effect. It arises from the non-trivial topology of the electronic band structure of the system, where an integer topological invariant (the first Chern number) leads to quantized Hall conductance. It has been shown theoretically that the quantum Hall effect can be generalized to four spatial dimensions, but so far this has not been realized experimentally because experimental systems are limited to three spatial dimensions. Here we use tunable 2D arrays of photonic waveguides to realize a dynamically generated four-dimensional (4D) quantum Hall system experimentally. The inter-waveguide separation in the array is constructed in such a way that the propagation of light through the device samples over momenta in two additional synthetic dimensions, thus realizing a 2D topological pump. As a result, the band structure has 4D topological invariants (known as second Chern numbers) that support a quantized bulk Hall response with 4D symmetry. In a finite-sized system, the 4D topological bulk response is carried by localized edge modes that cross the sample when the synthetic momenta are modulated. We observe this crossing directly through photon pumping of our system from edge to edge and corner to corner. These crossings are equivalent to charge pumping across a 4D system from one three-dimensional hypersurface to the spatially opposite one and from one 2D hyperedge to another. Our results provide a platform for the study of higher-dimensional topological physics.

Photonic topological boundary pumping as a probe of 4D quantum Hall physics.

PubMed

Zilberberg, Oded; Huang, Sheng; Guglielmon, Jonathan; Wang, Mohan; Chen, Kevin P; Kraus, Yaacov E; Rechtsman, Mikael C

2018-01-03

When a two-dimensional (2D) electron gas is placed in a perpendicular magnetic field, its in-plane transverse conductance becomes quantized; this is known as the quantum Hall effect. It arises from the non-trivial topology of the electronic band structure of the system, where an integer topological invariant (the first Chern number) leads to quantized Hall conductance. It has been shown theoretically that the quantum Hall effect can be generalized to four spatial dimensions, but so far this has not been realized experimentally because experimental systems are limited to three spatial dimensions. Here we use tunable 2D arrays of photonic waveguides to realize a dynamically generated four-dimensional (4D) quantum Hall system experimentally. The inter-waveguide separation in the array is constructed in such a way that the propagation of light through the device samples over momenta in two additional synthetic dimensions, thus realizing a 2D topological pump. As a result, the band structure has 4D topological invariants (known as second Chern numbers) that support a quantized bulk Hall response with 4D symmetry. In a finite-sized system, the 4D topological bulk response is carried by localized edge modes that cross the sample when the synthetic momenta are modulated. We observe this crossing directly through photon pumping of our system from edge to edge and corner to corner. These crossings are equivalent to charge pumping across a 4D system from one three-dimensional hypersurface to the spatially opposite one and from one 2D hyperedge to another. Our results provide a platform for the study of higher-dimensional topological physics.

Quantum mechanical probability current as electromagnetic 4-current from topological EM fields

NASA Astrophysics Data System (ADS)

van der Mark, Martin B.

2015-09-01

Starting from a complex 4-potential A = αdβ we show that the 4-current density in electromagnetism and the probability current density in relativistic quantum mechanics are of identical form. With the Dirac-Clifford algebra Cl1,3 as mathematical basis, the given 4-potential allows topological solutions of the fields, quite similar to Bateman's construction, but with a double field solution that was overlooked previously. A more general nullvector condition is found and wave-functions of charged and neutral particles appear as topological configurations of the electromagnetic fields.

Colloidal CdSe Quantum Rings.

PubMed

Fedin, Igor; Talapin, Dmitri V

2016-08-10

Semiconductor quantum rings are of great fundamental interest because their non-trivial topology creates novel physical properties. At the same time, toroidal topology is difficult to achieve for colloidal nanocrystals and epitaxially grown semiconductor nanostructures. In this work, we introduce the synthesis of luminescent colloidal CdSe nanorings and nanostructures with double and triple toroidal topology. The nanorings form during controlled etching and rearrangement of two-dimensional nanoplatelets. We discuss a possible mechanism of the transformation of nanoplatelets into nanorings and potential utility of colloidal nanorings for magneto-optical (e.g., Aharonov-Bohm effect) and other applications.

Numerical studies of the topological Chern numbers in two dimensional electron system

NASA Astrophysics Data System (ADS)

Sheng, Donna

2004-03-01

I will report on the numerical results of the exact calculation of the topological Chern numbers in fractional and bilayer quantum Hall systems[1]. I will show that following the evolution of the Chern numbers as a function of the disorder strength and/or layer separations, various quantum phase transitions as well as the characteristic transport properties of the phases, can be determined. The hidden topological ordering in other two dimensional electron systems will also be discussed. 1. D. N. Sheng et. al., Phys. Rev. Lett. 90, 256802 (2003).

Topological magnon bands and unconventional thermal Hall effect on the frustrated honeycomb and bilayer triangular lattice.

PubMed

Owerre, S A

2017-09-27

In the conventional ferromagnetic systems, topological magnon bands and thermal Hall effect are due to the Dzyaloshinskii-Moriya interaction (DMI). In principle, however, the DMI is either negligible or it is not allowed by symmetry in some quantum magnets. Therefore, we expect that topological magnon features will not be present in those systems. In addition, quantum magnets on the triangular-lattice are not expected to possess topological features as the DMI or spin-chirality cancels out due to equal and opposite contributions from adjacent triangles. Here, however, we predict that the isomorphic frustrated honeycomb-lattice and bilayer triangular-lattice antiferromagnetic system will exhibit topological magnon bands and topological thermal Hall effect in the absence of an intrinsic DMI. These unconventional topological magnon features are present as a result of magnetic-field-induced non-coplanar spin configurations with nonzero scalar spin chirality. The relevance of the results to realistic bilayer triangular antiferromagnetic materials are discussed.

Topological BF field theory description of topological insulators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cho, Gil Young; Moore, Joel E., E-mail: jemoore@berkeley.edu; Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720

2011-06-15

Research Highlights: > We show that a BF theory is the effective theory of 2D and 3D topological insulators. > The non-gauge-invariance of the bulk theory yields surface terms for a bosonized Dirac fermion. > The 'axion' term in electromagnetism is correctly obtained from gapped surfaces. > Generalizations to possible fractional phases are discussed in closing. - Abstract: Topological phases of matter are described universally by topological field theories in the same way that symmetry-breaking phases of matter are described by Landau-Ginzburg field theories. We propose that topological insulators in two and three dimensions are described by a version ofmore » abelian BF theory. For the two-dimensional topological insulator or quantum spin Hall state, this description is essentially equivalent to a pair of Chern-Simons theories, consistent with the realization of this phase as paired integer quantum Hall effect states. The BF description can be motivated from the local excitations produced when a {pi} flux is threaded through this state. For the three-dimensional topological insulator, the BF description is less obvious but quite versatile: it contains a gapless surface Dirac fermion when time-reversal-symmetry is preserved and yields 'axion electrodynamics', i.e., an electromagnetic E . B term, when time-reversal symmetry is broken and the surfaces are gapped. Just as changing the coefficients and charges of 2D Chern-Simons theory allows one to obtain fractional quantum Hall states starting from integer states, BF theory could also describe (at a macroscopic level) fractional 3D topological insulators with fractional statistics of point-like and line-like objects.« less

Can chaos be observed in quantum gravity?

NASA Astrophysics Data System (ADS)

Dittrich, Bianca; Höhn, Philipp A.; Koslowski, Tim A.; Nelson, Mike I.

2017-06-01

Full general relativity is almost certainly 'chaotic'. We argue that this entails a notion of non-integrability: a generic general relativistic model, at least when coupled to cosmologically interesting matter, likely possesses neither differentiable Dirac observables nor a reduced phase space. It follows that the standard notion of observable has to be extended to include non-differentiable or even discontinuous generalized observables. These cannot carry Poisson-algebraic structures and do not admit a standard quantization; one thus faces a quantum representation problem of gravitational observables. This has deep consequences for a quantum theory of gravity, which we investigate in a simple model for a system with Hamiltonian constraint that fails to be completely integrable. We show that basing the quantization on standard topology precludes a semiclassical limit and can even prohibit any solutions to the quantum constraints. Our proposed solution to this problem is to refine topology such that a complete set of Dirac observables becomes continuous. In the toy model, it turns out that a refinement to a polymer-type topology, as e.g. used in loop gravity, is sufficient. Basing quantization of the toy model on this finer topology, we find a complete set of quantum Dirac observables and a suitable semiclassical limit. This strategy is applicable to realistic candidate theories of quantum gravity and thereby suggests a solution to a long-standing problem which implies ramifications for the very concept of quantization. Our work reveals a qualitatively novel facet of chaos in physics and opens up a new avenue of research on chaos in gravity which hints at deep insights into the structure of quantum gravity.

Structural and Galvanomagnetic properties in Mn-Bi2Te3 thin films

NASA Astrophysics Data System (ADS)

Bidinakis, K.; Speliotis, Th.

2017-12-01

Bismuth-based binary chalcogenide compounds such as Bi2Te3 and Bi2Se3 are well known materials for their excellent thermoelectric properties due to their near-gap electronic structure. In the last few years these materials have received attention for exhibiting new physics of 3D topological insulators (TI). Possible applications of TI based devices range from quantum computing, spin based logic and memory to electrodynamics. The 3D TIs present spin-momentum-locked surface states by time reversal symmetry (TRS). Introducing magnetic doping in a TI, brakes the TRS and is predicted to open the gap at Dirac point, resulting in exotic quantum phenomena. This interaction between magnetism and topologically protected states is of potential attention for applications in modern spintronics. Quantum phenomena such as weak antilocalization observed in these nanostructures are described. In this work, granular Mn-Bi2Te3 thin films were grown by DC magnetron sputtering on Si(111) substrates and were submitted to ex situ annealing. We present results for the crystal structure of sputtered and annealed films characterized with X-ray diffraction and high-resolution scanning electron microscopy (HRSEM). The surface analysis was studied with atomic force microscopy (AFM). Magnetotransport measurements were performed using standard four probe technique with Hall and MR configurations, with perpendicular magnetic fields up to 9T and temperatures from 300 to 3K.

Atomic layer-by-layer thermoelectric conversion in topological insulator bismuth/antimony tellurides.

PubMed

Sung, Ji Ho; Heo, Hoseok; Hwang, Inchan; Lim, Myungsoo; Lee, Donghun; Kang, Kibum; Choi, Hee Cheul; Park, Jae-Hoon; Jhi, Seung-Hoon; Jo, Moon-Ho

2014-07-09

Material design for direct heat-to-electricity conversion with substantial efficiency essentially requires cooperative control of electrical and thermal transport. Bismuth telluride (Bi2Te3) and antimony telluride (Sb2Te3), displaying the highest thermoelectric power at room temperature, are also known as topological insulators (TIs) whose electronic structures are modified by electronic confinements and strong spin-orbit interaction in a-few-monolayers thickness regime, thus possibly providing another degree of freedom for electron and phonon transport at surfaces. Here, we explore novel thermoelectric conversion in the atomic monolayer steps of a-few-layer topological insulating Bi2Te3 (n-type) and Sb2Te3 (p-type). Specifically, by scanning photoinduced thermoelectric current imaging at the monolayer steps, we show that efficient thermoelectric conversion is accomplished by optothermal motion of hot electrons (Bi2Te3) and holes (Sb2Te3) through 2D subbands and topologically protected surface states in a geometrically deterministic manner. Our discovery suggests that the thermoelectric conversion can be interiorly achieved at the atomic steps of a homogeneous medium by direct exploiting of quantum nature of TIs, thus providing a new design rule for the compact thermoelectric circuitry at the ultimate size limit.

Topological quantum error correction in the Kitaev honeycomb model

NASA Astrophysics Data System (ADS)

Lee, Yi-Chan; Brell, Courtney G.; Flammia, Steven T.

2017-08-01

The Kitaev honeycomb model is an approximate topological quantum error correcting code in the same phase as the toric code, but requiring only a 2-body Hamiltonian. As a frustrated spin model, it is well outside the commuting models of topological quantum codes that are typically studied, but its exact solubility makes it more amenable to analysis of effects arising in this noncommutative setting than a generic topologically ordered Hamiltonian. Here we study quantum error correction in the honeycomb model using both analytic and numerical techniques. We first prove explicit exponential bounds on the approximate degeneracy, local indistinguishability, and correctability of the code space. These bounds are tighter than can be achieved using known general properties of topological phases. Our proofs are specialized to the honeycomb model, but some of the methods may nonetheless be of broader interest. Following this, we numerically study noise caused by thermalization processes in the perturbative regime close to the toric code renormalization group fixed point. The appearance of non-topological excitations in this setting has no significant effect on the error correction properties of the honeycomb model in the regimes we study. Although the behavior of this model is found to be qualitatively similar to that of the standard toric code in most regimes, we find numerical evidence of an interesting effect in the low-temperature, finite-size regime where a preferred lattice direction emerges and anyon diffusion is geometrically constrained. We expect this effect to yield an improvement in the scaling of the lifetime with system size as compared to the standard toric code.

Toric-boson model: Toward a topological quantum memory at finite temperature

NASA Astrophysics Data System (ADS)

Hamma, Alioscia; Castelnovo, Claudio; Chamon, Claudio

2009-06-01

We discuss the existence of stable topological quantum memory at finite temperature. At stake here is the fundamental question of whether it is, in principle, possible to store quantum information for macroscopic times without the intervention from the external world, that is, without error correction. We study the toric code in two dimensions with an additional bosonic field that couples to the defects, in the presence of a generic environment at finite temperature: the toric-boson model. Although the coupling constants for the bare model are not finite in the thermodynamic limit, the model has a finite spectrum. We show that in the topological phase, there is a finite temperature below which open strings are confined and therefore the lifetime of the memory can be made arbitrarily (polynomially) long in system size. The interaction with the bosonic field yields a long-range attractive force between the end points of open strings but leaves closed strings and topological order intact.

Stable topological insulators achieved using high energy electron beams

PubMed Central

Zhao, Lukas; Konczykowski, Marcin; Deng, Haiming; Korzhovska, Inna; Begliarbekov, Milan; Chen, Zhiyi; Papalazarou, Evangelos; Marsi, Marino; Perfetti, Luca; Hruban, Andrzej; Wołoś, Agnieszka; Krusin-Elbaum, Lia

2016-01-01

Topological insulators are potentially transformative quantum solids with metallic surface states which have Dirac band structure and are immune to disorder. Ubiquitous charged bulk defects, however, pull the Fermi energy into the bulk bands, denying access to surface charge transport. Here we demonstrate that irradiation with swift (∼2.5 MeV energy) electron beams allows to compensate these defects, bring the Fermi level back into the bulk gap and reach the charge neutrality point (CNP). Controlling the beam fluence, we tune bulk conductivity from p- (hole-like) to n-type (electron-like), crossing the Dirac point and back, while preserving the Dirac energy dispersion. The CNP conductance has a two-dimensional character on the order of ten conductance quanta and reveals, both in Bi2Te3 and Bi2Se3, the presence of only two quantum channels corresponding to two topological surfaces. The intrinsic quantum transport of the topological states is accessible disregarding the bulk size. PMID:26961901

Anomalous quantum diffusion and the topological metal

NASA Astrophysics Data System (ADS)

Tian, Chushun

2012-09-01

Electron wave scattering off disorders provides a key to many fascinating transport phenomena recently observed in topological insulators. Here, we present a nonperturbative diagrammatic theory of this subject. Surprisingly, quantum superdiffusion is found on the surface of three-dimensional strong topological insulators regardless of disorder strength (but not vanishing), where the diffusion coefficient grows in time logarithmically. Such a transport anomaly serves as a main characteristic of the novel quantum metal, the so-called “topological metal,” and indicates that it is a hybridization of Ohmic and perfect metals. It washes out the Anderson transition occurring in two-dimensional normal metals with disordered spin-orbit coupling, and leads to a logarithmic divergence of the conductance in the sample size instead. Therefore, the present work provides an analytical proof of the transport anomaly discovered numerically [Nomura, Koshino, and Ryu, Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.99.146806 99, 146806 (2007); Bardarson , Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.99.106801 99, 106801 (2007)].

Study of anyon condensation and topological phase transitions from a Z4 topological phase using the projected entangled pair states approach

NASA Astrophysics Data System (ADS)

Iqbal, Mohsin; Duivenvoorden, Kasper; Schuch, Norbert

2018-05-01

We use projected entangled pair states (PEPS) to study topological quantum phase transitions. The local description of topological order in the PEPS formalism allows us to set up order parameters which measure condensation and deconfinement of anyons and serve as substitutes for conventional order parameters. We apply these order parameters, together with anyon-anyon correlation functions and some further probes, to characterize topological phases and phase transitions within a family of models based on a Z4 symmetry, which contains Z4 quantum double, toric code, double semion, and trivial phases. We find a diverse phase diagram which exhibits a variety of different phase transitions of both first and second order which we comprehensively characterize, including direct transitions between the toric code and the double semion phase.

Topological networks for quantum communication between distant qubits

NASA Astrophysics Data System (ADS)

Lang, Nicolai; Büchler, Hans Peter

2017-11-01

Efficient communication between qubits relies on robust networks, which allow for fast and coherent transfer of quantum information. It seems natural to harvest the remarkable properties of systems characterized by topological invariants to perform this task. Here, we show that a linear network of coupled bosonic degrees of freedom, characterized by topological bands, can be employed for the efficient exchange of quantum information over large distances. Important features of our setup are that it is robust against quenched disorder, all relevant operations can be performed by global variations of parameters, and the time required for communication between distant qubits approaches linear scaling with their distance. We demonstrate that our concept can be extended to an ensemble of qubits embedded in a two-dimensional network to allow for communication between all of them.

Snake states and their symmetries in graphene

NASA Astrophysics Data System (ADS)

Liu, Yang; Tiwari, Rakesh P.; Brada, Matej; Bruder, C.; Kusmartsev, F. V.; Mele, E. J.

2015-12-01

Snake states are open trajectories for charged particles propagating in two dimensions under the influence of a spatially varying perpendicular magnetic field. In the quantum limit they are protected edge modes that separate topologically inequivalent ground states and can also occur when the particle density rather than the field is made nonuniform. We examine the correspondence of snake trajectories in single-layer graphene in the quantum limit for two families of domain walls: (a) a uniform doped carrier density in an antisymmetric field profile and (b) antisymmetric carrier distribution in a uniform field. These families support different internal symmetries but the same pattern of boundary and interface currents. We demonstrate that these physically different situations are gauge equivalent when rewritten in a Nambu doubled formulation of the two limiting problems. Using gauge transformations in particle-hole space to connect these problems, we map the protected interfacial modes to the Bogoliubov quasiparticles of an interfacial one-dimensional p -wave paired state. A variational model is introduced to interpret the interfacial solutions of both domain wall problems.

Topological invariant and cotranslational symmetry in strongly interacting multi-magnon systems

NASA Astrophysics Data System (ADS)

Qin, Xizhou; Mei, Feng; Ke, Yongguan; Zhang, Li; Lee, Chaohong

2018-01-01

It is still an outstanding challenge to characterize and understand the topological features of strongly interacting states such as bound states in interacting quantum systems. Here, by introducing a cotranslational symmetry in an interacting multi-particle quantum system, we systematically develop a method to define a Chern invariant, which is a generalization of the well-known Thouless-Kohmoto-Nightingale-den Nijs invariant, for identifying strongly interacting topological states. As an example, we study the topological multi-magnon states in a generalized Heisenberg XXZ model, which can be realized by the currently available experiment techniques of cold atoms (Aidelsburger et al 2013 Phys. Rev. Lett. 111, 185301; Miyake et al 2013 Phys. Rev. Lett. 111, 185302). Through calculating the two-magnon excitation spectrum and the defined Chern number, we explore the emergence of topological edge bound states and give their topological phase diagram. We also analytically derive an effective single-particle Hofstadter superlattice model for a better understanding of the topological bound states. Our results not only provide a new approach to defining a topological invariant for interacting multi-particle systems, but also give insights into the characterization and understanding of strongly interacting topological states.

Entanglement from topology in Chern-Simons theory

NASA Astrophysics Data System (ADS)

Salton, Grant; Swingle, Brian; Walter, Michael

2017-05-01

The way in which geometry encodes entanglement is a topic of much recent interest in quantum many-body physics and the AdS/CFT duality. This relation is particularly pronounced in the case of topological quantum field theories, where topology alone determines the quantum states of the theory. In this work, we study the set of quantum states that can be prepared by the Euclidean path integral in three-dimensional Chern-Simons theory. Specifically, we consider arbitrary three-manifolds with a fixed number of torus boundaries in both Abelian U (1 ) and non-Abelian S O (3 ) Chern-Simons theory. For the Abelian theory, we find that the states that can be prepared coincide precisely with the set of stabilizer states from quantum information theory. This constrains the multipartite entanglement present in this theory, but it also reveals that stabilizer states can be described by topology. In particular, we find an explicit expression for the entanglement entropy of a many-torus subsystem using only a single replica, as well as a concrete formula for the number of GHZ states that can be distilled from a tripartite state prepared through path integration. For the non-Abelian theory, we find a notion of "state universality," namely that any state can be prepared to an arbitrarily good approximation. The manifolds we consider can also be viewed as toy models of multiboundary wormholes in AdS/CFT.

Influence of magnetic disorders on quantum anomalous Hall effect in magnetic topological insulator films beyond the two-dimensional limit

NASA Astrophysics Data System (ADS)

Xing, Yanxia; Xu, Fuming; Cheung, King Tai; Sun, Qing-feng; Wang, Jian; Yao, Yugui

2018-04-01

Quantum anomalous Hall effect (QAHE) has been experimentally realized in magnetic topological insulator (MTI) thin films fabricated on magnetically doped {({{Bi}},{{Sb}})}2{{{Te}}}3. In an MTI thin film with the magnetic easy axis along the normal direction (z-direction), orientations of magnetic dopants are randomly distributed around the magnetic easy axis, acting as magnetic disorders. With the aid of the non-equilibrium Green's function and Landauer–Büttiker formalism, we numerically study the influence of magnetic disorders on QAHE in an MTI thin film modeled by a three-dimensional tight-binding Hamiltonian. It is found that, due to the existence of gapless side surface states, QAHE is protected even in the presence of magnetic disorders as long as the z-component of magnetic moment of all magnetic dopants are positive. More importantly, such magnetic disorders also suppress the dissipation of the chiral edge states and enhance the quality of QAHE in MTI films. In addition, the effect of magnetic disorders depends very much on the film thickness, and the optimal influence is achieved at certain thickness. These findings are new features for QAHE in three-dimensional systems, not present in two-dimensional systems.

Thin film three-dimensional topological insulator metal-oxide-semiconductor field-effect-transistors: A candidate for sub-10 nm devices

DOE Office of Scientific and Technical Information (OSTI.GOV)

Akhavan, N. D., E-mail: nima.dehdashti@uwa.edu.au; Jolley, G.; Umana-Membreno, G. A.

2014-08-28

Three-dimensional (3D) topological insulators (TI) are a new state of quantum matter in which surface states reside in the bulk insulating energy bandgap and are protected by time-reversal symmetry. It is possible to create an energy bandgap as a consequence of the interaction between the conduction band and valence band surface states from the opposite surfaces of a TI thin film, and the width of the bandgap can be controlled by the thin film thickness. The formation of an energy bandgap raises the possibility of thin-film TI-based metal-oxide-semiconductor field-effect-transistors (MOSFETs). In this paper, we explore the performance of MOSFETs basedmore » on thin film 3D-TI structures by employing quantum ballistic transport simulations using the effective continuous Hamiltonian with fitting parameters extracted from ab-initio calculations. We demonstrate that thin film transistors based on a 3D-TI structure provide similar electrical characteristics compared to a Si-MOSFET for gate lengths down to 10 nm. Thus, such a device can be a potential candidate to replace Si-based MOSFETs in the sub-10 nm regime.« less

Ferroelectric symmetry-protected multibit memory cell

NASA Astrophysics Data System (ADS)

Baudry, Laurent; Lukyanchuk, Igor; Vinokur, Valerii M.

2017-02-01

The tunability of electrical polarization in ferroelectrics is instrumental to their applications in information-storage devices. The existing ferroelectric memory cells are based on the two-level storage capacity with the standard binary logics. However, the latter have reached its fundamental limitations. Here we propose ferroelectric multibit cells (FMBC) utilizing the ability of multiaxial ferroelectric materials to pin the polarization at a sequence of the multistable states. Employing the catastrophe theory principles we show that these states are symmetry-protected against the information loss and thus realize novel topologically-controlled access memory (TAM). Our findings enable developing a platform for the emergent many-valued non-Boolean information technology and target challenges posed by needs of quantum and neuromorphic computing.

Terahertz spectroscopy on Faraday and Kerr rotations in a quantum anomalous Hall state.

PubMed

Okada, Ken N; Takahashi, Youtarou; Mogi, Masataka; Yoshimi, Ryutaro; Tsukazaki, Atsushi; Takahashi, Kei S; Ogawa, Naoki; Kawasaki, Masashi; Tokura, Yoshinori

2016-07-20

Electrodynamic responses from three-dimensional topological insulators are characterized by the universal magnetoelectric term constituent of the Lagrangian formalism. The quantized magnetoelectric coupling, which is generally referred to as topological magnetoelectric effect, has been predicted to induce exotic phenomena including the universal low-energy magneto-optical effects. Here we report the experimental indication of the topological magnetoelectric effect, which is exemplified by magneto-optical Faraday and Kerr rotations in the quantum anomalous Hall states of magnetic topological insulator surfaces by terahertz magneto-optics. The universal relation composed of the observed Faraday and Kerr rotation angles but not of any material parameters (for example, dielectric constant and magnetic susceptibility) well exhibits the trajectory towards the fine structure constant in the quantized limit.

Quantum teleportation and Birman-Murakami-Wenzl algebra

NASA Astrophysics Data System (ADS)

Zhang, Kun; Zhang, Yong

2017-02-01

In this paper, we investigate the relationship of quantum teleportation in quantum information science and the Birman-Murakami-Wenzl (BMW) algebra in low-dimensional topology. For simplicity, we focus on the two spin-1/2 representation of the BMW algebra, which is generated by both the Temperley-Lieb projector and the Yang-Baxter gate. We describe quantum teleportation using the Temperley-Lieb projector and the Yang-Baxter gate, respectively, and study teleportation-based quantum computation using the Yang-Baxter gate. On the other hand, we exploit the extended Temperley-Lieb diagrammatical approach to clearly show that the tangle relations of the BMW algebra have a natural interpretation of quantum teleportation. Inspired by this interpretation, we construct a general representation of the tangle relations of the BMW algebra and obtain interesting representations of the BMW algebra. Therefore, our research sheds a light on a link between quantum information science and low-dimensional topology.

Edge-entanglement spectrum correspondence in a nonchiral topological phase and Kramers-Wannier duality

NASA Astrophysics Data System (ADS)

Ho, Wen Wei; Cincio, Lukasz; Moradi, Heidar; Gaiotto, Davide; Vidal, Guifre

2015-03-01

In a system with chiral topological order, there is a remarkable correspondence between the edge and entanglement spectra: the low-energy spectrum of the system in the presence of a physical edge coincides with the lowest part of the entanglement spectrum (ES) across a virtual cut of the system into two parts, up to rescaling and shifting. This correspondence is believed to be due to the existence of protected gapless edge modes. In this paper, we explore whether the edge-entanglement spectrum correspondence extends to nonchiral topological phases, where there are no protected gapless edge modes. Specifically, we consider the Wen-plaquette model, which is equivalent to the Kitaev toric code model and has Z2 topological order (quantum double of Z2) . The unperturbed Wen-plaquette model displays an exact correspondence: both the edge and entanglement spectra within each topological sector a (a =1 ,⋯,4 ) are flat and equally degenerate. Here, we show, through a detailed microscopic calculation, that in the presence of generic local perturbations: (i) the effective degrees of freedom for both the physical edge and the entanglement cut consist of a (spin-1 /2 ) spin chain, with effective Hamiltonians Hedgea and Henta, respectively, both of which have a Z2 symmetry enforced by the bulk topological order; (ii) there is in general no match between the low-energy spectra of Hedgea and Henta, that is, there is no edge-ES correspondence. However, if supplement the Z2 topological order with a global symmetry (translational invariance along the edge/entanglement cut), i.e., by considering the Wen-plaquette model as a symmetry-enriched topological phase (SET), then there is a finite domain in Hamiltonian space in which both Hedgea and Henta realize the critical Ising model, whose low-energy effective theory is the c =1 /2 Ising CFT. This is achieved because the presence of the global symmetry implies that the effective degrees of freedom of both the edge and entanglement cut are governed by Kramers-Wannier self-dual Hamiltonians, in addition to them being Z2 symmetric, which is imposed by the topological order. Thus, by considering the Wen-plaquette model as a SET, the topological order in the bulk together with the translation invariance of the perturbations along the edge/cut imply an edge-ES correspondence at least in some finite domain in Hamiltonian space.

Topological entanglement entropy with a twist.

PubMed

Brown, Benjamin J; Bartlett, Stephen D; Doherty, Andrew C; Barrett, Sean D

2013-11-27

Defects in topologically ordered models have interesting properties that are reminiscent of the anyonic excitations of the models themselves. For example, dislocations in the toric code model are known as twists and possess properties that are analogous to Ising anyons. We strengthen this analogy by using the topological entanglement entropy as a diagnostic tool to identify properties of both defects and excitations in the toric code. Specifically, we show, through explicit calculation, that the toric code model including twists and dyon excitations has the same quantum dimensions, the same total quantum dimension, and the same fusion rules as an Ising anyon model.

Spacetime topology change and black hole information

NASA Astrophysics Data System (ADS)

Hsu, Stephen D. H.

2007-01-01

Topology change-the creation of a disconnected baby universe-due to black hole collapse may resolve the information loss paradox. Evolution from an early time Cauchy surface to a final surface which includes a slice of the disconnected region can be unitary and consistent with conventional quantum mechanics. We discuss the issue of cluster decomposition, showing that any violations thereof are likely to be unobservably small. Topology change is similar to the black hole remnant scenario and only requires assumptions about the behavior of quantum gravity in Planckian regimes. It does not require non-locality or any modification of low-energy physics.

QSTR of the toxicity of some organophosphorus compounds by using the quantum chemical and topological descriptors.

PubMed

Senior, Samir A; Madbouly, Magdy D; El massry, Abdel-Moneim

2011-09-01

Quantum chemical and topological descriptors of some organophosphorus compounds (OP) were correlated with their toxicity LD(50) as a dermal. The quantum chemical parameters were obtained using B3LYP/LANL2DZdp-ECP optimization. Using linear regression analysis, equations were derived to calculate the theoretical LD(50) of the studied compounds. The inclusion of quantum parameters, having both charge indices and topological indices, affects the toxicity of the studied compounds resulting in high correlation coefficient factors for the obtained equations. Two of the new four firstly supposed descriptors give higher correlation coefficients namely the Heteroatom Corrected Extended Connectivity Randic index ((1)X(HCEC)) and the Density Randic index ((1)X(Den)). The obtained linear equations were applied to predict the toxicity of some related structures. It was found that the sulfur atoms in these compounds must be replaced by oxygen atoms to achieve improved toxicity. Copyright © 2011 Elsevier Ltd. All rights reserved.

Stanene cyanide: a novel candidate of Quantum Spin Hall insulator at high temperature

PubMed Central

Ji, Wei-xiao; Zhang, Chang-wen; Ding, Meng; Li, Ping; Li, Feng; Ren, Miao-juan; Wang, Pei-ji; Hu, Shu-jun; Yan, Shi-shen

2015-01-01

The search for quantum spin Hall (QSH) insulators with high stability, large and tunable gap and topological robustness, is critical for their realistic application at high temperature. Using first-principle calculations, we predict the cyanogen saturated stanene SnCN as novel topological insulators material, with a bulk gap as large as 203 meV, which can be engineered by applying biaxial strain and electric field. The band topology is identified by Z2 topological invariant together with helical edge states, and the mechanism is s-pxy band inversion at G point induced by spin-orbit coupling (SOC). Remarkably, these systems have robust topology against chemical impurities, based on the calculations on halogen and cyano group co-decorated stanene SnXxX′1−x (X,X′  =  F, Cl, Br, I and CN), which makes it an appropriate and flexible candidate material for spintronic devices. PMID:26688269

Realizing Haldane model in Fe-based honeycomb ferromagnetic insulators

NASA Astrophysics Data System (ADS)

Kim, Heung-Sik; Kee, Hae-Young

2017-12-01

The topological Haldane model on a honeycomb lattice is a prototype of systems hosting topological phases of matter without external fields. It is the simplest model exhibiting the quantum Hall effect without Landau levels, which motivated theoretical and experimental explorations of topological insulators and superconductors. Despite its simplicity, its realization in condensed matter systems has been elusive due to a seemingly difficult condition of spinless fermions with sublattice-dependent magnetic flux terms. While there have been theoretical proposals including elaborate atomic-scale engineering, identifying candidate topological Haldane model materials has not been successful, and the first experimental realization was recently made in ultracold atoms. Here, we suggest that a series of Fe-based honeycomb ferromagnetic insulators, AFe2(PO4)2 (A=Ba, Cs, K, La) possess Chern bands described by the topological Haldane model. How to detect the quantum anomalous Hall effect is also discussed.

Engineering three-dimensional topological insulators in Rashba-type spin-orbit coupled heterostructures

PubMed Central

Das, Tanmoy; Balatsky, A. V.

2013-01-01

Topological insulators represent a new class of quantum phase defined by invariant symmetries and spin-orbit coupling that guarantees metallic Dirac excitations at its surface. The discoveries of these states have sparked the hope of realizing non-trivial excitations and novel effects such as a magnetoelectric effect and topological Majorana excitations. Here we develop a theoretical formalism to show that a three-dimensional topological insulator can be designed artificially via stacking bilayers of two-dimensional Fermi gases with opposite Rashba-type spin-orbit coupling on adjacent layers, and with interlayer quantum tunneling. We demonstrate that in the stack of bilayers grown along a (001)-direction, a non-trivial topological phase transition occurs above a critical number of Rashba bilayers. In the topological phase, we find the formation of a single spin-polarized Dirac cone at the -point. This approach offers an accessible way to design artificial topological insulators in a set up that takes full advantage of the atomic layer deposition approach. This design principle is tunable and also allows us to bypass limitations imposed by bulk crystal geometry. PMID:23739724

Dimensional crossover and cold-atom realization of topological Mott insulators

PubMed Central

Scheurer, Mathias S.; Rachel, Stephan; Orth, Peter P.

2015-01-01

Interacting cold-atomic gases in optical lattices offer an experimental approach to outstanding problems of many body physics. One important example is the interplay of interaction and topology which promises to generate a variety of exotic phases such as the fractionalized Chern insulator or the topological Mott insulator. Both theoretically understanding these states of matter and finding suitable systems that host them have proven to be challenging problems. Here we propose a cold-atom setup where Hubbard on-site interactions give rise to spin liquid-like phases: weak and strong topological Mott insulators. They represent the celebrated paradigm of an interacting and topological quantum state with fractionalized spinon excitations that inherit the topology of the non-interacting system. Our proposal shall help to pave the way for a controlled experimental investigation of this exotic state of matter in optical lattices. Furthermore, it allows for the investigation of a dimensional crossover from a two-dimensional quantum spin Hall insulating phase to a three-dimensional strong topological insulator by tuning the hopping between the layers. PMID:25669431

Majorana Fermions in Particle Physics, Solid State and Quantum Information

NASA Astrophysics Data System (ADS)

Borsten, L.; Duff, M. J.

This review is based on lectures given by M. J. Duff summarising the far reaching contributions of Ettore Majorana to fundamental physics, with special focus on Majorana fermions in all their guises. The theoretical discovery of the eponymous fcrmion in 1937 has since had profound implications for particlc physics, solid state and quantum computation. The breadth of these disciplines is testimony to Majorana's genius, which continues to permeate physics today. These lectures offer a whistle-stop tour through some limited subset of the key ideas. In addition to touching on these various applications, we will draw out some fascinating relations connecting the normed division algebras R, ℂ, H, O to spinors, trialities. K-theory and the classification of stable topological states of symmetry-protected gapped free-fermion systems.

Localization in a quantum spin Hall system.

PubMed

Onoda, Masaru; Avishai, Yshai; Nagaosa, Naoto

2007-02-16

The localization problem of electronic states in a two-dimensional quantum spin Hall system (that is, a symplectic ensemble with topological term) is studied by the transfer matrix method. The phase diagram in the plane of energy and disorder strength is exposed, and demonstrates "levitation" and "pair annihilation" of the domains of extended states analogous to that of the integer quantum Hall system. The critical exponent nu for the divergence of the localization length is estimated as nu congruent with 1.6, which is distinct from both exponents pertaining to the conventional symplectic and the unitary quantum Hall systems. Our analysis strongly suggests a different universality class related to the topology of the pertinent system.

Gap Reversal at Filling Factors 3 +1 /3 and 3 +1 /5 : Towards Novel Topological Order in the Fractional Quantum Hall Regime

NASA Astrophysics Data System (ADS)

Kleinbaum, Ethan; Kumar, Ashwani; Pfeiffer, L. N.; West, K. W.; Csáthy, G. A.

2015-02-01

In the region of the second Landau level several theories predict fractional quantum Hall states with novel topological order. We report the opening of an energy gap at the filling factor ν =3 +1 /3 , firmly establishing the ground state as a fractional quantum Hall state. This and other odd-denominator states unexpectedly break particle-hole symmetry. Specifically, we find that the relative magnitudes of the energy gaps of the ν =3 +1 /3 and 3 +1 /5 states from the upper spin branch are reversed when compared to the ν =2 +1 /3 and 2 +1 /5 counterpart states in the lower spin branch. Our findings raise the possibility that at least one of the former states is of an unusual topological order.

Majorana fermion surface code for universal quantum computation

DOE PAGES

Vijay, Sagar; Hsieh, Timothy H.; Fu, Liang

2015-12-10

In this study, we introduce an exactly solvable model of interacting Majorana fermions realizing Z 2 topological order with a Z 2 fermion parity grading and lattice symmetries permuting the three fundamental anyon types. We propose a concrete physical realization by utilizing quantum phase slips in an array of Josephson-coupled mesoscopic topological superconductors, which can be implemented in a wide range of solid-state systems, including topological insulators, nanowires, or two-dimensional electron gases, proximitized by s-wave superconductors. Our model finds a natural application as a Majorana fermion surface code for universal quantum computation, with a single-step stabilizer measurement requiring no physicalmore » ancilla qubits, increased error tolerance, and simpler logical gates than a surface code with bosonic physical qubits. We thoroughly discuss protocols for stabilizer measurements, encoding and manipulating logical qubits, and gate implementations.« less

Non-abelian anyons and topological quantum information processing in 1D wire networks

NASA Astrophysics Data System (ADS)

Alicea, Jason

2012-02-01

Topological quantum computation provides an elegant solution to decoherence, circumventing this infamous problem at the hardware level. The most basic requirement in this approach is the ability to stabilize and manipulate particles exhibiting non-Abelian exchange statistics -- Majorana fermions being the simplest example. Curiously, Majorana fermions have been predicted to arise both in 2D systems, where non-Abelian statistics is well established, and in 1D, where exchange statistics of any type is ill-defined. An important question then arises: do Majorana fermions in 1D hold the same technological promise as their 2D counterparts? In this talk I will answer this question in the affirmative, describing how one can indeed manipulate and harness the non-Abelian statistics of Majoranas in a remarkably simple fashion using networks formed by quantum wires or topological insulator edges.

Manipulating topological-insulator properties using quantum confinement

NASA Astrophysics Data System (ADS)

Kotulla, M.; Zülicke, U.

2017-07-01

Recent discoveries have spurred the theoretical prediction and experimental realization of novel materials that have topological properties arising from band inversion. Such topological insulators are insulating in the bulk but have conductive surface or edge states. Topological materials show various unusual physical properties and are surmised to enable the creation of exotic Majorana-fermion quasiparticles. How the signatures of topological behavior evolve when the system size is reduced is interesting from both a fundamental and an application-oriented point of view, as such understanding may form the basis for tailoring systems to be in specific topological phases. This work considers the specific case of quantum-well confinement defining two-dimensional layers. Based on the effective-Hamiltonian description of bulk topological insulators, and using a harmonic-oscillator potential as an example for a softer-than-hard-wall confinement, we have studied the interplay of band inversion and size quantization. Our model system provides a useful platform for systematic study of the transition between the normal and topological phases, including the development of band inversion and the formation of massless-Dirac-fermion surface states. The effects of bare size quantization, two-dimensional-subband mixing, and electron-hole asymmetry are disentangled and their respective physical consequences elucidated.

(3 + 1)-dimensional topological phases and self-dual quantum geometries encoded on Heegaard surfaces

NASA Astrophysics Data System (ADS)

Dittrich, Bianca

2017-05-01

We apply the recently suggested strategy to lift state spaces and operators for (2 + 1)-dimensional topological quantum field theories to state spaces and operators for a (3 + 1)-dimensional TQFT with defects. We start from the (2 + 1)-dimensional TuraevViro theory and obtain a state space, consistent with the state space expected from the Crane-Yetter model with line defects.

Non-Abelian Geometric Phases Carried by the Quantum Noise Matrix

NASA Astrophysics Data System (ADS)

Bharath, H. M.; Boguslawski, Matthew; Barrios, Maryrose; Chapman, Michael

2017-04-01

Topological phases of matter are characterized by topological order parameters that are built using Berry's geometric phase. Berry's phase is the geometric information stored in the overall phase of a quantum state. We show that geometric information is also stored in the second and higher order spin moments of a quantum spin system, captured by a non-abelian geometric phase. The quantum state of a spin-S system is uniquely characterized by its spin moments up to order 2S. The first-order spin moment is the spin vector, and the second-order spin moment represents the spin fluctuation tensor, i.e., the quantum noise matrix. When the spin vector is transported along a loop in the Bloch ball, we show that the quantum noise matrix picks up a geometric phase. Considering spin-1 systems, we formulate this geometric phase as an SO(3) operator. Geometric phases are usually interpreted in terms of the solid angle subtended by the loop at the center. However, solid angles are not well defined for loops that pass through the center. Here, we introduce a generalized solid angle which is well defined for all loops inside the Bloch ball, in terms of which, we interpret the SO(3) geometric phase. This geometric phase can be used to characterize topological spin textures in cold atomic clouds.

Realization of two-dimensional spin-orbit coupling for Bose-Einstein condensates.

PubMed

Wu, Zhan; Zhang, Long; Sun, Wei; Xu, Xiao-Tian; Wang, Bao-Zong; Ji, Si-Cong; Deng, Youjin; Chen, Shuai; Liu, Xiong-Jun; Pan, Jian-Wei

2016-10-07

Cold atoms with laser-induced spin-orbit (SO) interactions provide a platform to explore quantum physics beyond natural conditions of solids. Here we propose and experimentally realize two-dimensional (2D) SO coupling and topological bands for a rubidium-87 degenerate gas through an optical Raman lattice, without phase-locking or fine-tuning of optical potentials. A controllable crossover between 2D and 1D SO couplings is studied, and the SO effects and nontrivial band topology are observed by measuring the atomic cloud distribution and spin texture in momentum space. Our realization of 2D SO coupling with advantages of small heating and topological stability opens a broad avenue in cold atoms to study exotic quantum phases, including topological superfluids. Copyright © 2016, American Association for the Advancement of Science.

Terahertz spectroscopy on Faraday and Kerr rotations in a quantum anomalous Hall state

PubMed Central

Okada, Ken N.; Takahashi, Youtarou; Mogi, Masataka; Yoshimi, Ryutaro; Tsukazaki, Atsushi; Takahashi, Kei S.; Ogawa, Naoki; Kawasaki, Masashi; Tokura, Yoshinori

2016-01-01

Electrodynamic responses from three-dimensional topological insulators are characterized by the universal magnetoelectric term constituent of the Lagrangian formalism. The quantized magnetoelectric coupling, which is generally referred to as topological magnetoelectric effect, has been predicted to induce exotic phenomena including the universal low-energy magneto-optical effects. Here we report the experimental indication of the topological magnetoelectric effect, which is exemplified by magneto-optical Faraday and Kerr rotations in the quantum anomalous Hall states of magnetic topological insulator surfaces by terahertz magneto-optics. The universal relation composed of the observed Faraday and Kerr rotation angles but not of any material parameters (for example, dielectric constant and magnetic susceptibility) well exhibits the trajectory towards the fine structure constant in the quantized limit. PMID:27436710

The physics of quantum materials

NASA Astrophysics Data System (ADS)

Keimer, B.; Moore, J. E.

2017-11-01

The physical description of all materials is rooted in quantum mechanics, which describes how atoms bond and electrons interact at a fundamental level. Although these quantum effects can in many cases be approximated by a classical description at the macroscopic level, in recent years there has been growing interest in material systems where quantum effects remain manifest over a wider range of energy and length scales. Such quantum materials include superconductors, graphene, topological insulators, Weyl semimetals, quantum spin liquids, and spin ices. Many of them derive their properties from reduced dimensionality, in particular from confinement of electrons to two-dimensional sheets. Moreover, they tend to be materials in which electrons cannot be considered as independent particles but interact strongly and give rise to collective excitations known as quasiparticles. In all cases, however, quantum-mechanical effects fundamentally alter properties of the material. This Review surveys the electronic properties of quantum materials through the prism of the electron wavefunction, and examines how its entanglement and topology give rise to a rich variety of quantum states and phases; these are less classically describable than conventional ordered states also driven by quantum mechanics, such as ferromagnetism.

Assessing the Progress of Trapped-Ion Processors Towards Fault-Tolerant Quantum Computation

NASA Astrophysics Data System (ADS)

Bermudez, A.; Xu, X.; Nigmatullin, R.; O'Gorman, J.; Negnevitsky, V.; Schindler, P.; Monz, T.; Poschinger, U. G.; Hempel, C.; Home, J.; Schmidt-Kaler, F.; Biercuk, M.; Blatt, R.; Benjamin, S.; Müller, M.

2017-10-01

A quantitative assessment of the progress of small prototype quantum processors towards fault-tolerant quantum computation is a problem of current interest in experimental and theoretical quantum information science. We introduce a necessary and fair criterion for quantum error correction (QEC), which must be achieved in the development of these quantum processors before their sizes are sufficiently big to consider the well-known QEC threshold. We apply this criterion to benchmark the ongoing effort in implementing QEC with topological color codes using trapped-ion quantum processors and, more importantly, to guide the future hardware developments that will be required in order to demonstrate beneficial QEC with small topological quantum codes. In doing so, we present a thorough description of a realistic trapped-ion toolbox for QEC and a physically motivated error model that goes beyond standard simplifications in the QEC literature. We focus on laser-based quantum gates realized in two-species trapped-ion crystals in high-optical aperture segmented traps. Our large-scale numerical analysis shows that, with the foreseen technological improvements described here, this platform is a very promising candidate for fault-tolerant quantum computation.

Bulk and surface states carried supercurrent in ballistic Nb-Dirac semimetal Cd3As2 nanowire-Nb junctions

NASA Astrophysics Data System (ADS)

Li, Cai-Zhen; Li, Chuan; Wang, Li-Xian; Wang, Shuo; Liao, Zhi-Min; Brinkman, Alexander; Yu, Da-Peng

2018-03-01

A three-dimensional Dirac semimetal has bulk Dirac cones in all three momentum directions and Fermi arc like surface states, and can be converted into a Weyl semimetal by breaking time-reversal symmetry. However, the highly conductive bulk state usually hides the electronic transport from the surface state in Dirac semimetal. Here, we demonstrate the supercurrent carried by bulk and surface states in Nb -Cd3As2 nanowire-Nb short and long junctions, respectively. For the ˜1 -μ m -long junction, the Fabry-Pérot interferences-induced oscillations of the critical supercurrent are observed, suggesting the ballistic transport of the surface states carried supercurrent, where the bulk states are decoherent and the topologically protected surface states still stay coherent. Moreover, a superconducting dome is observed in the long junction, which is attributed to the enhanced dephasing from the interaction between surface and bulk states as tuning gate voltage to increase the carrier density. The superconductivity of topological semimetal nanowire is promising for braiding of Majorana fermions toward topological quantum computing.

Scanning quantum gas atom chip microscopy of strongly correlated and topologically nontrivial materials

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lev, Benjamin

The SQCRAMscope, Scanning Quantum Cryogenic Atom Microscope, is a novel scanning probe microscope we developed during this DOE fund period. It is now capable of imaging transport in cryogenically cooled solid-state samples, as we have recently demonstrated with iron-based pnictide superconductors. As such, it opens a new frontier in the quantum-based metrology of materials and is the first example of the direct marriage of ultracold AMO physics with condensed matter physics. We predict the SQCRAMscope will become an important element in the toolbox for exploring strongly correlated and topologically nontrivial materials.

Anomalous Rashba spin-orbit interaction in electrically controlled topological insulator based on InN/GaN quantum wells

NASA Astrophysics Data System (ADS)

Łepkowski, Sławomir P.; Bardyszewski, Witold

2017-05-01

We study theoretically the topological phase transition and the Rashba spin-orbit interaction in electrically biased InN/GaN quantum wells. We show that that for properly chosen widths of quantum wells and barriers, one can effectively tune the system through the topological phase transition applying an external electric field perpendicular to the QW plane. We find that in InN/GaN quantum wells with the inverted band structure, when the conduction band s-type level is below the heavy hole and light hole p-type levels, the spin splitting of the subbands decreases with increasing the amplitude of the electric field in the quantum wells, which reveals the anomalous Rashba effect. Derived effective Rashba Hamiltonians can describe the subband spin splitting only for very small wave vectors due to strong coupling between the subbands. Furthermore, we demonstrate that for InN/GaN quantum wells in a Hall bar geometry, the critical voltage for the topological phase transition depends distinctly on the width of the structure and a significant spin splitting of the edge states lying in the 2D band gap can be almost switched off by increasing the electric field in quantum wells only by a few percent. We show that the dependence of the spin splitting of the upper branch of the edge state dispersion curve on the wave vector has a threshold-like behavior with the on/off spin splitting ratio reaching two orders of magnitude for narrow Hall bars. The threshold wave vector depends weakly on the Hall bar width, whereas it increases significantly with the bias voltage due to an increase of the energetic distance between the s-type and p-type quantum well energy levels and a reduction of the coupling between the subbands.

Anomalous Rashba spin-orbit interaction in electrically controlled topological insulator based on InN/GaN quantum wells.

PubMed

Łepkowski, Sławomir P; Bardyszewski, Witold

2017-05-17

We study theoretically the topological phase transition and the Rashba spin-orbit interaction in electrically biased InN/GaN quantum wells. We show that that for properly chosen widths of quantum wells and barriers, one can effectively tune the system through the topological phase transition applying an external electric field perpendicular to the QW plane. We find that in InN/GaN quantum wells with the inverted band structure, when the conduction band s-type level is below the heavy hole and light hole p-type levels, the spin splitting of the subbands decreases with increasing the amplitude of the electric field in the quantum wells, which reveals the anomalous Rashba effect. Derived effective Rashba Hamiltonians can describe the subband spin splitting only for very small wave vectors due to strong coupling between the subbands. Furthermore, we demonstrate that for InN/GaN quantum wells in a Hall bar geometry, the critical voltage for the topological phase transition depends distinctly on the width of the structure and a significant spin splitting of the edge states lying in the 2D band gap can be almost switched off by increasing the electric field in quantum wells only by a few percent. We show that the dependence of the spin splitting of the upper branch of the edge state dispersion curve on the wave vector has a threshold-like behavior with the on/off spin splitting ratio reaching two orders of magnitude for narrow Hall bars. The threshold wave vector depends weakly on the Hall bar width, whereas it increases significantly with the bias voltage due to an increase of the energetic distance between the s-type and p-type quantum well energy levels and a reduction of the coupling between the subbands.

Rhorix: An interface between quantum chemical topology and the 3D graphics program blender

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mills, Matthew J. L.; Sale, Kenneth L.; Simmons, Blake A.

Journal of Computational Chemistry Published by Wiley Periodicals, Inc. Chemical research is assisted by the creation of visual representations that map concepts (such as atoms and bonds) to 3D objects. These concepts are rooted in chemical theory that predates routine solution of the Schrödinger equation for systems of interesting size. The method of Quantum Chemical Topology (QCT) provides an alternative, parameter-free means to understand chemical phenomena directly from quantum mechanical principles. Representation of the topological elements of QCT has lagged behind the best tools available. Here, we describe a general abstraction (and corresponding file format) that permits the definition ofmore » mappings between topological objects and their 3D representations. Possible mappings are discussed and a canonical example is suggested, which has been implemented as a Python “Add-On” named Rhorix for the state-of-the-art 3D modeling program Blender. This allows chemists to use modern drawing tools and artists to access QCT data in a familiar context. Finally, a number of examples are discussed..« less

Rhorix: An interface between quantum chemical topology and the 3D graphics program blender

PubMed Central

Sale, Kenneth L.; Simmons, Blake A.; Popelier, Paul L. A.

2017-01-01

Chemical research is assisted by the creation of visual representations that map concepts (such as atoms and bonds) to 3D objects. These concepts are rooted in chemical theory that predates routine solution of the Schrödinger equation for systems of interesting size. The method of Quantum Chemical Topology (QCT) provides an alternative, parameter‐free means to understand chemical phenomena directly from quantum mechanical principles. Representation of the topological elements of QCT has lagged behind the best tools available. Here, we describe a general abstraction (and corresponding file format) that permits the definition of mappings between topological objects and their 3D representations. Possible mappings are discussed and a canonical example is suggested, which has been implemented as a Python “Add‐On” named Rhorix for the state‐of‐the‐art 3D modeling program Blender. This allows chemists to use modern drawing tools and artists to access QCT data in a familiar context. A number of examples are discussed. © 2017 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc. PMID:28857244

rf Quantum Capacitance of the Topological Insulator Bi2Se3 in the Bulk Depleted Regime for Field-Effect Transistors

NASA Astrophysics Data System (ADS)

Inhofer, A.; Duffy, J.; Boukhicha, M.; Bocquillon, E.; Palomo, J.; Watanabe, K.; Taniguchi, T.; Estève, I.; Berroir, J. M.; Fève, G.; Plaçais, B.; Assaf, B. A.

2018-02-01

A metal-dielectric topological-insulator capacitor device based on hexagonal-boron-nitrate- (h -BN) encapsulated CVD-grown Bi2Se3 is realized and investigated in the radio-frequency regime. The rf quantum capacitance and device resistance are extracted for frequencies as high as 10 GHz and studied as a function of the applied gate voltage. The superior quality h -BN gate dielectric combined with the optimized transport characteristics of CVD-grown Bi2Se3 (n ˜1018 cm-3 in 8 nm) on h -BN allow us to attain a bulk depleted regime by dielectric gating. A quantum-capacitance minimum and a linear variation of the capacitance with the chemical potential are observed revealing a Dirac regime. The topological surface state in proximity to the gate is seen to reach charge neutrality, but the bottom surface state remains charged and capacitively coupled to the top via the insulating bulk. Our work paves the way toward implementation of topological materials in rf devices.

Rhorix: An interface between quantum chemical topology and the 3D graphics program blender

DOE PAGES

Mills, Matthew J. L.; Sale, Kenneth L.; Simmons, Blake A.; ...

2017-08-31

Journal of Computational Chemistry Published by Wiley Periodicals, Inc. Chemical research is assisted by the creation of visual representations that map concepts (such as atoms and bonds) to 3D objects. These concepts are rooted in chemical theory that predates routine solution of the Schrödinger equation for systems of interesting size. The method of Quantum Chemical Topology (QCT) provides an alternative, parameter-free means to understand chemical phenomena directly from quantum mechanical principles. Representation of the topological elements of QCT has lagged behind the best tools available. Here, we describe a general abstraction (and corresponding file format) that permits the definition ofmore » mappings between topological objects and their 3D representations. Possible mappings are discussed and a canonical example is suggested, which has been implemented as a Python “Add-On” named Rhorix for the state-of-the-art 3D modeling program Blender. This allows chemists to use modern drawing tools and artists to access QCT data in a familiar context. Finally, a number of examples are discussed..« less

Mapping the Braiding Properties of Non-Abelian FQHE Liquids.

NASA Astrophysics Data System (ADS)

Prodan, Emil; Haldane, F. D. M.

2007-03-01

Non-Abelian FQHE (NAFQHE) states have elementary excitations that cannot be individually locally-created. When widely separated, they give rise to topological (quasi-)degeneracy of the quantum states; braiding of such non-Abelian quasiparticles (NAQP's) implements unitary transformations among the degenerate states that may be useful for ``topological quantum computing'' (TQC). We have developed a new technique for explicit computation of NAQP braiding in models exhibiting ideal NAFQHE behavior (where the topological degeneracy is exact), in particular the Moore-Read ν = 5/2 state. For systems of small numbers of NAQP's on a sphere, we have computed the non-Abelian Berry curvature and Hilbert space metric, as one NAQP is moved relative to a fixed configuration of the others, showing how the topological properties develop as the system size (NAQP separation) increases. We also studied the effect of perturbations (Coulomb interaction and substrate potentials) that lift the exact degeneracy, and become the dominant corrections when NAQP's are brought together so that quantum measurements can be made; these effects are likely to be crucial in determining whether TQC is viable in NAFQHE systems.

Topological interface physics in spinor Bose-Einstein condensates

NASA Astrophysics Data System (ADS)

Borgh, Magnus; Ruostekoski, Janne

2013-05-01

We present an experimentally viable scheme whereby the physics of coherent interfaces between topologically distinct regions can be studied in an atomic quantum gas. The interface engineering is achieved using the internal spin structures of atoms together with local control over interaction strengths. We consider a coherent interface between polar and ferromagnetic regions of a spin-1 Bose-Einstein condensate and show that defects representing different topologies can connect continuously across the boundary. We show that energy minimization leads to nontrivial interface-crossing defect structures, demonstrating how the method can be used to study stability properties of field-theoretical solitons. We demonstrate, e.g., the formation of a half-quantum vortex arch, an Alice arch, on the interface, exhibiting the topological charge of a point defect. We also demonstrate an energetically stable connection of a coreless vortex to two half-quantum vortices. Our method can be extended to study interface physics in spin-2 and spin-3 BECs with richer phenomenology, or in strongly correlated optical-lattice systems. We acknowledge financial support from the Leverhulme Trust.

Growth and quantum transport properties of vertical Bi2Se3 nanoplate films on Si substrates.

PubMed

Li, Mingze; Wang, Zhenhua; Yang, Liang; Pan, Desheng; Li, Da; Gao, Xuan P A; Zhang, Zhidong

2018-08-03

Controlling the growth direction (planar versus vertical) and surface-to-bulk ratio can lead to lots of unique properties for two-dimensional layered materials. We report a simple method to fabricate continuous films of vertical Bi 2 Se 3 nanoplates on Si substrate and investigate the quantum transport properties of such films. In contrast to (001) oriented planar Bi 2 Se 3 nanoplate film, vertical Bi 2 Se 3 nanoplate films are enclosed by (015) facets, which possess high surface-to-bulk ratio that can enhance the quantum transport property of topological surface states. And by controlling the compactness of vertical Bi 2 Se 3 nanoplates, we realized an effective tuning of the weak antilocalization effect from topological surface states in Bi 2 Se 3 films. Our work paves a way for exploring the unique transport properties of this unconventional structure topological insulator film.

Non-Abelian Parton Fractional Quantum Hall Effect in Multilayer Graphene.

PubMed

Wu, Ying-Hai; Shi, Tao; Jain, Jainendra K

2017-08-09

The current proposals for producing non-Abelian anyons and Majorana particles, which are neither fermions nor bosons, are primarily based on the realization of topological superconductivity in two dimensions. We show theoretically that the unique Landau level structure of bilayer graphene provides a new possible avenue for achieving such exotic particles. Specifically, we demonstrate the feasibility of a "parton" fractional quantum Hall (FQH) state, which supports non-Abelian particles without the usual topological superconductivity. Furthermore, we advance this state as the fundamental explanation of the puzzling 1/2 FQH effect observed in bilayer graphene [ Kim et al. Nano Lett. 2015 , 15 , 7445 ] and predict that it will also occur in trilayer graphene. We indicate experimental signatures that differentiate the parton state from other candidate non-Abelian FQH states and predict that a transverse electric field can induce a topological quantum phase transition between two distinct non-Abelian FQH states.

Fractionally charged skyrmions in fractional quantum Hall effect

PubMed Central

Balram, Ajit C.; Wurstbauer, U.; Wójs, A.; Pinczuk, A.; Jain, J. K.

2015-01-01

The fractional quantum Hall effect has inspired searches for exotic emergent topological particles, such as fractionally charged excitations, composite fermions, abelian and nonabelian anyons and Majorana fermions. Fractionally charged skyrmions, which support both topological charge and topological vortex-like spin structure, have also been predicted to occur in the vicinity of 1/3 filling of the lowest Landau level. The fractional skyrmions, however, are anticipated to be exceedingly fragile, suppressed by very small Zeeman energies. Here we show that, slightly away from 1/3 filling, the smallest manifestations of the fractional skyrmion exist in the excitation spectrum for a broad range of Zeeman energies, and appear in resonant inelastic light scattering experiments as well-defined resonances slightly below the long wavelength spin wave mode. The spectroscopy of these exotic bound states serves as a sensitive tool for investigating the residual interaction between composite fermions, responsible for delicate new fractional quantum Hall states in this filling factor region. PMID:26608906

ER = EPR and non-perturbative action integrals for quantum gravity

NASA Astrophysics Data System (ADS)

Alsaleh, Salwa; Alasfar, Lina

In this paper, we construct and calculate non-perturbative path integrals in a multiply-connected spacetime. This is done by summing over homotopy classes of paths. The topology of the spacetime is defined by Einstein-Rosen bridges (ERB) forming from the entanglement of quantum foam described by virtual black holes. As these “bubbles” are entangled, they are connected by Planckian ERBs because of the ER = EPR conjecture. Hence, the spacetime will possess a large first Betti number B1. For any compact 2-surface in the spacetime, the topology (in particular the homotopy) of that surface is non-trivial due to the large number of Planckian ERBs that define homotopy through this surface. The quantization of spacetime with this topology — along with the proper choice of the 2-surfaces — is conjectured to allow non-perturbative path integrals of quantum gravity theory over the spacetime manifold.

Quantum phase transition of chiral Majorana fermions in the presence of disorder

NASA Astrophysics Data System (ADS)

Lian, Biao; Wang, Jing; Sun, Xiao-Qi; Vaezi, Abolhassan; Zhang, Shou-Cheng

2018-03-01

We study the quantum phase transitions of a disordered two-dimensional quantum anomalous Hall insulator with s -wave superconducting proximity, which are governed by the percolation theory of chiral Majorana fermions. Based on symmetry arguments and a renormalization-group analysis, we show there are generically two phase transitions from Bogoliubov-de Gennes Chern number N =0 to N =1 (p +i p chiral topological superconductor) and then to N =2 , in agreement with the conclusion from the band theory without disorders. Further, we discuss the critical scaling behavior of the e2/2 h conductance half plateau induced by the N =1 chiral topological superconductor recently observed in the experiment. In particular, we compare the critical behavior of the half plateau induced by the topological superconductor with that predicted recently by alternative explanations of the half plateau and show that they can be distinguished in experiments.

Quantum phase transition of chiral Majorana fermions in the presence of disorder

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lian, Biao; Wang, Jing; Sun, Xiao -Qi

Here, we study the quantum phase transitions of a disordered two-dimensional quantum anomalous Hall insulator with s-wave superconducting proximity, which are governed by the percolation theory of chiral Majorana fermions. Based on symmetry arguments and a renormalization-group analysis, we show there are generically two phase transitions from Bogoliubov–de Gennes Chern number N=0 to N=1(p+ip chiral topological superconductor) and then to N=2, in agreement with the conclusion from the band theory without disorders. Further, we discuss the critical scaling behavior of the e 2/2h conductance half plateau induced by the N=1 chiral topological superconductor recently observed in the experiment. In particular,more » we compare the critical behavior of the half plateau induced by the topological superconductor with that predicted recently by alternative explanations of the half plateau and show that they can be distinguished in experiments.« less

Quantum phase transition of chiral Majorana fermions in the presence of disorder

DOE PAGES

Lian, Biao; Wang, Jing; Sun, Xiao -Qi; ...

2018-03-09

Here, we study the quantum phase transitions of a disordered two-dimensional quantum anomalous Hall insulator with s-wave superconducting proximity, which are governed by the percolation theory of chiral Majorana fermions. Based on symmetry arguments and a renormalization-group analysis, we show there are generically two phase transitions from Bogoliubov–de Gennes Chern number N=0 to N=1(p+ip chiral topological superconductor) and then to N=2, in agreement with the conclusion from the band theory without disorders. Further, we discuss the critical scaling behavior of the e 2/2h conductance half plateau induced by the N=1 chiral topological superconductor recently observed in the experiment. In particular,more » we compare the critical behavior of the half plateau induced by the topological superconductor with that predicted recently by alternative explanations of the half plateau and show that they can be distinguished in experiments.« less

Dirac Magnon Nodal Loops in Quasi-2D Quantum Magnets.

PubMed

Owerre, S A

2017-07-31

In this report, we propose a new concept of one-dimensional (1D) closed lines of Dirac magnon nodes in two-dimensional (2D) momentum space of quasi-2D quantum magnetic systems. They are termed "2D Dirac magnon nodal-line loops". We utilize the bilayer honeycomb ferromagnets with intralayer coupling J and interlayer coupling J L , which is realizable in the honeycomb chromium compounds CrX 3 (X ≡ Br, Cl, and I). However, our results can also exist in other layered quasi-2D quantum magnetic systems. Here, we show that the magnon bands of the bilayer honeycomb ferromagnets overlap for J L  ≠ 0 and form 1D closed lines of Dirac magnon nodes in 2D momentum space. The 2D Dirac magnon nodal-line loops are topologically protected by inversion and time-reversal symmetry. Furthermore, we show that they are robust against weak Dzyaloshinskii-Moriya interaction Δ DM  < J L and possess chiral magnon edge modes.

BFV approach to geometric quantization

NASA Astrophysics Data System (ADS)

Fradkin, E. S.; Linetsky, V. Ya.

1994-12-01

A gauge-invariant approach to geometric quantization is developed. It yields a complete quantum description for dynamical systems with non-trivial geometry and topology of the phase space. The method is a global version of the gauge-invariant approach to quantization of second-class constraints developed by Batalin, Fradkin and Fradkina (BFF). Physical quantum states and quantum observables are respectively described by covariantly constant sections of the Fock bundle and the bundle of hermitian operators over the phase space with a flat connection defined by the nilpotent BVF-BRST operator. Perturbative calculation of the first non-trivial quantum correction to the Poisson brackets leads to the Chevalley cocycle known in deformation quantization. Consistency conditions lead to a topological quantization condition with metaplectic anomaly.

Design and experimental observation of valley-Hall edge states in diatomic-graphene-like elastic waveguides

NASA Astrophysics Data System (ADS)

Zhu, Hongfei; Liu, Ting-Wei; Semperlotti, Fabio

2018-05-01

We report on the design and experimental validation of a two-dimensional phononic elastic waveguide exhibiting topological valley-Hall edge states. The lattice structure of the waveguide is inspired by diatomic graphene, and it is imprinted in an initially flat plate by means of geometric indentations. The indentations are distributed according to a hexagonal lattice structure which guarantees the existence of Dirac dispersion at the boundary of the Brillouin zone. Starting from this basic material, domain walls capable of supporting edge states can be obtained by contrasting waveguides having broken space-inversion symmetry (SIS) achieved by using local resonant elements. Our theoretical study shows that such material maps into the acoustic analog of the quantum valley-Hall effect, while numerical and experimental results confirm the existence of protected edge states traveling along the walls of topologically distinct domains.

Symmetry-protected gapless Z2 spin liquids

NASA Astrophysics Data System (ADS)

Lu, Yuan-Ming

2018-03-01

Despite rapid progress in understanding gapped topological states, much less is known about gapless topological phases of matter, especially in strongly correlated electrons. In this work, we discuss a large class of robust gapless quantum spin liquids in frustrated magnets made of half-integer spins, which are described by gapless fermionic spinons coupled to dynamical Z2 gauge fields. Requiring U(1 ) spin conservation, time-reversal, and certain space-group symmetries, we show that certain spinon symmetry fractionalization class necessarily leads to a gapless spectrum. These gapless excitations are stable against any perturbations, as long as the required symmetries are preserved. Applying these gapless criteria to spin-1/2 systems on square, triangular, and kagome lattices, we show that all gapped symmetric Z2 spin liquids in Abrikosov-fermion representation can also be realized in Schwinger-boson representation. This leads to 64 gapped Z2 spin liquids on square lattice, and 8 gapped states on both kagome and triangular lattices.

Topological Triply Degenerate Points Induced by Spin-Tensor-Momentum Couplings

NASA Astrophysics Data System (ADS)

Hu, Haiping; Hou, Junpeng; Zhang, Fan; Zhang, Chuanwei

2018-06-01

The recent discovery of triply degenerate points (TDPs) in topological materials has opened a new perspective toward the realization of novel quasiparticles without counterparts in quantum field theory. The emergence of such protected nodes is often attributed to spin-vector-momentum couplings. We show that the interplay between spin-tensor- and spin-vector-momentum couplings can induce three types of TDPs, classified by different monopole charges (C =±2 , ±1 , 0). A Zeeman field can lift them into Weyl points with distinct numbers and charges. Different TDPs of the same type are connected by intriguing Fermi arcs at surfaces, and transitions between different types are accompanied by level crossings along high-symmetry lines. We further propose an experimental scheme to realize such TDPs in cold-atom optical lattices. Our results provide a framework for studying spin-tensor-momentum coupling-induced TDPs and other exotic quasiparticles.

Coherent frequency bridge between visible and telecommunications band for vortex light.

PubMed

Liu, Shi-Long; Liu, Shi-Kai; Li, Yin-Hai; Shi, Shuai; Zhou, Zhi-Yuan; Shi, Bao-Sen

2017-10-02

In quantum communications, vortex photons can encode higher-dimensional quantum states and build high-dimensional communication networks (HDCNs). The interfaces that connect different wavelengths are significant in HDCNs. We construct a coherent orbital angular momentum (OAM) frequency bridge via difference frequency conversion in a nonlinear bulk crystal for HDCNs. Using a single resonant cavity, maximum quantum conversion efficiencies from visible to infrared are 36%, 15%, and 7.8% for topological charges of 0,1, and 2, respectively. The average fidelity obtained using quantum state tomography for the down-converted infrared OAM-state of topological charge 1 is 96.51%. We also prove that the OAM is conserved in this process by measuring visible and infrared interference patterns. This coherent OAM frequency-down conversion bridge represents a basis for an interface between two high-dimensional quantum systems operating with different spectra.

Squeezed Dirac and topological magnons in a bosonic honeycomb optical lattice

NASA Astrophysics Data System (ADS)

Owerre, S. A.; Nsofini, J.

2017-11-01

Quantum information storage using charge-neutral quasiparticles is expected to play a crucial role in the future of quantum computers. In this regard, magnons or collective spin-wave excitations in solid-state materials are promising candidates in the future of quantum computing. Here, we study the quantum squeezing of Dirac and topological magnons in a bosonic honeycomb optical lattice with spin-orbit interaction by utilizing the mapping to quantum spin-1/2 XYZ Heisenberg model on the honeycomb lattice with discrete Z2 symmetry and a Dzyaloshinskii-Moriya interaction. We show that the squeezed magnons can be controlled by the Z2 anisotropy and demonstrate how the noise in the system is periodically modified in the ferromagnetic and antiferromagnetic phases of the model. Our results also apply to solid-state honeycomb (anti)ferromagnetic insulators.

Squeezed Dirac and Topological Magnons in a Bosonic Honeycomb Optical Lattice.

PubMed

Owerre, Solomon; Nsofini, Joachim

2017-09-20

Quantum information storage using charge-neutral quasiparticles are expected to play a crucial role in the future of quantum computers. In this regard, magnons or collective spin-wave excitations in solid-state materials are promising candidates in the future of quantum computing. Here, we study the quantum squeezing of Dirac and topological magnons in a bosonic honeycomb optical lattice with spin-orbit interaction by utilizing the mapping to quantum spin-$1/2$ XYZ Heisenberg model on the honeycomb lattice with discrete Z$_2$ symmetry and a Dzyaloshinskii-Moriya interaction. We show that the squeezed magnons can be controlled by the Z$_2$ anisotropy and demonstrate how the noise in the system is periodically modified in the ferromagnetic and antiferromagnetic phases of the model. Our results also apply to solid-state honeycomb (anti)ferromagnetic insulators. . © 2017 IOP Publishing Ltd.

Squeezed Dirac and topological magnons in a bosonic honeycomb optical lattice.

PubMed

Owerre, S A; Nsofini, J

2017-10-19

Quantum information storage using charge-neutral quasiparticles is expected to play a crucial role in the future of quantum computers. In this regard, magnons or collective spin-wave excitations in solid-state materials are promising candidates in the future of quantum computing. Here, we study the quantum squeezing of Dirac and topological magnons in a bosonic honeycomb optical lattice with spin-orbit interaction by utilizing the mapping to quantum spin-[Formula: see text] XYZ Heisenberg model on the honeycomb lattice with discrete Z 2 symmetry and a Dzyaloshinskii-Moriya interaction. We show that the squeezed magnons can be controlled by the Z 2 anisotropy and demonstrate how the noise in the system is periodically modified in the ferromagnetic and antiferromagnetic phases of the model. Our results also apply to solid-state honeycomb (anti)ferromagnetic insulators.

Ferroelectric symmetry-protected multibit memory cell

DOE PAGES

Baudry, Laurent; Lukyanchuk, Igor; Vinokur, Valerii M.

2017-02-08

Here, the tunability of electrical polarization in ferroelectrics is instrumental to their applications in information-storage devices. The existing ferroelectric memory cells are based on the two-level storage capacity with the standard binary logics. However, the latter have reached its fundamental limitations. Here we propose ferroelectric multibit cells (FMBC) utilizing the ability of multiaxial ferroelectric materials to pin the polarization at a sequence of the multistable states. Employing the catastrophe theory principles we show that these states are symmetry-protected against the information loss and thus realize novel topologically-controlled access memory (TAM). Our findings enable developing a platform for the emergent many-valuedmore » non-Boolean information technology and target challenges posed by needs of quantum and neuromorphic computing.« less

Magnetically Defined Qubits on 3D Topological Insulators

NASA Astrophysics Data System (ADS)

Ferreira, Gerson J.; Loss, Daniel

2014-03-01

We explore potentials that break time-reversal symmetry to confine the surface states of 3D topological insulators into quantum wires and quantum dots. A magnetic domain wall on a ferromagnet insulator cap layer provides interfacial states predicted to show the quantum anomalous Hall effect. Here, we show that confinement can also occur at magnetic domain heterostructures, with states extended in the inner domain, as well as interfacial QAHE states at the surrounding domain walls. The proposed geometry allows the isolation of the wire and dot from spurious circumventing surface states. For the quantum dots, we find that highly spin-polarized quantized QAHE states at the dot edge constitute a promising candidate for quantum computing qubits. See [Ferreira and Loss, Phys. Rev. Lett. 111, 106802 (2013)]. We explore potentials that break time-reversal symmetry to confine the surface states of 3D topological insulators into quantum wires and quantum dots. A magnetic domain wall on a ferromagnet insulator cap layer provides interfacial states predicted to show the quantum anomalous Hall effect. Here, we show that confinement can also occur at magnetic domain heterostructures, with states extended in the inner domain, as well as interfacial QAHE states at the surrounding domain walls. The proposed geometry allows the isolation of the wire and dot from spurious circumventing surface states. For the quantum dots, we find that highly spin-polarized quantized QAHE states at the dot edge constitute a promising candidate for quantum computing qubits. See [Ferreira and Loss, Phys. Rev. Lett. 111, 106802 (2013)]. We acknowledge support from the Swiss NSF, NCCR Nanoscience, NCCR QSIT, and the Brazillian Research Support Center Initiative (NAP Q-NANO) from Pró-Reitoria de Pesquisa (PRP/USP).

Colloquium: Zoo of quantum-topological phases of matter

NASA Astrophysics Data System (ADS)

Wen, Xiao-Gang

2017-10-01

What are topological phases of matter? First, they are phases of matter at zero temperature. Second, they have a nonzero energy gap for the excitations above the ground state. Third, they are disordered liquids that seem to have no feature. But those disordered liquids actually can have rich patterns of many-body entanglement representing new kinds of order. This Colloquium gives a simple introduction and a brief survey of topological phases of matter. First topological phases with topological order (i.e., with long-range entanglement) are discussed. Then topological phases without topological order (i.e., with short-range entanglement) are covered.

Quantum oscillations and coherent interlayer transport in a new topological Dirac semimetal candidate YbMnSb2

NASA Astrophysics Data System (ADS)

Wang, Yi-Yan; Xu, Sheng; Sun, Lin-Lin; Xia, Tian-Long

2018-02-01

Dirac semimetals, which host Dirac fermions and represent a new state of quantum matter, have been studied intensively in condensed-matter physics. The exploration of new materials with topological states is important in both physics and materials science. We report the synthesis and the transport properties of high-quality single crystals of YbMnSb2. YbMnSb2 is a new compound with metallic behavior. Quantum oscillations, including Shubnikov-de Haas (SdH) oscillation and de Haas-van Alphen-type oscillation, have been observed at low temperature and high magnetic field. Small effective masses and nontrivial Berry phase are extracted from the analyses of quantum oscillations, which provide the transport evidence for the possible existence of Dirac fermions in YbMnSb2. The measurements of angular-dependent interlayer magnetoresistance indicate that the interlayer transport is coherent. The Fermi surface of YbMnSb2 possesses a quasi-two-dimensional characteristic as determined by the angular dependence of SdH oscillation frequency. These findings suggest that YbMnSb2 is a new candidate of topological Dirac semimetals.

Coupling effect of topological states and Chern insulators in two-dimensional triangular lattices

NASA Astrophysics Data System (ADS)

Zhang, Jiayong; Zhao, Bao; Xue, Yang; Zhou, Tong; Yang, Zhongqin

2018-03-01

We investigate topological states of two-dimensional (2D) triangular lattices with multiorbitals. Tight-binding model calculations of a 2D triangular lattice based on px and py orbitals exhibit very interesting doubly degenerate energy points at different positions (Γ and K /K' ) in momentum space, with quadratic non-Dirac and linear Dirac band dispersions, respectively. Counterintuitively, the system shows a global topologically trivial rather than nontrivial state with consideration of spin-orbit coupling due to the "destructive interference effect" between the topological states at the Γ and K /K' points. The topologically nontrivial state can emerge by introducing another set of triangular lattices to the system (bitriangular lattices) due to the breakdown of the interference effect. With first-principles calculations, we predict an intrinsic Chern insulating behavior (quantum anomalous Hall effect) in a family of the 2D triangular lattice metal-organic framework of Co(C21N3H15) (TPyB-Co) from this scheme. Our results provide a different path and theoretical guidance for the search for and design of new 2D topological quantum materials.

Surface quantum oscillations and weak antilocalization effect in topological insulator (Bi0.3Sb0.7)2Te3

NASA Astrophysics Data System (ADS)

Urkude, Rajashri; Rawat, Rajeev; Palikundwar, Umesh

2018-04-01

In 3D topological insulators, achieving a genuine bulk-insulating state is an important topic of research. The material system (Bi,Sb)2(Te,Se)3 has been proposed as a topological insulator with high resistivity and low carrier concentration. Topological insulators are predicted to present interesting surface transport phenomena but their experimental studies have been hindered by metallic bulk conduction that overwhelms the surface transport. Here we present a study of the bulk-insulating properties of (Bi0.3Sb0.7)2Te3. We show that a high resistivity exceeding 1 Ωm as a result of variable-range hopping behavior of state and Shubnikov-de Haas oscillations as coming from the topological surface state. We have been able to clarify both the bulk and surface transport channels, establishing a comprehensive understanding of the transport properties in this material. Our results demonstrate that (Bi0.3Sb0.7)2Te3 is a good material for studying the surface quantum transport in a topological insulator.

Pseudospin Dependent One-Way Transmission in Graphene-Based Topological Plasmonic Crystals

NASA Astrophysics Data System (ADS)

Qiu, Pingping; Qiu, Weibin; Ren, Junbo; Lin, Zhili; Wang, Zeyu; Wang, Jia-Xian; Kan, Qiang; Pan, Jiao-Qing

2018-04-01

Originating from the investigation of condensed matter states, the concept of quantum Hall effect and quantum spin Hall effect (QSHE) has recently been expanded to other field of physics and engineering, e.g., photonics and phononics, giving rise to strikingly unconventional edge modes immune to scattering. Here, we present the plasmonic analog of QSHE in graphene plasmonic crystal (GPC) in mid-infrared frequencies. The band inversion occurs when deforming the honeycomb lattice GPCs, which further leads to the topological band gaps and pseudospin features of the edge states. By overlapping the band gaps with different topologies, we numerically simulated the pseudospin-dependent one-way propagation of edge states. The designed GPC may find potential applications in the fields of topological plasmonics and trigger the exploration of the technique of the pseudospin multiplexing in high-density nanophotonic integrated circuits.

Emergent Topological order from Spin-Orbit Density wave

NASA Astrophysics Data System (ADS)

Gupta, Gaurav; Das, Tanmoy

We study the emergence of a Z2 -type topological order because of Landau type symmetry breaking order parameter. When two Rashba type SOC bands of different chirality become nested by a magic wavevector [(0, ∖pi) or (∖pi,0)], it introduces the inversion of chirality between different lattice sites. Such a density wave state is known as spin-orbit density wave. The resulting quantum order is associated with the topological order which is classified by a Z2 invariant. So, this system can simultaneously be classified by both a symmetry breaking order parameter and the associated Z2 topological invariant. This order parameter can be realized or engineered in two- or quasi-two-dimensional fermionic lattices, quantum wires, with tunable RSOC and correlation strength. The work is facilitated by the computer cluster facility at Department of Physics, Indian Institute of Science.

Topological color codes on Union Jack lattices: a stable implementation of the whole Clifford group

DOE Office of Scientific and Technical Information (OSTI.GOV)

Katzgraber, Helmut G.; Theoretische Physik, ETH Zurich, CH-8093 Zurich; Bombin, H.

We study the error threshold of topological color codes on Union Jack lattices that allow for the full implementation of the whole Clifford group of quantum gates. After mapping the error-correction process onto a statistical mechanical random three-body Ising model on a Union Jack lattice, we compute its phase diagram in the temperature-disorder plane using Monte Carlo simulations. Surprisingly, topological color codes on Union Jack lattices have a similar error stability to color codes on triangular lattices, as well as to the Kitaev toric code. The enhanced computational capabilities of the topological color codes on Union Jack lattices with respectmore » to triangular lattices and the toric code combined with the inherent robustness of this implementation show good prospects for future stable quantum computer implementations.« less

Tunable multifunctional topological insulators in ternary Heusler and related compounds

NASA Astrophysics Data System (ADS)

Felser, Claudia

2011-03-01

Recently the quantum spin Hall effect was theoretically predicted and experimentally realized in quantum wells based on the binary semiconductor HgTe. The quantum spin Hall state and topological insulators are new states of quantum matter interesting for both fundamental condensed-matter physics and material science. Many Heusler compounds with C1b structure are ternary semiconductors that are structurally and electronically related to the binary semiconductors. The diversity of Heusler materials opens wide possibilities for tuning the bandgap and setting the desired band inversion by choosing compounds with appropriate hybridization strength (by the lattice parameter) and magnitude of spin--orbit coupling (by the atomic charge). Based on first-principle calculations we demonstrate that around 50 Heusler compounds show band inversion similar to that of HgTe. The topological state in these zero-gap semiconductors can be created by applying strain or by designing an appropriate quantumwell structure, similar to the case of HgTe. Many of these ternary zero-gap semiconductors (LnAuPb, LnPdBi, LnPtSb and LnPtBi) contain the rare-earth element Ln, which can realize additional properties ranging from superconductivity (for example LaPtBi) to magnetism (for example GdPtBi) and heavy fermion behaviour (for example YbPtBi). These properties can open new research directions in realizing the quantized anomalous Hall effect and topological superconductors. Heusler compounds are similar to a stuffed diamond, correspondingly, it should be possible to find the ``high Z'' equivalent of graphene in a graphite-like structure with 18 valence electrons and with inverted bands. Indeed the ternary compounds, such as LiAuSe and KHgSb with a honeycomb structure of their Au-Se and Hg-Sb layers feature band inversion very similar to HgTe which is a strong precondition for existence of the topological surface states. These materials have a gap at the Fermi energy and are therefore candidates for 3D-topological insulators. Additionally they are centro-symmetric, therefore, it is possible to determine the parity of their wave functions, and hence, their topological character. Surprisingly, the compound KHgSb with the strong SOC is topologically trivial, whereas LiAuSe is found to be a topological non-trivial insulator.

Hg-Based Epitaxial Materials for Topological Insulators

DTIC Science & Technology

2014-07-01

Research Laboratory for investigation of properties. 15. SUBJECT TERMS EOARD, topological insulator , diluted magnetic ...topological superconductors and spintronics to quantum computation (e.g. see C.L.Kane and J.E.Moore "Topological Insulators " Physics World (2011) 24...tetradymite semiconductors Bi2Te3, Bi2Se3, and Sb2Te3 which form magnetically ordered insulators when doped with transition metal elements Cr or Fe (Rui Yu et

Topological quantum phase transitions and edge states in spin-orbital coupled Fermi gases.

PubMed

Zhou, Tao; Gao, Yi; Wang, Z D

2014-06-11

We study superconducting states in the presence of spin-orbital coupling and Zeeman field. It is found that a phase transition from a Fulde-Ferrell-Larkin-Ovchinnikov state to the topological superconducting state occurs upon increasing the spin-orbital coupling. The nature of this topological phase transition and its critical property are investigated numerically. Physical properties of the topological superconducting phase are also explored. Moreover, the local density of states is calculated, through which the topological feature may be tested experimentally.

Scalable quantum information processing with photons and atoms

NASA Astrophysics Data System (ADS)

Pan, Jian-Wei

Over the past three decades, the promises of super-fast quantum computing and secure quantum cryptography have spurred a world-wide interest in quantum information, generating fascinating quantum technologies for coherent manipulation of individual quantum systems. However, the distance of fiber-based quantum communications is limited due to intrinsic fiber loss and decreasing of entanglement quality. Moreover, probabilistic single-photon source and entanglement source demand exponentially increased overheads for scalable quantum information processing. To overcome these problems, we are taking two paths in parallel: quantum repeaters and through satellite. We used the decoy-state QKD protocol to close the loophole of imperfect photon source, and used the measurement-device-independent QKD protocol to close the loophole of imperfect photon detectors--two main loopholes in quantum cryptograph. Based on these techniques, we are now building world's biggest quantum secure communication backbone, from Beijing to Shanghai, with a distance exceeding 2000 km. Meanwhile, we are developing practically useful quantum repeaters that combine entanglement swapping, entanglement purification, and quantum memory for the ultra-long distance quantum communication. The second line is satellite-based global quantum communication, taking advantage of the negligible photon loss and decoherence in the atmosphere. We realized teleportation and entanglement distribution over 100 km, and later on a rapidly moving platform. We are also making efforts toward the generation of multiphoton entanglement and its use in teleportation of multiple properties of a single quantum particle, topological error correction, quantum algorithms for solving systems of linear equations and machine learning. Finally, I will talk about our recent experiments on quantum simulations on ultracold atoms. On the one hand, by applying an optical Raman lattice technique, we realized a two-dimensional spin-obit (SO) coupling and topological bands with ultracold bosonic atoms. A controllable crossover between 2D and 1D SO couplings is studied, and the SO effects and nontrivial band topology are observe. On the other hand, utilizing a two-dimensional spin-dependent optical superlattice and a single layer of atom cloud, we directly observed the four-body ring-exchange coupling and the Anyonic fractional statistics.

Short-ranged interaction effects on Z2 topological phase transitions: The perturbative mean-field method

NASA Astrophysics Data System (ADS)

Lai, Hsin-Hua; Hung, Hsiang-Hsuan

2015-02-01

Time-reversal symmetric topological insulator (TI) is a novel state of matter that a bulk-insulating state carries dissipationless spin transport along the surfaces, embedded by the Z2 topological invariant. In the noninteracting limit, this exotic state has been intensively studied and explored with realistic systems, such as HgTe/(Hg, Cd)Te quantum wells. On the other hand, electronic correlation plays a significant role in many solid-state systems, which further influences topological properties and triggers topological phase transitions. Yet an interacting TI is still an elusive subject and most related analyses rely on the mean-field approximation and numerical simulations. Among the approaches, the mean-field approximation fails to predict the topological phase transition, in particular at intermediate interaction strength without spontaneously breaking symmetry. In this paper, we develop an analytical approach based on a combined perturbative and self-consistent mean-field treatment of interactions that is capable of capturing topological phase transitions beyond either method when used independently. As an illustration of the method, we study the effects of short-ranged interactions on the Z2 TI phase, also known as the quantum spin Hall (QSH) phase, in three generalized versions of the Kane-Mele (KM) model at half-filling on the honeycomb lattice. The results are in excellent agreement with quantum Monte Carlo (QMC) calculations on the same model and cannot be reproduced by either a perturbative treatment or a self-consistent mean-field treatment of the interactions. Our analytical approach helps to clarify how the symmetries of the one-body terms of the Hamiltonian determine whether interactions tend to stabilize or destabilize a topological phase. Moreover, our method should be applicable to a wide class of models where topological transitions due to interactions are in principle possible, but are not correctly predicted by either perturbative or self-consistent treatments.

Time-reversal-invariant spin-orbit-coupled bilayer Bose-Einstein condensates

NASA Astrophysics Data System (ADS)

Maisberger, Matthew; Wang, Lin-Cheng; Sun, Kuei; Xu, Yong; Zhang, Chuanwei

2018-05-01

Time-reversal invariance plays a crucial role for many exotic quantum phases, particularly for topologically nontrivial states, in spin-orbit coupled electronic systems. Recently realized spin-orbit coupled cold-atom systems, however, lack the time-reversal symmetry due to the inevitable presence of an effective transverse Zeeman field. We address this issue by analyzing a realistic scheme to preserve time-reversal symmetry in spin-orbit-coupled ultracold atoms, with the use of Hermite-Gaussian-laser-induced Raman transitions that preserve spin-layer time-reversal symmetry. We find that the system's quantum states form Kramers pairs, resulting in symmetry-protected gap closing of the lowest two bands at arbitrarily large Raman coupling. We also show that Bose gases in this setup exhibit interaction-induced layer-stripe and uniform phases as well as intriguing spin-layer symmetry and spin-layer correlation.

Enhanced zero-bias Majorana peak in the differential tunneling conductance of disordered multisubband quantum-wire/superconductor junctions.

PubMed

Pientka, Falko; Kells, Graham; Romito, Alessandro; Brouwer, Piet W; von Oppen, Felix

2012-11-30

A recent experiment Mourik et al. [Science 336, 1003 (2012)] on InSb quantum wires provides possible evidence for the realization of a topological superconducting phase and the formation of Majorana bound states. Motivated by this experiment, we consider the signature of Majorana bound states in the differential tunneling conductance of multisubband wires. We show that the weight of the Majorana-induced zero-bias peak is strongly enhanced by mixing of subbands, when disorder is added to the end of the quantum wire. We also consider how the topological phase transition is reflected in the gap structure of the current-voltage characteristic.

One-Loop Test of Quantum Black Holes in anti–de Sitter Space

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, James T.; Pando Zayas, Leopoldo A.; Rathee, Vimal

Within 11-dimensional supergravity we compute the logarithmic correction to the entropy of magnetically charged asymptotically AdS4 black holes with arbitrary horizon topology. We find perfect agreement with the expected microscopic result arising from the dual field theory computation of the topologically twisted index. Our result relies crucially on a particular limit to the extremal black hole case and clarifies some aspects of quantum corrections in asymptotically AdS spacetimes.

One-Loop Test of Quantum Black Holes in anti–de Sitter Space

DOE PAGES

Liu, James T.; Pando Zayas, Leopoldo A.; Rathee, Vimal; ...

2018-06-01

Within 11-dimensional supergravity we compute the logarithmic correction to the entropy of magnetically charged asymptotically AdS4 black holes with arbitrary horizon topology. We find perfect agreement with the expected microscopic result arising from the dual field theory computation of the topologically twisted index. Our result relies crucially on a particular limit to the extremal black hole case and clarifies some aspects of quantum corrections in asymptotically AdS spacetimes.

One-Loop Test of Quantum Black Holes in anti-de Sitter Space

NASA Astrophysics Data System (ADS)

Liu, James T.; Pando Zayas, Leopoldo A.; Rathee, Vimal; Zhao, Wenli

2018-06-01

Within 11-dimensional supergravity we compute the logarithmic correction to the entropy of magnetically charged asymptotically AdS4 black holes with arbitrary horizon topology. We find perfect agreement with the expected microscopic result arising from the dual field theory computation of the topologically twisted index. Our result relies crucially on a particular limit to the extremal black hole case and clarifies some aspects of quantum corrections in asymptotically AdS spacetimes.

Anonymous broadcasting of classical information with a continuous-variable topological quantum code

NASA Astrophysics Data System (ADS)

Menicucci, Nicolas C.; Baragiola, Ben Q.; Demarie, Tommaso F.; Brennen, Gavin K.

2018-03-01

Broadcasting information anonymously becomes more difficult as surveillance technology improves, but remarkably, quantum protocols exist that enable provably traceless broadcasting. The difficulty is making scalable entangled resource states that are robust to errors. We propose an anonymous broadcasting protocol that uses a continuous-variable surface-code state that can be produced using current technology. High squeezing enables large transmission bandwidth and strong anonymity, and the topological nature of the state enables local error mitigation.

One-Loop Test of Quantum Black Holes in anti-de Sitter Space.

PubMed

Liu, James T; Pando Zayas, Leopoldo A; Rathee, Vimal; Zhao, Wenli

2018-06-01

Within 11-dimensional supergravity we compute the logarithmic correction to the entropy of magnetically charged asymptotically AdS_{4} black holes with arbitrary horizon topology. We find perfect agreement with the expected microscopic result arising from the dual field theory computation of the topologically twisted index. Our result relies crucially on a particular limit to the extremal black hole case and clarifies some aspects of quantum corrections in asymptotically AdS spacetimes.

Chiral magnetic and vortical effects in high-energy nuclear collisions—A status report

DOE PAGES

Kharzeev, D. E.; Liao, J.; Voloshin, S. A.; ...

2016-05-01

Here, the interplay of quantum anomalies with magnetic field and vorticity results in a variety of novel non-dissipative transport phenomena in systems with chiral fermions, including the quark–gluon plasma. Among them is the Chiral Magnetic Effect (CME)—the generation of electric current along an external magnetic field induced by chirality imbalance. Because the chirality imbalance is related to the global topology of gauge fields, the CME current is topologically protected and hence non-dissipative even in the presence of strong interactions. As a result, the CME and related quantum phenomena affect the hydrodynamical and transport behavior of strongly coupled quark–gluon plasma, andmore » can be studied in relativistic heavy ion collisions where strong magnetic fields are created by the colliding ions. Evidence for the CME and related phenomena has been reported by the STAR Collaboration at Relativistic Heavy Ion Collider at BNL, and by the ALICE Collaboration at the Large Hadron Collider at CERN. The goal of the present review is to provide an elementary introduction into the physics of anomalous chiral effects, to describe the current status of experimental studies in heavy ion physics, and to outline the future work, both in experiment and theory, needed to eliminate the existing uncertainties in the interpretation of the data.« less

Higher (odd) dimensional quantum Hall effect and extended dimensional hierarchy

NASA Astrophysics Data System (ADS)

Hasebe, Kazuki

2017-07-01

We demonstrate dimensional ladder of higher dimensional quantum Hall effects by exploiting quantum Hall effects on arbitrary odd dimensional spheres. Non-relativistic and relativistic Landau models are analyzed on S 2 k - 1 in the SO (2 k - 1) monopole background. The total sub-band degeneracy of the odd dimensional lowest Landau level is shown to be equal to the winding number from the base-manifold S 2 k - 1 to the one-dimension higher SO (2 k) gauge group. Based on the chiral Hopf maps, we clarify the underlying quantum Nambu geometry for odd dimensional quantum Hall effect and the resulting quantum geometry is naturally embedded also in one-dimension higher quantum geometry. An origin of such dimensional ladder connecting even and odd dimensional quantum Hall effects is illuminated from a viewpoint of the spectral flow of Atiyah-Patodi-Singer index theorem in differential topology. We also present a BF topological field theory as an effective field theory in which membranes with different dimensions undergo non-trivial linking in odd dimensional space. Finally, an extended version of the dimensional hierarchy for higher dimensional quantum Hall liquids is proposed, and its relationship to quantum anomaly and D-brane physics is discussed.

Probing topological protection using a designer surface plasmon structure

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gao, Fei; Gao, Zhen; Shi, Xihang

Topological photonic states, inspired by robust chiral edge states in topological insulators, have recently been demonstrated in a few photonic systems, including an array of coupled on-chip ring resonators at communication wavelengths. However, the intrinsic difference between electrons and photons determines that the 'topological protection' in time-reversal-invariant photonic systems does not share the same robustness as its counterpart in electronic topological insulators. Here in a designer surface plasmon platform consisting of tunable metallic sub-wavelength structures, we construct photonic topological edge states and probe their robustness against a variety of defect classes, including some common time-reversal-invariant photonic defects that can breakmore » the topological protection, but do not exist in electronic topological insulators. Furthermore, this is also an experimental realization of anomalous Floquet topological edge states, whose topological phase cannot be predicted by the usual Chern number topological invariants.« less

Probing topological protection using a designer surface plasmon structure

DOE PAGES

Gao, Fei; Gao, Zhen; Shi, Xihang; ...

2016-05-20

Topological photonic states, inspired by robust chiral edge states in topological insulators, have recently been demonstrated in a few photonic systems, including an array of coupled on-chip ring resonators at communication wavelengths. However, the intrinsic difference between electrons and photons determines that the 'topological protection' in time-reversal-invariant photonic systems does not share the same robustness as its counterpart in electronic topological insulators. Here in a designer surface plasmon platform consisting of tunable metallic sub-wavelength structures, we construct photonic topological edge states and probe their robustness against a variety of defect classes, including some common time-reversal-invariant photonic defects that can breakmore » the topological protection, but do not exist in electronic topological insulators. Furthermore, this is also an experimental realization of anomalous Floquet topological edge states, whose topological phase cannot be predicted by the usual Chern number topological invariants.« less

Quantum corrections crossover and ferromagnetism in magnetic topological insulators.

PubMed

Bao, Lihong; Wang, Weiyi; Meyer, Nicholas; Liu, Yanwen; Zhang, Cheng; Wang, Kai; Ai, Ping; Xiu, Faxian

2013-01-01

Revelation of emerging exotic states of topological insulators (TIs) for future quantum computing applications relies on breaking time-reversal symmetry and opening a surface energy gap. Here, we report on the transport response of Bi2Te3 TI thin films in the presence of varying Cr dopants. By tracking the magnetoconductance (MC) in a low doping regime we observed a progressive crossover from weak antilocalization (WAL) to weak localization (WL) as the Cr concentration increases. In a high doping regime, however, increasing Cr concentration yields a monotonically enhanced anomalous Hall effect (AHE) accompanied by an increasing carrier density. Our results demonstrate a possibility of manipulating bulk ferromagnetism and quantum transport in magnetic TI, thus providing an alternative way for experimentally realizing exotic quantum states required by spintronic applications.

Topologically-protected one-way leaky waves in nonreciprocal plasmonic structures

NASA Astrophysics Data System (ADS)

Hassani Gangaraj, S. Ali; Monticone, Francesco

2018-03-01

We investigate topologically-protected unidirectional leaky waves on magnetized plasmonic structures acting as homogeneous photonic topological insulators. Our theoretical analyses and numerical experiments aim at unveiling the general properties of these exotic surface waves, and their nonreciprocal and topological nature. In particular, we study the behavior of topological leaky modes in stratified structures composed of a magnetized plasma at the interface with isotropic conventional media, and we show how to engineer their propagation and radiation properties, leading to topologically-protected backscattering-immune wave propagation, and highly directive and tunable radiation. Taking advantage of the non-trivial topological properties of these leaky modes, we also theoretically demonstrate advanced functionalities, including arbitrary re-routing of leaky waves on the surface of bodies with complex shapes, as well as the realization of topological leaky-wave (nano)antennas with isolated channels of radiation that are completely independent and separately tunable. Our findings help shedding light on the behavior of topologically-protected modes in open wave-guiding structures, and may open intriguing directions for future antenna generations based on topological structures, at microwaves and optical frequencies.

Quantum phase transitions between a class of symmetry protected topological states

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tsui, Lokman; Jiang, Hong-Chen; Lu, Yuan-Ming

2015-07-01

The subject of this paper is the phase transition between symmetry protected topological states (SPTs). We consider spatial dimension d and symmetry group G so that the cohomology group, Hd+1(G,U(1)), contains at least one Z2n or Z factor. We show that the phase transition between the trivial SPT and the root states that generate the Z2n or Z groups can be induced on the boundary of a (d+1)-dimensional View the MathML source-symmetric SPT by a View the MathML source symmetry breaking field. Moreover we show these boundary phase transitions can be “transplanted” to d dimensions and realized in lattice modelsmore » as a function of a tuning parameter. The price one pays is for the critical value of the tuning parameter there is an extra non-local (duality-like) symmetry. In the case where the phase transition is continuous, our theory predicts the presence of unusual (sometimes fractionalized) excitations corresponding to delocalized boundary excitations of the non-trivial SPT on one side of the transition. This theory also predicts other phase transition scenarios including first order transition and transition via an intermediate symmetry breaking phase.« less

Quantum phase transitions between a class of symmetry protected topological states

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tsui, Lokman; Jiang, Hong -Chen; Lu, Yuan -Ming

2015-04-30

The subject of this paper is the phase transition between symmetry protected topological states (SPTs). We consider spatial dimension d and symmetry group G so that the cohomology group, H d+1(G,U(1)), contains at least one Z 2n or Z factor. We show that the phase transition between the trivial SPT and the root states that generate the Z 2n or Z groups can be induced on the boundary of a (d+1)-dimensional G x Z T 2-symmetric SPT by a Z T 2 symmetry breaking field. Moreover we show these boundary phase transitions can be “transplanted” to d dimensions and realizedmore » in lattice models as a function of a tuning parameter. The price one pays is for the critical value of the tuning parameter there is an extra non-local (duality-like) symmetry. In the case where the phase transition is continuous, our theory predicts the presence of unusual (sometimes fractionalized) excitations corresponding to delocalized boundary excitations of the non-trivial SPT on one side of the transition. This theory also predicts other phase transition scenarios including first order transition and transition via an intermediate symmetry breaking phase.« less

Gauge invariance of fractionally charged quasiparticles and hidden topological Zn symmetry

NASA Astrophysics Data System (ADS)

Wu, Yong-Shi; Hatsugai, Yasuhiro; Kohmoto, Mahito

1991-02-01

Using the braid-group formalism we study the consequences of gauge invariance for fractionally charged anyonic quasiparticles in a two-dimensional multiply connected system. It is shown that gauge invariance requires multicomponent wave functions, and leads to the emergence of a hidden topological Zn symmetry with associated quantum number and unavoidable occurrence of level crossings for many-body eigenstates. In certain situations, it relates the fractional charge to anyon statistics. The implications for the fractional quantum Hall effect are also discussed.

Quantum anomalous Hall phase in a one-dimensional optical lattice

NASA Astrophysics Data System (ADS)

Liu, Sheng; Shao, L. B.; Hou, Qi-Zhe; Xue, Zheng-Yuan

2018-03-01

We propose to simulate and detect quantum anomalous Hall phase with ultracold atoms in a one-dimensional optical lattice, with the other synthetic dimension being realized by modulating spin-orbit coupling. We show that the system manifests a topologically nontrivial phase with two chiral edge states which can be readily detected in this synthetic two-dimensional system. Moreover, it is interesting that at the phase transition point there is a flat energy band and this system can also be in a topologically nontrivial phase with two Fermi zero modes existing at the boundaries by considering the synthetic dimension as a modulated parameter. We also show how to measure these topological phases experimentally in ultracold atoms. Another model with a random Rashba and Dresselhaus spin-orbit coupling strength is also found to exhibit topological nontrivial phase, and the impact of the disorder to the system is revealed.

Quon 3D language for quantum information

PubMed Central

Liu, Zhengwei; Wozniakowski, Alex; Jaffe, Arthur M.

2017-01-01

We present a 3D topological picture-language for quantum information. Our approach combines charged excitations carried by strings, with topological properties that arise from embedding the strings in the interior of a 3D manifold with boundary. A quon is a composite that acts as a particle. Specifically, a quon is a hemisphere containing a neutral pair of open strings with opposite charge. We interpret multiquons and their transformations in a natural way. We obtain a type of relation, a string–genus “joint relation,” involving both a string and the 3D manifold. We use the joint relation to obtain a topological interpretation of the C∗-Hopf algebra relations, which are widely used in tensor networks. We obtain a 3D representation of the controlled NOT (CNOT) gate that is considerably simpler than earlier work, and a 3D topological protocol for teleportation. PMID:28167790

Photonic simulation of topological superconductor edge state and zero-energy mode at a vortex

PubMed Central

Tan, Wei; Chen, Liang; Ji, Xia; Lin, Hai-Qing

2014-01-01

Photonic simulations of quantum Hall edge states and topological insulators have inspired considerable interest in recent years. Interestingly, there are theoretical predictions for another type of topological states in topological superconductors, but debates over their experimental observations still remain. Here we investigate the photonic analogue of the px + ipy model of topological superconductor. Two essential characteristics of topological superconductor, particle-hole symmetry and px + ipy pairing potentials, are well emulated in photonic systems. Its topological features are presented by chiral edge state and zero-energy mode at a vortex. This work may fertilize the study of photonic topological states, and open up the possibility for emulating wave behaviors in superconductors. PMID:25488408

Materials considerations for forming the topological insulator phase in InAs/GaSb heterostructures

NASA Astrophysics Data System (ADS)

Shojaei, B.; McFadden, A. P.; Pendharkar, M.; Lee, J. S.; Flatté, M. E.; Palmstrøm, C. J.

2018-06-01

In an ideal InAs/GaSb bilayer of appropriate dimension, in-plane electron and hole bands overlap and hybridize, and a topologically nontrivial, or quantum spin Hall (QSH) insulator, phase is predicted to exist. The in-plane dispersion's potential landscape, however, is subject to microscopic perturbations originating from material imperfections. In this work, the effect of disorder on the electronic structure of InAs/GaSb (001) bilayers was studied by observing the temperature and magnetic-field dependence of the resistance of a dual-gated heterostructure gate-tuned through the inverted to normal gap regimes. Conduction with the electronic structure tuned to the inverted (predicted topological) regime and the Fermi level in the hybridization gap was qualitatively similar to behavior in a disordered two-dimensional system. The impact of charged impurities and interface roughness on the formation of topologically protected edge states and an insulating bulk was estimated. The experimental evidence and estimates of disorder in the potential landscape indicated that the potential fluctuations in state-of-the-art films are sufficiently strong such that conduction with the electronic structure tuned to the predicted topological insulator (TI) regime and the Fermi level in the hybridization gap was dominated by a symplectic metal phase rather than a TI phase. The implications are that future efforts must address disorder in this system, and focus must be placed on the reduction of defects and disorder in these heterostructures if a TI regime is to be achieved.

Probing spin helical surface states in topological HgTe nanowires

NASA Astrophysics Data System (ADS)

Ziegler, J.; Kozlovsky, R.; Gorini, C.; Liu, M.-H.; Weishäupl, S.; Maier, H.; Fischer, R.; Kozlov, D. A.; Kvon, Z. D.; Mikhailov, N.; Dvoretsky, S. A.; Richter, K.; Weiss, D.

2018-01-01

Nanowires with helical surface states represent key prerequisites for observing and exploiting phase-coherent topological conductance phenomena, such as spin-momentum locked quantum transport or topological superconductivity. We demonstrate in a joint experimental and theoretical study that gated nanowires fabricated from high-mobility strained HgTe, known as a bulk topological insulator, indeed preserve the topological nature of the surface states, that moreover extend phase-coherently across the entire wire geometry. The phase-coherence lengths are enhanced up to 5 μ m when tuning the wires into the bulk gap, so as to single out topological transport. The nanowires exhibit distinct conductance oscillations, both as a function of the flux due to an axial magnetic field and of a gate voltage. The observed h /e -periodic Aharonov-Bohm-type modulations indicate surface-mediated quasiballistic transport. Furthermore, an in-depth analysis of the scaling of the observed gate-dependent conductance oscillations reveals the topological nature of these surface states. To this end we combined numerical tight-binding calculations of the quantum magnetoconductance with simulations of the electrostatics, accounting for the gate-induced inhomogeneous charge carrier densities around the wires. We find that helical transport prevails even for strongly inhomogeneous gating and is governed by flux-sensitive high-angular momentum surface states that extend around the entire wire circumference.

Electronic-topological study of the structure-activity relationships in a series of steroids with mineralocorticoid binding affinity.

PubMed

Kandemirli, Fatma; Tokay, Nesrin; Shvets, Nataly M; Dimoglo, Anatoly S

2003-01-01

Conformational analysis and quantum chemical calculations were carried out using molecular mechanics (MMP2) and semi-empirical quantum chemistry (CNDO/2) methods for 51 steroid homologues belonging to a series of 17-spirolactones. Matrices called Electronic-Topological Matrices of Conjunction (ETMCs) were formed using data obtained from quantum chemical calculations. A structural fragment of activity was identified in the series of steroids. As seen from the fragment's properties, active compounds are characterized by the presence of two atoms of oxygen, O1 and O3, which are situated at a distance of 13.5 A and possess high negative charges (-0.29 to -0.31 e).

Macroscopic Quantum Tunneling in Superconducting Junctions of β-Ag2Se Topological Insulator Nanowire.

PubMed

Kim, Jihwan; Kim, Bum-Kyu; Kim, Hong-Seok; Hwang, Ahreum; Kim, Bongsoo; Doh, Yong-Joo

2017-11-08

We report on the fabrication and electrical transport properties of superconducting junctions made of β-Ag 2 Se topological insulator (TI) nanowires in contact with Al superconducting electrodes. The temperature dependence of the critical current indicates that the superconducting junction belongs to a short and diffusive junction regime. As a characteristic feature of the narrow junction, the critical current decreases monotonously with increasing magnetic field. The stochastic distribution of the switching current exhibits the macroscopic quantum tunneling behavior, which is robust up to T = 0.8 K. Our observations indicate that the TI nanowire-based Josephson junctions can be a promising building block for the development of nanohybrid superconducting quantum bits.

Fractionally charged skyrmions in fractional quantum Hall effect

DOE PAGES

Balram, Ajit C.; Wurstbauer, U.; Wójs, A.; ...

2015-11-26

The fractional quantum Hall effect has inspired searches for exotic emergent topological particles, such as fractionally charged excitations, composite fermions, abelian and nonabelian anyons and Majorana fermions. Fractionally charged skyrmions, which support both topological charge and topological vortex-like spin structure, have also been predicted to occur in the vicinity of 1/3 filling of the lowest Landau level. The fractional skyrmions, however, are anticipated to be exceedingly fragile, suppressed by very small Zeeman energies. Here we show that, slightly away from 1/3 filling, the smallest manifestations of the fractional skyrmion exist in the excitation spectrum for a broad range of Zeemanmore » energies, and appear in resonant inelastic light scattering experiments as well-defined resonances slightly below the long wavelength spin wave mode. The spectroscopy of these exotic bound states serves as a sensitive tool for investigating the residual interaction between composite fermions, responsible for delicate new fractional quantum Hall states in this filling factor region.« less

Quantum anomalous Hall effect in time-reversal-symmetry breaking topological insulators

NASA Astrophysics Data System (ADS)

Chang, Cui-Zu; Li, Mingda

2016-03-01

The quantum anomalous Hall effect (QAHE), the last member of Hall family, was predicted to exhibit quantized Hall conductivity {σyx}=\\frac{{{e}2}}{h} without any external magnetic field. The QAHE shares a similar physical phenomenon with the integer quantum Hall effect (QHE), whereas its physical origin relies on the intrinsic topological inverted band structure and ferromagnetism. Since the QAHE does not require external energy input in the form of magnetic field, it is believed that this effect has unique potential for applications in future electronic devices with low-power consumption. More recently, the QAHE has been experimentally observed in thin films of the time-reversal symmetry breaking ferromagnetic (FM) topological insulators (TI), Cr- and V- doped (Bi,Sb)2Te3. In this topical review, we review the history of TI based QAHE, the route to the experimental observation of the QAHE in the above two systems, the current status of the research of the QAHE, and finally the prospects for future studies.

Fingerprints of quantum spin ice in Raman scattering

NASA Astrophysics Data System (ADS)

Perkins, Natalia

Quantum spin liquids (QSLs) emerging in frustrated magnetic systems have been a fascinating and challenging subject in modern condensed matter physics for over four decades. In these systems the conventional ordering is suppressed and, instead, unusual behaviors strongly dependent on the topology of the system are observed. The difficulty in the experimental observation of QSLs comes from the fact that unlike the states with broken symmetry, the topological order characteristic of cannot be captured by a local order parameter and thus cannot be detected by local measurements. Identifying QSLs therefore requires reconsideration of experimental probes to find ones sensitive to features characteristic of topological order. The fractionalization of excitations associated with this order can offer signatures that can be probed by conventional methods such as inelastic neutron scattering, Raman or Resonant X-ray scattering experiments. In my talk I will discuss the possibility to use Raman scattering to probe the excitations of Quantum Spin Ice, a model which has long been believed to host a U(1) spin liquid ground state. NSF DMR-1511768.

No-go theorem for boson condensation in topologically ordered quantum liquids

DOE Office of Scientific and Technical Information (OSTI.GOV)

Neupert, Titus; He, Huan; Keyserlingk, Curt von

Certain phase transitions between topological quantum field theories (TQFTs) are driven by the condensation of bosonic anyons. However, as bosons in a TQFT are themselves nontrivial collective excitations, there can be topological obstructions that prevent them from condensing. Here we formulate such an obstruction in the form of a no-go theorem. We use it to show that no condensation is possible in SO(3) k TQFTs with odd k. We further show that a 'layered' theory obtained by tensoring SO(3) k TQFT with itself any integer number of times does not admit condensation transitions either. Furthermore, this includes (as the casemore » k = 3) the noncondensability of any number of layers of the Fibonacci TQFT.« less

Spin-polarized charge transport in HgTe/CdTe quantum well topological insulator under a ferromagnetic metal strip

NASA Astrophysics Data System (ADS)

Wu, Zhenhua; Luo, Kun; Yu, Jiahan; Wu, Xiaobo; Lin, Liangzhong

2018-02-01

Electron tunneling through a single magnetic barrier in a HgTe topological insulator has been theoretically investigated. We find that the perpendicular magnetic field would not lead to spin-flip of the edge states due to the conservation of the angular moment. By tuning the magnetic field and the Fermi energy, the edge channels can be transited from switch-on states to switch-off states and the current from unpolarized states can be filtered to fully spin polarized states. These features offer us an efficient way to control charge/spin transport in a HgTe/CdTe quantum well, and pave a way to construct the nanoelectronic devices utilizing the topological edge states.

Two-leg Su-Schrieffer-Heeger chain with glide reflection symmetry

NASA Astrophysics Data System (ADS)

Zhang, Shao-Liang; Zhou, Qi

2017-06-01

The Su-Schrieffer-Heeger (SSH) model lays the foundation of many important concepts in quantum topological matters. Here, we show that a spin-dependent double-well optical lattice allows one to couple two topologically distinct SSH chains in the bulk and realize a glided-two-leg SSH model that respects the glide reflection symmetry. Such a model gives rise to intriguing quantum phenomena beyond the paradigm of a traditional SSH model. It is characterized by Wilson lines that require non-Abelian Berry connections, and the interplay between the glide symmetry and interaction automatically leads to charge fractionalization without jointing two lattice potentials at an interface. Our work demonstrates the versatility of ultracold atoms to create new theoretical models for studying topological matters.

No-go theorem for boson condensation in topologically ordered quantum liquids

DOE PAGES

Neupert, Titus; He, Huan; Keyserlingk, Curt von; ...

2016-12-07

Certain phase transitions between topological quantum field theories (TQFTs) are driven by the condensation of bosonic anyons. However, as bosons in a TQFT are themselves nontrivial collective excitations, there can be topological obstructions that prevent them from condensing. Here we formulate such an obstruction in the form of a no-go theorem. We use it to show that no condensation is possible in SO(3) k TQFTs with odd k. We further show that a 'layered' theory obtained by tensoring SO(3) k TQFT with itself any integer number of times does not admit condensation transitions either. Furthermore, this includes (as the casemore » k = 3) the noncondensability of any number of layers of the Fibonacci TQFT.« less

Quantized Rabi oscillations and circular dichroism in quantum Hall systems

NASA Astrophysics Data System (ADS)

Tran, D. T.; Cooper, N. R.; Goldman, N.

2018-06-01

The dissipative response of a quantum system upon periodic driving can be exploited as a probe of its topological properties. Here we explore the implications of such phenomena in two-dimensional gases subjected to a uniform magnetic field. It is shown that a filled Landau level exhibits a quantized circular dichroism, which can be traced back to its underlying nontrivial topology. Based on selection rules, we find that this quantized effect can be suitably described in terms of Rabi oscillations, whose frequencies satisfy simple quantization laws. We discuss how quantized dissipative responses can be probed locally, both in the bulk and at the boundaries of the system. This work suggests alternative forms of topological probes based on circular dichroism.

Autonomous stabilizer for incompressible photon fluids and solids

NASA Astrophysics Data System (ADS)

Ma, Ruichao; Owens, Clai; Houck, Andrew; Schuster, David I.; Simon, Jonathan

2017-04-01

We suggest a simple approach to populate photonic quantum materials at nonzero chemical potential and near-zero temperature. Taking inspiration from forced evaporation in cold-atom experiments, the essential ingredients for our low-entropy thermal reservoir are (a) interparticle interactions and (b) energy-dependent loss. The resulting thermal reservoir may then be coupled to a broad class of Hamiltonian systems to produce low-entropy quantum phases. We present an idealized picture of such a reservoir, deriving the scaling of reservoir entropy with system parameters, and then propose several practical implementations using only standard circuit quantum electrodynamics tools, and extract the fundamental performance limits. Finally, we explore, both analytically and numerically, the coupling of such a thermalizer to the paradigmatic Bose-Hubbard chain, where we employ it to stabilize an n =1 Mott phase. In this case, the performance is limited by the interplay of dynamically arrested thermalization of the Mott insulator and finite heat capacity of the thermalizer, characterized by its repumping rate. This work explores an approach to preparation of quantum phases of strongly interacting photons, and provides a potential route to topologically protected phases that are difficult to reach through adiabatic evolution.

Critical behavior of the extended Hubbard model with bond dimerization

NASA Astrophysics Data System (ADS)

Ejima, Satoshi; Lange, Florian; Essler, Fabian H. L.; Fehske, Holger

2018-05-01

Exploiting the matrix-product-state based density-matrix renormalization group (DMRG) technique we study the one-dimensional extended (U-V) Hubbard model with explicit bond dimerization in the half-filled band sector. In particular we investigate the nature of the quantum phase transition, taking place with growing ratio V / U between the symmetry-protected-topological and charge-density-wave insulating states. The (weak-coupling) critical line of continuous Ising transitions with central charge c = 1 / 2 terminates at a tricritical point belonging to the universality class of the dilute Ising model with c = 7 / 10 . We demonstrate that our DMRG data perfectly match with (tricritical) Ising exponents, e.g., for the order parameter β = 1 / 8 (1/24) and correlation length ν = 1 (5/9). Beyond the tricritical Ising point, in the strong-coupling regime, the quantum phase transition becomes first order.

Anomalous low-temperature Coulomb drag in graphene-GaAs heterostructures.

PubMed

Gamucci, A; Spirito, D; Carrega, M; Karmakar, B; Lombardo, A; Bruna, M; Pfeiffer, L N; West, K W; Ferrari, A C; Polini, M; Pellegrini, V

2014-12-19

Vertical heterostructures combining different layered materials offer novel opportunities for applications and fundamental studies. Here we report a new class of heterostructures comprising a single-layer (or bilayer) graphene in close proximity to a quantum well created in GaAs and supporting a high-mobility two-dimensional electron gas. In our devices, graphene is naturally hole-doped, thereby allowing for the investigation of electron-hole interactions. We focus on the Coulomb drag transport measurements, which are sensitive to many-body effects, and find that the Coulomb drag resistivity significantly increases for temperatures <5-10 K. The low-temperature data follow a logarithmic law, therefore displaying a notable departure from the ordinary quadratic temperature dependence expected in a weakly correlated Fermi-liquid. This anomalous behaviour is consistent with the onset of strong interlayer correlations. Our heterostructures represent a new platform for the creation of coherent circuits and topologically protected quantum bits.

Focus on topological physics: from condensed matter to cold atoms and optics

NASA Astrophysics Data System (ADS)

Zhai, Hui; Rechtsman, Mikael; Lu, Yuan-Ming; Yang, Kun

2016-08-01

The notions of a topological phase and topological order were first introduced in the studies of integer and fractional quantum Hall effects, and further developed in the study of topological insulators and topological superconductors in the past decade. Topological concepts are now widely used in many branches of physics, not only limited to condensed matter systems but also in ultracold atomic systems, photonic materials and trapped ions. Papers published in this focus issue are direct testaments of that, and readers will gain a global view of how topology impacts different branches of contemporary physics. We hope that these pages will inspire new ideas through communication between different fields.

Towards laboratory detection of topological vortices in superfluid phases of QCD

NASA Astrophysics Data System (ADS)

Das, Arpan; Dave, Shreyansh S.; de, Somnath; Srivastava, Ajit M.

2017-10-01

Topological defects arise in a variety of systems, e.g. vortices in superfluid helium to cosmic strings in the early universe. There is an indirect evidence of neutron superfluid vortices from the glitches in pulsars. One also expects that the topological defects may arise in various high baryon density phases of quantum chromodynamics (QCD), e.g. superfluid topological vortices in the color flavor locked (CFL) phase. Though vastly different in energy/length scales, there are universal features in the formation of all these defects. Utilizing this universality, we investigate the possibility of detecting these topological superfluid vortices in laboratory experiments, namely heavy-ion collisions (HICs). Using hydrodynamic simulations, we show that vortices can qualitatively affect the power spectrum of flow fluctuations. This can give an unambiguous signal for superfluid transition resulting in vortices, allowing for the check of defect formation theories in a relativistic quantum field theory system, and the detection of superfluid phases of QCD. Detection of nucleonic superfluid vortices in low energy HICs will give opportunity for laboratory controlled study of their properties, providing crucial inputs for the physics of pulsars.

Strain-induced topological quantum phase transition in phosphorene oxide

NASA Astrophysics Data System (ADS)

Kang, Seoung-Hun; Park, Jejune; Woo, Sungjong; Kwon, Young-Kyun

Using ab initio density functional theory, we investigate the structural stability and electronic properties of phosphorene oxides (POx) with different oxygen compositions x. A variety of configurations are modeled and optimized geometrically to search for the equilibrium structure for each x value. Our electronic structure calculations on the equilibrium configuration obtained for each x reveal that the band gap tends to increase with the oxygen composition of x < 0.5, and then to decrease with x > 0.5. We further explore the strain effect on the electronic structure of the fully oxidized phosphorene, PO, with x = 1. At a particular strain without spin-orbit coupling (SOC) is observed a band gap closure near the Γ point in the k space. We further find the strain in tandem with SOC induces an interesting band inversion with a reopened very small band gap (5 meV), and thus gives rise to a topological quantum phase transition from a normal insulator to a topological insulator. Such a topological phase transition is confirmed by the wave function analysis and the band topology identified by the Z2 invariant calculation.

Experimentally probing topological order and its breakdown through modular matrices

NASA Astrophysics Data System (ADS)

Luo, Zhihuang; Li, Jun; Li, Zhaokai; Hung, Ling-Yan; Wan, Yidun; Peng, Xinhua; Du, Jiangfeng

2018-02-01

The modern concept of phases of matter has undergone tremendous developments since the first observation of topologically ordered states in fractional quantum Hall systems in the 1980s. In this paper, we explore the following question: in principle, how much detail of the physics of topological orders can be observed using state of the art technologies? We find that using surprisingly little data, namely the toric code Hamiltonian in the presence of generic disorders and detuning from its exactly solvable point, the modular matrices--characterizing anyonic statistics that are some of the most fundamental fingerprints of topological orders--can be reconstructed with very good accuracy solely by experimental means. This is an experimental realization of these fundamental signatures of a topological order, a test of their robustness against perturbations, and a proof of principle--that current technologies have attained the precision to identify phases of matter and, as such, probe an extended region of phase space around the soluble point before its breakdown. Given the special role of anyonic statistics in quantum computation, our work promises myriad applications both in probing and realistically harnessing these exotic phases of matter.

Topology-preserving quantum deformation with non-numerical parameter

NASA Astrophysics Data System (ADS)

Aukhadiev, Marat; Grigoryan, Suren; Lipacheva, Ekaterina

2013-11-01

We introduce a class of compact quantum semigroups, that we call semigroup deformations of compact Abelian qroups. These objects arise from reduced semigroup -algebras, the generalization of the Toeplitz algebra. We study quantum subgroups, quantum projective spaces and quantum quotient groups for such objects, and show that the group is contained as a compact quantum subgroup in the deformation of itself. The connection with the weak Hopf algebra notion is described. We give a grading on the -algebra of the compact quantum semigroups constructed.

Superconductivity and ferromagnetism in topological insulators

NASA Astrophysics Data System (ADS)

Zhang, Duming

Topological insulators, a new state of matter discovered recently, have attracted great interest due to their novel properties. They are insulating inside the bulk, but conducting at the surface or edges. This peculiar behavior is characterized by an insulating bulk energy gap and gapless surface or edge states, which originate from strong spin-orbit coupling and time-reversal symmetry. The spin and momentum locked surface states not only provide a model system to study fundamental physics, but can also lead to applications in spintronics and dissipationless electronics. While topological insulators are interesting by themselves, more exotic behaviors are predicted when an energy gap is induced at the surface. This dissertation explores two types of surface state gap in topological insulators, a superconducting gap induced by proximity effect and a magnetic gap induced by chemical doping. The first three chapters provide introductory theory and experimental details of my research. Chapter 1 provides a brief introduction to the theoretical background of topological insulators. Chapter 2 is dedicated to material synthesis principles and techniques. I will focus on two major synthesis methods: molecular beam epitaxy for the growth of Bi2Se3 thin films and chemical vapor deposition for the growth of Bi2Se3 nanoribbons and nanowires. Material characterization is discussed in Chapter 3. I will describe structural, morphological, magnetic, electrical, and electronic characterization techniques used to study topological insulators. Chapter 4 discusses the experiments on proximity-induced superconductivity in topological insulator (Bi2Se3) nanoribbons. This work is motivated by the search for the elusive Majorana fermions, which act as their own antiparticles. They were proposed by Ettore Majorara in 1937, but have remained undiscovered. Recently, Majorana's concept has been revived in condensed matter physics: a condensed matter analog of Majorana fermions is predicted to exist when topological insulators are interfaced with superconductors. The observation of Majorana fermions would not only be fundamentally important, but would also lead to applications in fault-tolerant topological quantum computation. By interfacing topological insulator nanoribbons with superconducting electrodes, we observe distinct signatures of proximity-induced superconductivity, which is found to be present in devices with channel lengths that are much longer than the normal transport characteristic lengths. This might suggest preferential coupling of the proximity effect to a ballistic surface channel of the topological insulator. In addition, when the electrodes are in the superconducting state, we observe periodic magnetoresistance oscillations which suggest the formation of vortices in the proximity-induced region of the nanoribbons. Our results demonstrate that proximity-induced superconductivity and vortices can be realized in our nanoribbon geometry, which accomplishes a first important step towards the search for Majorana fermions in condensed matter. In Chapter 5, I will discuss experiments on a magnetically-doped topological insulator (Mn-doped Bi2Se3) to induce a surface state gap. The metallic Dirac cone surface states of a topological insulator are expected to be protected against small perturbations by time-reversal symmetry. However, these surface states can be dramatically modified and a finite energy gap can be opened at the Dirac point by breaking the time-reversal symmetry via magnetic doping. The interplay between magnetism and topological surface states is predicted to yield novel phenomena of fundamental interest such as a topological magneto-electric effect, a quantized anomalous Hall effect, and the induction of magnetic monopoles. Our systematic measurements reveal a close correlation between the onset of ferromagnetism and quantum corrections to diffusive transport, which crosses over from the symplectic (weak anti-localization) to the unitary (weak localization) class. A comprehensive interpretation of data obtained from electrical transport, angle-resolved photoemission spectroscopy, superconducting quantum interference device magnetometry, and scanning tunneling microscopy indicates that the ferromagnetism responsible for modifications in the surface states occurs in nanoscale regions on the surface where magnetic atoms segregate during sample growth. This suggests that some aspects of the observed magnetoconductance may indeed originate from surface transport despite the non-ideal nature of the samples. These observations are consistent with the prediction of a time-reversal symmetry breaking gap, which is further supported by angle-resolved photoemission spectroscopy measurements.

Can Topology and Geometry be Measured by an Operator Measurement in Quantum Gravity?

PubMed

Berenstein, David; Miller, Alexandra

2017-06-30

In the context of Lin-Lunin-Maldacena geometries, we show that superpositions of classical coherent states of trivial topology can give rise to new classical limits where the topology of spacetime has changed. We argue that this phenomenon implies that neither the topology nor the geometry of spacetime can be the result of an operator measurement. We address how to reconcile these statements with the usual semiclassical analysis of low energy effective field theory for gravity.

Regular and irregular dynamics of spin-polarized wavepackets in a mesoscopic quantum dot at the edge of topological insulator

NASA Astrophysics Data System (ADS)

Khomitsky, D. V.; Chubanov, A. A.; Konakov, A. A.

2016-12-01

The dynamics of Dirac-Weyl spin-polarized wavepackets driven by a periodic electric field is considered for the electrons in a mesoscopic quantum dot formed at the edge of the two-dimensional HgTe/CdTe topological insulator with Dirac-Weyl massless energy spectra, where the motion of carriers is less sensitive to disorder and impurity potentials. It is observed that the interplay of strongly coupled spin and charge degrees of freedom creates the regimes of irregular dynamics in both coordinate and spin channels. The border between the regular and irregular regimes determined by the strength and frequency of the driving field is found analytically within the quasiclassical approach by means of the Ince-Strutt diagram for the Mathieu equation, and is supported by full quantum-mechanical simulations of the driven dynamics. The investigation of quasienergy spectrum by Floquet approach reveals the presence of non-Poissonian level statistics, which indicates the possibility of chaotic quantum dynamics and corresponds to the areas of parameters for irregular regimes within the quasiclassical approach. We find that the influence of weak disorder leads to partial suppression of the dynamical chaos. Our findings are of interest both for progress in the fundamental field of quantum chaotic dynamics and for further experimental and technological applications of spindependent phenomena in nanostructures based on topological insulators.

Regular and irregular dynamics of spin-polarized wavepackets in a mesoscopic quantum dot at the edge of topological insulator

DOE Office of Scientific and Technical Information (OSTI.GOV)

Khomitsky, D. V., E-mail: khomitsky@phys.unn.ru; Chubanov, A. A.; Konakov, A. A.

2016-12-15

The dynamics of Dirac–Weyl spin-polarized wavepackets driven by a periodic electric field is considered for the electrons in a mesoscopic quantum dot formed at the edge of the two-dimensional HgTe/CdTe topological insulator with Dirac–Weyl massless energy spectra, where the motion of carriers is less sensitive to disorder and impurity potentials. It is observed that the interplay of strongly coupled spin and charge degrees of freedom creates the regimes of irregular dynamics in both coordinate and spin channels. The border between the regular and irregular regimes determined by the strength and frequency of the driving field is found analytically within themore » quasiclassical approach by means of the Ince–Strutt diagram for the Mathieu equation, and is supported by full quantum-mechanical simulations of the driven dynamics. The investigation of quasienergy spectrum by Floquet approach reveals the presence of non-Poissonian level statistics, which indicates the possibility of chaotic quantum dynamics and corresponds to the areas of parameters for irregular regimes within the quasiclassical approach. We find that the influence of weak disorder leads to partial suppression of the dynamical chaos. Our findings are of interest both for progress in the fundamental field of quantum chaotic dynamics and for further experimental and technological applications of spindependent phenomena in nanostructures based on topological insulators.« less

Nanoscale Device Properties of Tellurium-based Chalcogenide Compounds

NASA Astrophysics Data System (ADS)

Dahal, Bishnu R.

The great progress achieved in miniaturization of microelectronic devices has now reached a distinct bottleneck, as devices are starting to approach the fundamental fabrication and performance limit. Even if a major breakthrough is made in the fabrication process, these scaled down electronic devices will not function properly since the quantum effects can no longer be neglected in the nanoscale regime. Advances in nanotechnology and new materials are driving novel technologies for future device applications. Current microelectronic devices have the smallest feature size, around 10 nm, and the industry is planning to switch away from silicon technology in the near future. The new technology will be fundamentally different. There are several leading technologies based on spintronics, tunneling transistors, and the newly discovered 2-dimensional material systems. All of these technologies are at the research level, and are far from ready for use in making devices in large volumes. This dissertation will focus on a very promising material system, Te-based chalcogenides, which have potential applications in spintronics, thermoelectricity and topological insulators that can lead to low-power-consumption electronics. Very recently it was predicted and experimentally observed that the spin-orbit interaction in certain materials can lead to a new electronic state called topological insulating phase. The topological insulator, like an ordinary insulator, has a bulk energy gap separating the highest occupied electronic band from the lowest empty band. However, the surface states in the case of a three-dimensional or edge states in a two-dimensional topological insulator allow electrons to conduct at the surface, due to the topological character of the bulk wavefunctions. These conducting states are protected by time-reversal symmetry, and cannot be eliminated by defects or chemical passivation. The edge/surface states satisfy Dirac dispersion relations, and hence the physics of relativistic Dirac fermions becomes relevant. This results in peculiar quantum oscillations in transport measurements which make it possible to unambiguously identify surface Dirac fermions. In order to lead us towards a better understanding of topological insulators and their applications, it is, however, necessary to develop techniques that will enable high quality materials to be obtained in a routine and reliable way. However, this has been an enormous challenge so far. Since highly volatile components are involved in most topological insulators, whether in bulk single crystal or epitaxial thin films or chemical vapor deposition grown nanoribbons, maintaining near stoichiometry has proven to be very difficult. Observing the predicted transport properties of these systems, particularly surface carriers of high mobility whilst maintaining bulk insulating states, is seriously impeded by the unintentional doping of bulk carriers. Moreover, in thin films and hetrostructures, at the all-important thickness range of a few nanometers, the additional limitation of the film-substrate lattice mismatch and the resulting strain in films is a major concern. In this thesis, we have developed a synthesis technique to obtain high quality SnTe nanoribbons, which is a topological crystalline insulator and its surface states are topologically protected by mirror symmetry of the lattice. The obtained ribbons are nearly stoichiometric and show strong semiconducting behavior with a bandgap of 240 meV. This is the first time high quality SnTe nanoribbons have been synthesized. High quality SnTe nanoribbons form a potential platform to understand the magnetic topological insulating behavior. In this thesis, it is also shown that magnetic behavior can be introduced in SnTe nanoribbons by means of chromium doping. Magnetically doped topological insulators, possessing an energy gap created at the Dirac point are predicted to exhibit exotic phenomena including the quantized anomalous Hall Effect and a dissipationless transport, which facilitate the development of low-power-consumption devices using electron spins. In addition, this thesis also discusses the growth and transport properties of another Te-based chalcogenide system, CoTe with ferrimagnetic and semiconducting behavior. We have shown that the structural, electrical and magnetic properties can be tuned by controlling the amount of cobalt in the system.

Topological Quantum Phase Transitions in Two-Dimensional Hexagonal Lattice Bilayers

NASA Astrophysics Data System (ADS)

Zhai, Xuechao; Jin, Guojun

2013-09-01

Since the successful fabrication of graphene, two-dimensional hexagonal lattice structures have become a research hotspot in condensed matter physics. In this short review, we theoretically focus on discussing the possible realization of a topological insulator (TI) phase in systems of graphene bilayer (GBL) and boron nitride bilayer (BNBL), whose band structures can be experimentally modulated by an interlayer bias voltage. Under the bias, a band gap can be opened in AB-stacked GBL but is still closed in AA-stacked GBL and significantly reduced in AA- or AB-stacked BNBL. In the presence of spin-orbit couplings (SOCs), further demonstrations indicate whether the topological quantum phase transition can be realized strongly depends on the stacking orders and symmetries of structures. It is observed that a bulk band gap can be first closed and then reopened when the Rashba SOC increases for gated AB-stacked GBL or when the intrinsic SOC increases for gated AA-stacked BNBL. This gives a distinct signal for a topological quantum phase transition, which is further characterized by a jump of the ℤ2 topological invariant. At fixed SOCs, the TI phase can be well switched by the interlayer bias and the phase boundaries are precisely determined. For AA-stacked GBL and AB-stacked BNBL, no strong TI phase exists, regardless of the strength of the intrinsic or Rashba SOCs. At last, a brief overview is given on other two-dimensional hexagonal materials including silicene and molybdenum disulfide bilayers.

Quantum Hall effect with small numbers of vortices in Bose-Einstein condensates

NASA Astrophysics Data System (ADS)

Byrnes, Tim; Dowling, Jonathan P.

2015-08-01

When vortices are displaced in Bose-Einstein condensates (BECs), the Magnus force gives the system a momentum transverse in the direction to the displacement. We show that BECs in long channels with vortices exhibit a quantization of the current response with respect to the spatial vortex distribution. The quantization originates from the well-known topological property of the phase around a vortex; it is an integer multiple of 2 π . In a way similar to that of the integer quantum Hall effect, the current along the channel is related to this topological phase and can be extracted from two experimentally measurable quantities: the total momentum of the BEC and the spatial distribution. The quantization is in units of m /2 h , where m is the mass of the atoms and h is Planck's constant. We derive an exact vortex momentum-displacement relation for BECs in long channels under general circumstances. Our results present the possibility that the configuration described here can be used as a novel way of measuring the mass of the atoms in the BEC using a topological invariant of the system. If an accurate determination of the plateaus are experimentally possible, this gives the possibility of a topological quantum mass standard and precise determination of the fine structure constant.

General response formula and application to topological insulator in quantum open system.

PubMed

Shen, H Z; Qin, M; Shao, X Q; Yi, X X

2015-11-01

It is well-known that the quantum linear response theory is based on the first-order perturbation theory for a system in thermal equilibrium. Hence, this theory breaks down when the system is in a steady state far from thermal equilibrium and the response up to higher order in perturbation is not negligible. In this paper, we develop a nonlinear response theory for such quantum open system. We first formulate this theory in terms of general susceptibility, after which we apply it to the derivation of Hall conductance for open system at finite temperature. As an example, the Hall conductance of the two-band model is derived. Then we calculate the Hall conductance for a two-dimensional ferromagnetic electron gas and a two-dimensional lattice model. The calculations show that the transition points of topological phase are robust against the environment. Our results provide a promising platform for the coherent manipulation of the nonlinear response in quantum open system, which has potential applications for quantum information processing and statistical physics.

Classifying quantum entanglement through topological links

NASA Astrophysics Data System (ADS)

Quinta, Gonçalo M.; André, Rui

2018-04-01

We propose an alternative classification scheme for quantum entanglement based on topological links. This is done by identifying a nonrigid ring to a particle, attributing the act of cutting and removing a ring to the operation of tracing out the particle, and associating linked rings to entangled particles. This analogy naturally leads us to a classification of multipartite quantum entanglement based on all possible distinct links for a given number of rings. To determine all different possibilities, we develop a formalism that associates any link to a polynomial, with each polynomial thereby defining a distinct equivalence class. To demonstrate the use of this classification scheme, we choose qubit quantum states as our example of physical system. A possible procedure to obtain qubit states from the polynomials is also introduced, providing an example state for each link class. We apply the formalism for the quantum systems of three and four qubits and demonstrate the potential of these tools in a context of qubit networks.

Observation of the Quantum Hall Effect in Confined Films of the Three-Dimensional Dirac Semimetal Cd3 As2

NASA Astrophysics Data System (ADS)

Schumann, Timo; Galletti, Luca; Kealhofer, David A.; Kim, Honggyu; Goyal, Manik; Stemmer, Susanne

2018-01-01

The magnetotransport properties of epitaxial films of Cd3 As2 , a paradigm three-dimensional Dirac semimetal, are investigated. We show that an energy gap opens in the bulk electronic states of sufficiently thin films and, at low temperatures, carriers residing in surface states dominate the electrical transport. The carriers in these states are sufficiently mobile to give rise to a quantized Hall effect. The sharp quantization demonstrates surface transport that is virtually free of parasitic bulk conduction and paves the way for novel quantum transport studies in this class of topological materials. Our results also demonstrate that heterostructuring approaches can be used to study and engineer quantum states in topological semimetals.

Quantum oscillations in nodal line systems

NASA Astrophysics Data System (ADS)

Yang, Hui; Moessner, Roderich; Lim, Lih-King

2018-04-01

We study signatures of magnetic quantum oscillations in three-dimensional nodal line semimetals at zero temperature. The extended nature of the degenerate bands can result in a Fermi surface geometry with topological genus one, as well as a Fermi surface of electron and hole pockets encapsulating the nodal line. Moreover, the underlying two-band model to describe a nodal line is not unique, in that there are two classes of Hamiltonian with distinct band topology giving rise to the same Fermi-surface geometry. After identifying the extremal cyclotron orbits in various magnetic field directions, we study their concomitant Landau levels and resulting quantum oscillation signatures. By Landau-fan-diagram analyses, we extract the nontrivial π Berry phase signature for extremal orbits linking the nodal line.

Graphene based d-character Dirac Systems

NASA Astrophysics Data System (ADS)

Li, Yuanchang; Zhang, S. B.; Duan, Wenhui

From graphene to topological insulators, Dirac material continues to be the hot topics in condensed matter physics. So far, almost all of the theoretically predicted or experimentally observed Dirac materials are composed of sp -electrons. By using first-principles calculations, we find the new Dirac system of transition-metal intercalated epitaxial graphene on SiC(0001). Intrinsically different from the conventional sp Dirac system, here the Dirac-fermions are dominantly contributed by the transition-metal d-electrons, which paves the way to incorporate correlation effect with Dirac-cone physics. Many intriguing quantum phenomena are proposed based on this system, including quantum spin Hall effect with large spin-orbital gap, quantum anomalous Hall effect, 100% spin-polarized Dirac fermions and ferromagnet-to-topological insulator transition.

Prediction of a Large-Gap and Switchable Kane-Mele Quantum Spin Hall Insulator

NASA Astrophysics Data System (ADS)

Marrazzo, Antimo; Gibertini, Marco; Campi, Davide; Mounet, Nicolas; Marzari, Nicola

2018-03-01

Fundamental research and technological applications of topological insulators are hindered by the rarity of materials exhibiting a robust topologically nontrivial phase, especially in two dimensions. Here, by means of extensive first-principles calculations, we propose a novel quantum spin Hall insulator with a sizable band gap of ˜0.5 eV that is a monolayer of jacutingaite, a naturally occurring layered mineral first discovered in 2008 in Brazil and recently synthesized. This system realizes the paradigmatic Kane-Mele model for quantum spin Hall insulators in a potentially exfoliable two-dimensional monolayer, with helical edge states that are robust and that can be manipulated exploiting a unique strong interplay between spin-orbit coupling, crystal-symmetry breaking, and dielectric response.

Classification of reflection-symmetry-protected topological semimetals and nodal superconductors

NASA Astrophysics Data System (ADS)

Chiu, Ching-Kai; Schnyder, Andreas P.

2014-11-01

While the topological classification of insulators, semimetals, and superconductors in terms of nonspatial symmetries is well understood, less is known about topological states protected by crystalline symmetries, such as mirror reflections and rotations. In this work, we systematically classify topological semimetals and nodal superconductors that are protected, not only by nonspatial (i.e., global) symmetries, but also by a crystal reflection symmetry. We find that the classification crucially depends on (i) the codimension of the Fermi surface (nodal line or point) of the semimetal (superconductor), (ii) whether the mirror symmetry commutes or anticommutes with the nonspatial symmetries, and (iii) how the Fermi surfaces (nodal lines or points) transform under the mirror reflection and nonspatial symmetries. The classification is derived by examining all possible symmetry-allowed mass terms that can be added to the Bloch or Bogoliubov-de Gennes Hamiltonian in a given symmetry class and by explicitly deriving topological invariants. We discuss several examples of reflection-symmetry-protected topological semimetals and nodal superconductors, including topological crystalline semimetals with mirror Z2 numbers and topological crystalline nodal superconductors with mirror winding numbers.

Braiding light quanta

NASA Astrophysics Data System (ADS)

Iadecola, Thomas; Schuster, Thomas; Chamon, Claudio

The possibility that anyons -- quantum particles other than fermions or bosons -- can emerge in condensed matter systems has motivated generations of physicists. In addition to being of fundamental scientific importance, so-called non-Abelian anyons are particularly sought-after for potential applications to quantum computing. However, experimental evidence of anyons in electronic systems remains inconclusive. We propose to demonstrate non-Abelian braiding by injecting coherent states of light into ``topological guided modes'' in specially-fabricated photonic waveguide arrays. These modes are photonic analogues of topological zero modes in electronic systems. Light traveling inside spatially well-separated topological guided modes can be braided, leading to the accumulation of non-Abelian phases. We propose an optical interference experiment to probe this non-Abelian braiding directly. T.I. is supported by a National Science Foundation Graduate Research Fellowship under Grant No. DGE-1247312.

Entanglement spectroscopy on a quantum computer

NASA Astrophysics Data System (ADS)

Johri, Sonika; Steiger, Damian S.; Troyer, Matthias

2017-11-01

We present a quantum algorithm to compute the entanglement spectrum of arbitrary quantum states. The interesting universal part of the entanglement spectrum is typically contained in the largest eigenvalues of the density matrix which can be obtained from the lower Renyi entropies through the Newton-Girard method. Obtaining the p largest eigenvalues (λ1>λ2⋯>λp ) requires a parallel circuit depth of O [p (λ1/λp) p] and O [p log(N )] qubits where up to p copies of the quantum state defined on a Hilbert space of size N are needed as the input. We validate this procedure for the entanglement spectrum of the topologically ordered Laughlin wave function corresponding to the quantum Hall state at filling factor ν =1 /3 . Our scaling analysis exposes the tradeoffs between time and number of qubits for obtaining the entanglement spectrum in the thermodynamic limit using finite-size digital quantum computers. We also illustrate the utility of the second Renyi entropy in predicting a topological phase transition and in extracting the localization length in a many-body localized system.

Bohm's Quantum Potential and the Visualization of Molecular Structure

NASA Technical Reports Server (NTRS)

Levit, Creon; Chancellor, Marisa K. (Technical Monitor)

1997-01-01

David Bohm's ontological interpretation of quantum theory can shed light on otherwise counter-intuitive quantum mechanical phenomena including chemical bonding. In the field of quantum chemistry, Richard Bader has shown that the topology of the Laplacian of the electronic charge density characterizes many features of molecular structure and reactivity. Visual and computational examination suggests that the Laplacian of Bader and the quantum potential of Bohm are morphologically equivalent. It appears that Bohmian mechanics and the quantum potential can make chemistry as clear as they makes physics.

Quantum Turbulence ---Another da Vinci Code---

NASA Astrophysics Data System (ADS)

Tsubota, M.

Quantum turbulence comprises a tangle of quantized vorticeswhich are stable topological defects created by Bose-Einstein condensation, being realized in superfluid helium and atomic Bose-Einstein condensates. In recent years there has been a growing interest in quantum turbulence. One of the important motivations is to understand the relation between quantum and classical turbulence. Quantum turbulence is expected to be much simpler than usual classical turbulence and give a prototype of turbulence. This article reviews shortly the recent research developments on quantum turbulence.

Magnification of signatures of a topological phase transition by quantum zero point motion

NASA Astrophysics Data System (ADS)

Lopes, Pedro L. e. S.; Ghaemi, Pouyan

2015-08-01

We show that the zero point motion of a vortex in superconducting doped topological insulators leads to significant changes in the electronic spectrum at the topological phase transition in this system. This topological phase transition is tuned by the doping level, and the corresponding effects are manifest in the density of states at energies which are on the order of the vortex fluctuation frequency. Although the electronic energy gap in the spectrum generated by a stationary vortex is but a small fraction of the bulk superconducting gap, the vortex fluctuation frequency may be much larger. As a result, this quantum zero point motion can induce a discontinuous change in the spectral features of the system at the topological vortex phase transition to energies which are well within the resolution of scanning tunneling microscopy. This discontinuous change is exclusive to superconducting systems in which we have a topological phase transition. Moreover, the phenomena studied in this paper present effects of Magnus forces on the vortex spectrum which are not present in the ordinary s -wave superconductors. Finally, we demonstrate explicitly that the vortex in this system is equivalent to a Kitaev chain. This allows for the mapping of the vortex fluctuating scenario in three dimensions into similar one-dimensional situations in which one may search for other novel signatures of topological phase transitions.

Topological Hall Effect in Skyrmions: A Nonequilibrium Coherent Transport Approach

NASA Astrophysics Data System (ADS)

Yin, Gen; Zang, Jiadong; Lake, Roger

2014-03-01

Skyrmion is a topological spin texture recently observed in many materials with broken inversion symmetry. In experiments, one effective method to detect the skyrmion crystal phase is the topological Hall measurement. At adiabatic approximation, previous theoretical studies show that the Hall signal is provided by an emergent magnetic field, which explains the topological Hall effect in the classical level. Motivated by the potential device application of skyrmions as digital bits, it is important to understand the topological Hall effect in the mesoscopic level, where the electron coherence should be considered. In this talk, we will discuss the quantum aspects of the topological Hall effect on a tight binding setup solved by nonequilibrium Green's function (NEGF). The charge distribution, Hall potential distribution, thermal broadening effect and the Hall resistivity are investigated in detail. The relation between the Hall resistance and the DM interaction is investigated. Driven by the spin transferred torque (SST), Skyrmion dynamics is previously studied within the adiabatic approximation. At the quantum transport level, this talk will also discuss the non-adiabatic effect in the skyrmion motion with the presence of the topological Hall effect. This material is based upon work supported by the National Science Foundation under Grant Nos. NSF 1128304 and NSF 1124733. It was also supported in part by FAME, one of six centers of STARnet, an SRC program sponsored by MARCO and DARPA.

Topological nanophononic states by band inversion

NASA Astrophysics Data System (ADS)

Esmann, Martin; Lamberti, Fabrice Roland; Senellart, Pascale; Favero, Ivan; Krebs, Olivier; Lanco, Loïc; Gomez Carbonell, Carmen; Lemaître, Aristide; Lanzillotti-Kimura, Norberto Daniel

2018-04-01

Nanophononics is essential for the engineering of thermal transport in nanostructured electronic devices, it greatly facilitates the manipulation of mechanical resonators in the quantum regime, and it could unveil a new route in quantum communications using phonons as carriers of information. Acoustic phonons also constitute a versatile platform for the study of fundamental wave dynamics, including Bloch oscillations, Wannier-Stark ladders, and other localization phenomena. Many of the phenomena studied in nanophononics were inspired by their counterparts in optics and electronics. In these fields, the consideration of topological invariants to control wave dynamics has already had a great impact for the generation of robust confined states. Interestingly, the use of topological phases to engineer nanophononic devices remains an unexplored and promising field. Conversely, the use of acoustic phonons could constitute a rich platform to study topological states. Here, we introduce the concept of topological invariants to nanophononics and experimentally implement a nanophononic system supporting a robust topological interface state at 350 GHz. The state is constructed through band inversion, i.e., by concatenating two semiconductor superlattices with inverted spatial mode symmetries. The existence of this state is purely determined by the Zak phases of the constituent superlattices, i.e., the one-dimensional Berry phase. We experimentally evidenced the mode through Raman spectroscopy. The reported robust topological interface states could become part of nanophononic devices requiring resonant structures such as sensors or phonon lasers.

From node-line semimetals to large-gap quantum spin Hall states in a family of pentagonal group-IVA chalcogenide

NASA Astrophysics Data System (ADS)

Zhang, Run-Wu; Liu, Cheng-Cheng; Ma, Da-Shuai; Yao, Yugui

2018-03-01

Two-dimensional (2D) topological insulators (TIs) have attracted tremendous research interest from both the theoretical and the experimental fields in recent years. However, it is much less investigated in realizing node line (NL) semimetals in 2D materials. Combining first-principles calculations and symmetry analysis, we find that NL phases emerge in p -CS2 and p -SiS2 , as well as other pentagonal IVX2 films, i.e., p -IVX2 (IV= C, Si, Ge, Sn, Pb; X=S, Se, Te) in the absence of spin-orbit coupling (SOC). The NLs in p -IVX2 consist of symbolic Fermi loops centered around the Γ point and are protected by mirror reflection symmetry. As the atomic number is downward shifted, the NL semimetals are driven into 2D TIs with the large bulk gap up to 0.715 eV induced by the remarkable SOC effect. The nontrivial bulk gap can be tunable under external biaxial strain and uniaxial strain. Moreover, we also propose a quantum well by sandwiching a p -PbTe2 crystal between two NaI sheets in which p -PbTe2 still keeps its nontrivial topology with a sizable band gap (˜0.5 eV). These findings provide a new 2D material platform for exploring fascinating physics in both NL semimetals and TIs.

Anomaly manifestation of Lieb-Schultz-Mattis theorem and topological phases

NASA Astrophysics Data System (ADS)

Cho, Gil Young; Hsieh, Chang-Tse; Ryu, Shinsei

2017-11-01

The Lieb-Schultz-Mattis (LSM) theorem dictates that emergent low-energy states from a lattice model cannot be a trivial symmetric insulator if the filling per unit cell is not integral and if the lattice translation symmetry and particle number conservation are strictly imposed. In this paper, we compare the one-dimensional gapless states enforced by the LSM theorem and the boundaries of one-higher dimensional strong symmetry-protected topological (SPT) phases from the perspective of quantum anomalies. We first note that they can both be described by the same low-energy effective field theory with the same effective symmetry realizations on low-energy modes, wherein non-on-site lattice translation symmetry is encoded as if it were an internal symmetry. In spite of the identical form of the low-energy effective field theories, we show that the quantum anomalies of the theories play different roles in the two systems. In particular, we find that the chiral anomaly is equivalent to the LSM theorem, whereas there is another anomaly that is not related to the LSM theorem but is intrinsic to the SPT states. As an application, we extend the conventional LSM theorem to multiple-charge multiple-species problems and construct several exotic symmetric insulators. We also find that the (3+1)d chiral anomaly provides only the perturbative stability of the gaplessness local in the parameter space.

Chiral topological superconductor and half-integer conductance plateau from quantum anomalous Hall plateau transition

DOE PAGES

Wang, Jing; Zhou, Quan; Lian, Biao; ...

2015-08-31

Here, we propose to realize a two-dimensional chiral topological superconducting (TSC) state from the quantum anomalous Hall plateau transition in a magnetic topological insulator thin film through the proximity effect to a conventional s -wave superconductor. This state has a full pairing gap in the bulk and a single chiral Majorana mode at the edge. The optimal condition for realizing such chiral TSC is to have inequivalent superconducting pairing amplitudes on top and bottom surfaces of the doped magnetic topological insulator. We further propose several transport experiments to detect the chiral TSC. One unique signature is that the conductance willmore » be quantized into a half-integer plateau at the coercive field in this hybrid system. In particular, with the point contact formed by a superconducting junction, the conductance oscillates between e 2 /2h and e2 /h with the frequency determined by the voltage across the junction. We close by discussing the feasibility of these experimental proposals.« less

Weyl-Kondo semimetal in heavy-fermion systems

NASA Astrophysics Data System (ADS)

Lai, Hsin-Hua; Grefe, Sarah E.; Paschen, Silke; Si, Qimiao

2018-01-01

Insulating states can be topologically nontrivial, a well-established notion that is exemplified by the quantum Hall effect and topological insulators. By contrast, topological metals have not been experimentally evidenced until recently. In systems with strong correlations, they have yet to be identified. Heavy-fermion semimetals are a prototype of strongly correlated systems and, given their strong spin-orbit coupling, present a natural setting to make progress. Here, we advance a Weyl-Kondo semimetal phase in a periodic Anderson model on a noncentrosymmetric lattice. The quasiparticles near the Weyl nodes develop out of the Kondo effect, as do the surface states that feature Fermi arcs. We determine the key signatures of this phase, which are realized in the heavy-fermion semimetal Ce3Bi4Pd3. Our findings provide the much-needed theoretical foundation for the experimental search of topological metals with strong correlations and open up an avenue for systematic studies of such quantum phases that naturally entangle multiple degrees of freedom.

Chiral topological superconductor and half-integer conductance plateau from quantum anomalous Hall plateau transition

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Jing; Zhou, Quan; Lian, Biao

Here, we propose to realize a two-dimensional chiral topological superconducting (TSC) state from the quantum anomalous Hall plateau transition in a magnetic topological insulator thin film through the proximity effect to a conventional s -wave superconductor. This state has a full pairing gap in the bulk and a single chiral Majorana mode at the edge. The optimal condition for realizing such chiral TSC is to have inequivalent superconducting pairing amplitudes on top and bottom surfaces of the doped magnetic topological insulator. We further propose several transport experiments to detect the chiral TSC. One unique signature is that the conductance willmore » be quantized into a half-integer plateau at the coercive field in this hybrid system. In particular, with the point contact formed by a superconducting junction, the conductance oscillates between e 2 /2h and e2 /h with the frequency determined by the voltage across the junction. We close by discussing the feasibility of these experimental proposals.« less

Chromium-induced ferromagnetism with perpendicular anisotropy in topological crystalline insulator SnTe (111) thin films

NASA Astrophysics Data System (ADS)

Wang, Fei; Zhang, Hongrui; Jiang, Jue; Zhao, Yi-Fan; Yu, Jia; Liu, Wei; Li, Da; Chan, Moses H. W.; Sun, Jirong; Zhang, Zhidong; Chang, Cui-Zu

2018-03-01

Topological crystalline insulator is a recently discovered topological phase of matter. It possesses multiple Dirac surface states, which are protected by the crystal symmetry. This is in contrast to the time-reversal symmetry that is operative in the well-known topological insulators. In the presence of a Zeeman field and/or strain, the multiple Dirac surface states are gapped. The high-Chern-number quantum anomalous Hall (QAH) state is predicted to emerge if the chemical potential resides in all the Zeeman gaps. Here, we use molecular-beam epitaxy to grow 12 double-layer (DL) pure and Cr-doped SnTe (111) thin film on heat-treated SrTi O3 (111) substrate using a quintuple layer of insulating (Bi0.2Sb0.8 ) 2T e3 topological insulator as a buffer film. The Hall traces of Cr-doped SnTe film at low temperatures display square hysteresis loops indicating long-range ferromagnetic order with perpendicular anisotropy. The Curie temperature of the 12 DL S n0.9C r0.1Te film is ˜110 K. Due to the chemical potential crossing the bulk valence bands, the anomalous Hall resistance of 12 DL S n0.9C r0.1Te film is substantially lower than the predicted quantized value (˜1 /4 h /e2 ). It is possible that with systematic tuning the chemical potential via chemical doping and electrical gating, the high-Chern-number QAH state can be realized in the Cr-doped SnTe (111) thin film.

Long-range doublon transfer in a dimer chain induced by topology and ac fields

NASA Astrophysics Data System (ADS)

Bello, M.; Creffield, C. E.; Platero, G.

2016-03-01

The controlled transfer of particles from one site of a spatial lattice to another is essential for many tasks in quantum information processing and quantum communication. In this work we study how to induce long-range transfer between the two ends of a dimer chain, by coupling states that are localized just on the chain’s end-points. This has the appealing feature that the transfer occurs only between the end-points - the particle does not pass through the intermediate sites-making the transfer less susceptible to decoherence. We first show how a repulsively bound-pair of fermions, known as a doublon, can be transferred from one end of the chain to the other via topological edge states. We then show how non-topological surface states of the familiar Shockley or Tamm type can be used to produce a similar form of transfer under the action of a periodic driving potential. Finally we show that combining these effects can produce transfer by means of more exotic topological effects, in which the driving field can be used to switch the topological character of the edge states, as measured by the Zak phase. Our results demonstrate how to induce long range transfer of strongly correlated particles by tuning both topology and driving.

Electronic structure and relaxation dynamics in a superconducting topological material

DOE PAGES

Neupane, Madhab; Ishida, Yukiaki; Sankar, Raman; ...

2016-03-03

Topological superconductors host new states of quantum matter which show a pairing gap in the bulk and gapless surface states providing a platform to realize Majorana fermions. Recently, alkaline-earth metal Sr intercalated Bi2Se3 has been reported to show superconductivity with a Tc~3K and a large shielding fraction. Here we report systematic normal state electronic structure studies of Sr0.06Bi2Se3 (Tc~2.5K) by performing photoemission spectroscopy. Using angle-resolved photoemission spectroscopy (ARPES), we observe a quantum well confined two-dimensional (2D) state coexisting with a topological surface state in Sr0.06Bi2Se3. Furthermore, our time-resolved ARPES reveals the relaxation dynamics showing different decay mechanism between the excitedmore » topological surface states and the two-dimensional states. Our experimental observation is understood by considering the intra-band scattering for topological surface states and an additional electron phonon scattering for the 2D states, which is responsible for the superconductivity. Our first-principles calculations agree with the more effective scattering and a shorter lifetime of the 2D states. In conclusion, our results will be helpful in understanding low temperature superconducting states of these topological materials.« less