Geometric Transitions, Topological Strings, and Generalized Complex Geometry
Chuang, Wu-yen; /SLAC /Stanford U., Phys. Dept.
2007-06-29
Mirror symmetry is one of the most beautiful symmetries in string theory. It helps us very effectively gain insights into non-perturbative worldsheet instanton effects. It was also shown that the study of mirror symmetry for Calabi-Yau flux compactification leads us to the territory of ''Non-Kaehlerity''. In this thesis we demonstrate how to construct a new class of symplectic non-Kaehler and complex non-Kaehler string theory vacua via generalized geometric transitions. The class admits a mirror pairing by construction. From a variety of sources, including super-gravity analysis and KK reduction on SU(3) structure manifolds, we conclude that string theory connects Calabi-Yau spaces to both complex non-Kaehler and symplectic non-Kaehler manifolds and the resulting manifolds lie in generalized complex geometry. We go on to study the topological twisted models on a class of generalized complex geometry, bi-Hermitian geometry, which is the most general target space for (2, 2) world-sheet theory with non-trivial H flux turned on. We show that the usual Kaehler A and B models are generalized in a natural way. Since the gauged supergravity is the low energy effective theory for the compactifications on generalized geometries, we study the fate of flux-induced isometry gauging in N = 2 IIA and heterotic strings under non-perturbative instanton effects. Interestingly, we find we have protection mechanisms preventing the corrections to the hyper moduli spaces. Besides generalized geometries, we also discuss the possibility of new NS-NS fluxes in a new doubled formalism.
Topological minimally entangled states via geometric measure
NASA Astrophysics Data System (ADS)
Buerschaper, Oliver; García-Saez, Artur; Orús, Román; Wei, Tzu-Chieh
2014-11-01
Here we show how the Minimally Entangled States (MES) of a 2d system with topological order can be identified using the geometric measure of entanglement. We show this by minimizing this measure for the doubled semion, doubled Fibonacci and toric code models on a torus with non-trivial topological partitions. Our calculations are done either quasi-exactly for small system sizes, or using the tensor network approach in Orús et al (arXiv:1406.0585) for large sizes. As a byproduct of our methods, we see that the minimisation of the geometric entanglement can also determine the number of Abelian quasiparticle excitations in a given model. The results in this paper provide a very efficient and accurate way of extracting the full topological information of a 2d quantum lattice model from the multipartite entanglement structure of its ground states.
Topological and differential geometrical gauge field theory
NASA Astrophysics Data System (ADS)
Saaty, Joseph
between bosons (quantized) and fermions (not quantized). Thus I produced results that were previously unobtainable. Furthermore, since topological charge takes place in Flat Spacetime, I investigated the quantization of the Curved Spacetime version of topological charge (Differential Geometrical Charge) by developing the differential geometrical Gauge Field Theory. It should be noted that the homotopy classification method is not at all applicable to Curved Spacetime. I also modified the Dirac equation in Curved Spacetime by using Einstein's field equation in order to account for the presence of matter. As a result, my method has allowed me to address four cases of topological charge (both spinless and spin one- half, in both Flat and in Curved Spacetime) whereas earlier methods had been blind to all but one of these cases (spinless in Flat Spacetime). (Abstract shortened by UMI.)
Frustrated topological symmetry breaking: Geometrical frustration and anyon condensation
NASA Astrophysics Data System (ADS)
Schulz, Marc D.; Burnell, Fiona J.
2016-10-01
We study the phase diagram of a topological string-net-type lattice model in the presence of geometrically frustrated interactions. These interactions drive several phase transitions that reduce the topological order, leading to a rich phase diagram including both Abelian (Z2) and non-Abelian (Ising×Ising¯ ) topologically ordered phases, as well as phases with broken translational symmetry. Interestingly, one of these phases simultaneously exhibits (Abelian) topological order and long-ranged order due to translational symmetry breaking, with nontrivial interactions between excitations in the topological order and defects in the long-ranged order. We introduce a variety of effective models, valid along certain lines in the phase diagram, which can be used to characterize both topological and symmetry-breaking order in these phases and in many cases allow us to characterize the phase transitions that separate them. We use exact diagonalization and high-order series expansion to study areas of the phase diagram where these models break down and to approximate the location of the phase boundaries.
Geometric stability of topological lattice phases
Jackson, T. S.; Möller, Gunnar; Roy, Rahul
2015-01-01
The fractional quantum Hall (FQH) effect illustrates the range of novel phenomena which can arise in a topologically ordered state in the presence of strong interactions. The possibility of realizing FQH-like phases in models with strong lattice effects has attracted intense interest as a more experimentally accessible venue for FQH phenomena which calls for more theoretical attention. Here we investigate the physical relevance of previously derived geometric conditions which quantify deviations from the Landau level physics of the FQHE. We conduct extensive numerical many-body simulations on several lattice models, obtaining new theoretical results in the process, and find remarkable correlation between these conditions and the many-body gap. These results indicate which physical factors are most relevant for the stability of FQH-like phases, a paradigm we refer to as the geometric stability hypothesis, and provide easily implementable guidelines for obtaining robust FQH-like phases in numerical or real-world experiments. PMID:26530311
Topology-driven magnetic quantum phase transition in topological insulators.
Zhang, Jinsong; Chang, Cui-Zu; Tang, Peizhe; Zhang, Zuocheng; Feng, Xiao; Li, Kang; Wang, Li-Li; Chen, Xi; Liu, Chaoxing; Duan, Wenhui; He, Ke; Xue, Qi-Kun; Ma, Xucun; Wang, Yayu
2013-03-29
The breaking of time reversal symmetry in topological insulators may create previously unknown quantum effects. We observed a magnetic quantum phase transition in Cr-doped Bi2(SexTe1-x)3 topological insulator films grown by means of molecular beam epitaxy. Across the critical point, a topological quantum phase transition is revealed through both angle-resolved photoemission measurements and density functional theory calculations. We present strong evidence that the bulk band topology is the fundamental driving force for the magnetic quantum phase transition. The tunable topological and magnetic properties in this system are well suited for realizing the exotic topological quantum phenomena in magnetic topological insulators.
Geometric Potential and Transport in Photonic Topological Crystals
Szameit, Alexander; Dreisow, Felix; Heinrich, Matthias; Keil, Robert; Nolte, Stefan; Tuennermann, Andreas; Longhi, Stefano
2010-04-16
We report on the experimental realization of an optical analogue of a quantum geometric potential for light wave packets constrained on thin dielectric guiding layers fabricated in silica by the femtosecond laser writing technology. We further demonstrate the optical version of a topological crystal, with the observation of Bloch oscillations and Zener tunneling of a purely geometric nature.
Finite octree meshing through topologically driven geometric operators
NASA Technical Reports Server (NTRS)
Grice, Kurt R.
1987-01-01
The octree technique is developed into the finite octree, and an overview is given. Modeler requirements are given. The octree discretization is discussed along with geometric communication operators. Geometric communication operators returning topological associativity and geometric communication operators returning spatial data are also discussed and illustrated. The advantages are given of the boundary representation and of geometric communication operators. The implementation plays an important role in the integration with a variety of geometric modelers. The capabilities of closed loop processes within a complete finite element system are presented.
Hagedorn transition and topological entanglement entropy
NASA Astrophysics Data System (ADS)
Zuo, Fen; Gao, Yi-Hong
2016-06-01
Induced by the Hagedorn instability, weakly-coupled U (N) gauge theories on a compact manifold exhibit a confinement/deconfinement phase transition in the large-N limit. Recently we discover that the thermal entropy of a free theory on S3 gets reduced by a universal constant term, -N2 / 4, compared to that from completely deconfined colored states. This entropy deficit is due to the persistence of Gauss's law, and actually independent of the shape of the manifold. In this paper we show that this universal term can be identified as the topological entangle entropy both in the corresponding 4 + 1 D bulk theory and the dimensionally reduced theory. First, entanglement entropy in the bulk theory contains the so-called "particle" contribution on the entangling surface, which naturally gives rise to an area-law term. The topological term results from the Gauss's constraint of these surface states. Secondly, the high-temperature limit also defines a dimensionally reduced theory. We calculate the geometric entropy in the reduced theory explicitly, and find that it is given by the same constant term after subtracting the leading term of O (β-1). The two procedures are then applied to the confining phase, by extending the temperature to the complex plane. Generalizing the recently proposed 2D modular description to an arbitrary matter content, we show the leading local term is missing and no topological term could be definitely isolated. For the special case of N = 4 super Yang-Mills theory, the results obtained here are compared with that at strong coupling from the holographic derivation.
Clique topology reveals intrinsic geometric structure in neural correlations
Giusti, Chad; Pastalkova, Eva; Curto, Carina; Itskov, Vladimir
2015-01-01
Detecting meaningful structure in neural activity and connectivity data is challenging in the presence of hidden nonlinearities, where traditional eigenvalue-based methods may be misleading. We introduce a novel approach to matrix analysis, called clique topology, that extracts features of the data invariant under nonlinear monotone transformations. These features can be used to detect both random and geometric structure, and depend only on the relative ordering of matrix entries. We then analyzed the activity of pyramidal neurons in rat hippocampus, recorded while the animal was exploring a 2D environment, and confirmed that our method is able to detect geometric organization using only the intrinsic pattern of neural correlations. Remarkably, we found similar results during nonspatial behaviors such as wheel running and rapid eye movement (REM) sleep. This suggests that the geometric structure of correlations is shaped by the underlying hippocampal circuits and is not merely a consequence of position coding. We propose that clique topology is a powerful new tool for matrix analysis in biological settings, where the relationship of observed quantities to more meaningful variables is often nonlinear and unknown. PMID:26487684
Clique topology reveals intrinsic geometric structure in neural correlations.
Giusti, Chad; Pastalkova, Eva; Curto, Carina; Itskov, Vladimir
2015-11-01
Detecting meaningful structure in neural activity and connectivity data is challenging in the presence of hidden nonlinearities, where traditional eigenvalue-based methods may be misleading. We introduce a novel approach to matrix analysis, called clique topology, that extracts features of the data invariant under nonlinear monotone transformations. These features can be used to detect both random and geometric structure, and depend only on the relative ordering of matrix entries. We then analyzed the activity of pyramidal neurons in rat hippocampus, recorded while the animal was exploring a 2D environment, and confirmed that our method is able to detect geometric organization using only the intrinsic pattern of neural correlations. Remarkably, we found similar results during nonspatial behaviors such as wheel running and rapid eye movement (REM) sleep. This suggests that the geometric structure of correlations is shaped by the underlying hippocampal circuits and is not merely a consequence of position coding. We propose that clique topology is a powerful new tool for matrix analysis in biological settings, where the relationship of observed quantities to more meaningful variables is often nonlinear and unknown.
Topological phase transitions in frustrated magnets
NASA Astrophysics Data System (ADS)
Southern, B. W.; Peles, A.
2006-06-01
The role of topological excitations in frustrated Heisenberg antiferromagnets between two and three spatial dimensions is considered. In particular, the antiferromagnetic Heisenberg model on a stacked triangular geometry with a finite number of layers is studied using Monte Carlo methods. A phase transition that is purely topological in nature occurs at a finite temperature for all film thicknesses. The results indicate that topological excitations are important for a complete understanding of the critical properties of the model between two and three dimensions.
Observation of topological transitions in interacting quantum circuits
NASA Astrophysics Data System (ADS)
Roushan, P.; Neill, C.; Chen, Yu; Kolodrubetz, M.; Quintana, C.; Leung, N.; Fang, M.; Barends, R.; Campbell, B.; Chen, Z.; Chiaro, B.; Dunsworth, A.; Jeffrey, E.; Kelly, J.; Megrant, A.; Mutus, J.; O'Malley, P. J. J.; Sank, D.; Vainsencher, A.; Wenner, J.; White, T.; Polkovnikov, A.; Cleland, A. N.; Martinis, J. M.
2014-11-01
Topology, with its abstract mathematical constructs, often manifests itself in physics and has a pivotal role in our understanding of natural phenomena. Notably, the discovery of topological phases in condensed-matter systems has changed the modern conception of phases of matter. The global nature of topological ordering, however, makes direct experimental probing an outstanding challenge. Present experimental tools are mainly indirect and, as a result, are inadequate for studying the topology of physical systems at a fundamental level. Here we employ the exquisite control afforded by state-of-the-art superconducting quantum circuits to investigate topological properties of various quantum systems. The essence of our approach is to infer geometric curvature by measuring the deflection of quantum trajectories in the curved space of the Hamiltonian. Topological properties are then revealed by integrating the curvature over closed surfaces, a quantum analogue of the Gauss-Bonnet theorem. We benchmark our technique by investigating basic topological concepts of the historically important Haldane model after mapping the momentum space of this condensed-matter model to the parameter space of a single-qubit Hamiltonian. In addition to constructing the topological phase diagram, we are able to visualize the microscopic spin texture of the associated states and their evolution across a topological phase transition. Going beyond non-interacting systems, we demonstrate the power of our method by studying topology in an interacting quantum system. This required a new qubit architecture that allows for simultaneous control over every term in a two-qubit Hamiltonian. By exploring the parameter space of this Hamiltonian, we discover the emergence of an interaction-induced topological phase. Our work establishes a powerful, generalizable experimental platform to study topological phenomena in quantum systems.
Observation of topological transitions in interacting quantum circuits.
Roushan, P; Neill, C; Chen, Yu; Kolodrubetz, M; Quintana, C; Leung, N; Fang, M; Barends, R; Campbell, B; Chen, Z; Chiaro, B; Dunsworth, A; Jeffrey, E; Kelly, J; Megrant, A; Mutus, J; O'Malley, P J J; Sank, D; Vainsencher, A; Wenner, J; White, T; Polkovnikov, A; Cleland, A N; Martinis, J M
2014-11-13
Topology, with its abstract mathematical constructs, often manifests itself in physics and has a pivotal role in our understanding of natural phenomena. Notably, the discovery of topological phases in condensed-matter systems has changed the modern conception of phases of matter. The global nature of topological ordering, however, makes direct experimental probing an outstanding challenge. Present experimental tools are mainly indirect and, as a result, are inadequate for studying the topology of physical systems at a fundamental level. Here we employ the exquisite control afforded by state-of-the-art superconducting quantum circuits to investigate topological properties of various quantum systems. The essence of our approach is to infer geometric curvature by measuring the deflection of quantum trajectories in the curved space of the Hamiltonian. Topological properties are then revealed by integrating the curvature over closed surfaces, a quantum analogue of the Gauss-Bonnet theorem. We benchmark our technique by investigating basic topological concepts of the historically important Haldane model after mapping the momentum space of this condensed-matter model to the parameter space of a single-qubit Hamiltonian. In addition to constructing the topological phase diagram, we are able to visualize the microscopic spin texture of the associated states and their evolution across a topological phase transition. Going beyond non-interacting systems, we demonstrate the power of our method by studying topology in an interacting quantum system. This required a new qubit architecture that allows for simultaneous control over every term in a two-qubit Hamiltonian. By exploring the parameter space of this Hamiltonian, we discover the emergence of an interaction-induced topological phase. Our work establishes a powerful, generalizable experimental platform to study topological phenomena in quantum systems.
Geometrical and topological issues in octree based automatic meshing
NASA Technical Reports Server (NTRS)
Saxena, Mukul; Perucchio, Renato
1987-01-01
Finite element meshes derived automatically from solid models through recursive spatial subdivision schemes (octrees) can be made to inherit the hierarchical structure and the spatial addressability intrinsic to the underlying grid. These two properties, together with the geometric regularity that can also be built into the mesh, make octree based meshes ideally suited for efficient analysis and self-adaptive remeshing and reanalysis. The element decomposition of the octal cells that intersect the boundary of the domain is discussed. The problem, central to octree based meshing, is solved by combining template mapping and element extraction into a procedure that utilizes both constructive solid geometry and boundary representation techniques. Boundary cells that are not intersected by the edge of the domain boundary are easily mapped to predefined element topology. Cells containing edges (and vertices) are first transformed into a planar polyhedron and then triangulated via element extractor. The modeling environments required for the derivation of planar polyhedra and for element extraction are analyzed.
A study of geometric phase topology using Fourier transform method
NASA Astrophysics Data System (ADS)
Samlan, C. T.; Naik, Dinesh N.; Viswanathan, Nirmal K.
2016-07-01
Topological aspect of the geometric phase (GP) due to pure polarization projection is studied using the 2D Fourier transform (2D-FT) method. Projection of orthogonal polarization state results in a phase singularity in the 2D parameter space of ellipticity and orientation of polarization ellipse. Projection of its surrounding states results in an accumulation of GP in different amount that form a spiral structure. A half wave plate-quarter wave plate combination is used to generate different polarization states which are projected using a polarizer. The accumulated phase for each orientation of the wave plate is extracted from 2D-FT of the interferogram, obtained by interfering it with a reference beam in a Mach-Zehnder like interferometer.
Geometric and Topological Invariants of the Hypothesis Space
NASA Astrophysics Data System (ADS)
Rodríguez, Carlos C.
2011-03-01
The form and shape of a hypothesis space imposes natural objective constraints to any inferential process. This contribution summarizes what is currently known and the mathematics that are thought to be needed for new developments in this area. For example, it is well known that the quality of best possible estimators deteriorates with increasing volume, dimension and curvature of the hypothesis space. It is also known that regular statistical parametric models are finite dimensional Riemannian manifolds admitting a family of dual affine connections. Fisher information is the metric induced on the hypothesis space by the Hellinger distance. Nonparametric models are infinite dimensional manifolds. Global negative curvature implies asymptotic inadmissibility of uniform priors. When there is uncertainty about the model and the prior, entropic methods are more robust than standard Bayesian inference. The presence of some types of singularities allow the existence of faster than normal estimators …, etc. The large number of fundamental statistical concepts with geometric and topological content suggest to try to look at Riemannian Geometry, Algebraic Geometry, K-theory, Algebraic Topology, Knot-theory and other branches of current mathematics, not as empty esoteric abstractions but as allies for statistical inference.
Lassoing saddle splay and the geometrical control of topological defects
NASA Astrophysics Data System (ADS)
Tran, Lisa; Lavrentovich, Maxim O.; Beller, Daniel A.; Li, Ningwei; Stebe, Kathleen J.; Kamien, Randall D.
2016-06-01
Systems with holes, such as colloidal handlebodies and toroidal droplets, have been studied in the nematic liquid crystal (NLC) 4-cyano-4'-pentylbiphenyl (5CB): Both point and ring topological defects can occur within each hole and around the system while conserving the system's overall topological charge. However, what has not been fully appreciated is the ability to manipulate the hole geometry with homeotropic (perpendicular) anchoring conditions to induce complex, saddle-like deformations. We exploit this by creating an array of holes suspended in an NLC cell with oriented planar (parallel) anchoring at the cell boundaries. We study both 5CB and a binary mixture of bicyclohexane derivatives (CCN-47 and CCN-55). Through simulations and experiments, we study how the bulk saddle deformations of each hole interact to create defect structures, including an array of disclination lines, reminiscent of those found in liquid-crystal blue phases. The line locations are tunable via the NLC elastic constants, the cell geometry, and the size and spacing of holes in the array. This research lays the groundwork for the control of complex elastic deformations of varying length scales via geometrical cues in materials that are renowned in the display industry for their stability and easy manipulability.
Continuous and discontinuous topological quantum phase transitions
NASA Astrophysics Data System (ADS)
Roy, Bitan; Goswami, Pallab; Sau, Jay D.
2016-07-01
The continuous quantum phase transition between noninteracting, time-reversal symmetric topological and trivial insulators in three dimensions is described by the massless Dirac fermion. We address the stability of this quantum critical point against short range electronic interactions by using renormalization group analysis and mean field theory. For sufficiently weak interactions, we show that the nature of the direct transition remains unchanged. Beyond a critical strength of interactions we find that either (i) there is a direct first order transition between two time reversal symmetric insulators or (ii) the direct transition is eliminated by an intervening time reversal and inversion odd "axionic" insulator. We also demonstrate the existence of an interaction driven first order quantum phase transition between topological and trivial gapped states in lower dimensions.
Scaling theory of topological phase transitions.
Chen, Wei
2016-02-10
Topologically ordered systems are characterized by topological invariants that are often calculated from the momentum space integration of a certain function that represents the curvature of the many-body state. The curvature function may be Berry curvature, Berry connection, or other quantities depending on the system. Akin to stretching a messy string to reveal the number of knots it contains, a scaling procedure is proposed for the curvature function in inversion symmetric systems, from which the topological phase transition can be identified from the flow of the driving energy parameters that control the topology (hopping, chemical potential, etc) under scaling. At an infinitesimal operation, one obtains the renormalization group (RG) equations for the driving energy parameters. A length scale defined from the curvature function near the gap-closing momentum is suggested to characterize the scale invariance at critical points and fixed points, and displays a universal critical behavior in a variety of systems examined. PMID:26790004
Scaling theory of topological phase transitions.
Chen, Wei
2016-02-10
Topologically ordered systems are characterized by topological invariants that are often calculated from the momentum space integration of a certain function that represents the curvature of the many-body state. The curvature function may be Berry curvature, Berry connection, or other quantities depending on the system. Akin to stretching a messy string to reveal the number of knots it contains, a scaling procedure is proposed for the curvature function in inversion symmetric systems, from which the topological phase transition can be identified from the flow of the driving energy parameters that control the topology (hopping, chemical potential, etc) under scaling. At an infinitesimal operation, one obtains the renormalization group (RG) equations for the driving energy parameters. A length scale defined from the curvature function near the gap-closing momentum is suggested to characterize the scale invariance at critical points and fixed points, and displays a universal critical behavior in a variety of systems examined.
A result about topologically transitive set
NASA Astrophysics Data System (ADS)
Liang, Chao
2016-06-01
In this paper, we prove that for any f∈Diff1 (M) and Λ ⊂ M be a nontrivial topologically transitive proper subset with a splitting Es ⊕ F (without hypothesis of domination), where Es is uniformly contracting, there is no arc of the stable manifold whole contained in Λ.
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.
Topological Phase Transition without Gap Closing
Ezawa, Motohiko; Tanaka, Yukio; Nagaosa, Naoto
2013-01-01
Topological phase transition is accompanied with a change of topological numbers. According to the bulk-edge correspondence, the gap closing and the breakdown of the adiabaticity are necessary at the phase transition point to make the topological number ill-defined. However, the gap closing is not always needed. In this paper, we show that two topological distinct phases can be continuously connected without gap closing, provided the symmetry of the system changes during the process. Here we propose the generic principles how this is possible by demonstrating various examples such as 1D polyacetylene with the charge-density-wave order, 2D silicene with the antiferromagnetic order, 2D silicene or quantum well made of HgTe with superconducting proximity effects and 3D superconductor Cu doped Bi2Se3. It is argued that such an unusual phenomenon can occur when we detour around the gap closing point provided the connection of the topological numbers is lost along the detour path. PMID:24071900
Topology Changing Transitions in Bubbling Geometries
Horava, Petr; Shepard, Peter G.
2005-02-15
Topological transitions in bubbling half-BPS Type IIB geometries with SO(4) x SO(4) symmetry can be decomposed into a sequence of n elementary transitions. The half-BPS solution that describes the elementary transition is seeded by a phase space distribution of fermions filling two diagonal quadrants. We study the geometry of this solution in some detail. We show that this solution can be interpreted as a time dependent geometry, interpolating between two asymptotic pp-waves in the far past and the far future. The singular solution at the transition can be resolved in two different ways, related by the particle-hole duality in the effective fermion description. Some universal features of the topology change are governed by two-dimensional Type 0B string theory, whose double scaling limit corresponds to the Penrose limit of AdS_5 x S^5 at topological transition. In addition, we present the full class of geometries describing the vicinity of the most general localized classical singularity that can occur in this class of half-BPS bubbling geometries.
Topology Changing Transitions in Bubbling Geometries
Horava, Petr; Shepard, Peter G.
2005-02-15
Topological transitions in bubbling half-BPS Type IIB geometries with SO(4) x SO(4) symmetry can be decomposed into a sequence of n elementary transitions. The half-BPS solution that describes the elementary transition is seeded by a phase space distribution of fermions filling two diagonal quadrants. We study the geometry of this solution in some detail. We show that this solution can be interpreted as a time dependent geometry, interpolating between two asymptotic pp-waves in the far past and the far future. The singular solution at the transition can be resolved in two different ways, related by the particle-hole duality in the effective fermion description. Some universal features of the topology change are governed by two-dimensional Type 0B string theory, whose double scaling limit corresponds to the Penrose limit of AdS_5 x S5 at topological transition. In addition, we present the full class of geometries describing the vicinity of the most general localized classical singularity that can occur in this class of half-BPS bubbling geometries.
Topological phase transition in layered transition metal dichalcogenides
NASA Astrophysics Data System (ADS)
Choe, Duk-Hyun; Sung, Ha-Jun; Chang, Kee Joo
Despite considerable interests in transition metal dichalcogenides (TMDs), such as MX2 with M = (Mo, W) and X = (S, Se, Te), the physical origin of their topological nature is still in its infancy. The conventional view of topological phase transition (TPT) in TMDs is that the band inversion occurs between the metal d and chalcogen p orbital bands. More precisely, the former is pulled down below the latter. Here we introduce an explicit scheme for analyzing TPT in topological materials and find that the TPT in TMDs is different from the conventional speculation. When the 1T phase undergoes a structural transformation to the 1T' phase in monolayer MX2, the band topology changes from trivial to non-trivial, leading to the TPT. We discuss the exact role of the metal d and chalcogen p orbital bands during the TPT. Our finding would provide clear guidelines for understanding the topological nature not only in TMDs but also in other topological materials yet to be explored.
Structural Transitions in Topologically Constrained DNA
NASA Astrophysics Data System (ADS)
Leger, J.; Romano, G.; Sarkar, A.; Robert, J.; Bourdieu, L.; Chatenay, D.; Marko, J. F.
2000-03-01
We propose a theoretical explanation for results of recent single molecule micromanipulation experiments (Leger et al, PRL 83, 1066, 1999) on double-stranded DNA with fixed linking number. The topological constraint leads to novel structural transitions, including a shift of the usual 60 pN B-form to S-form transition force plateau up to a force of 100 pN when linking is fixed at zero. Our model needs five distinct states to explain the four different observed transitions. The various constant-force plateaus observed for different fixed values of linking correspond to a mixture of different pairs of states, weighted to satisfy the topological constraint. Our model allows us to conclude that sufficiently overtwisted DNA (positive linkage number) undergoes a transition from B-form DNA to a mixture of S-form and P-form DNA at a force plateau near 45 pN, and then to homogeneous P-form DNA at a force plateau near 110 pN. A similar two-step transition occurs for undertwisted DNA, and by analysing the twisting necessary to produce pure S-form DNA we conclude that the S-state has helix repeat of 38 bp. Support from the Whitaker Foundation, the NSF, the ACS-PRF and Research Corporation is gratefully acknowledged.
Observation of topological phase transitions in photonic quasicrystals.
Verbin, Mor; Zilberberg, Oded; Kraus, Yaacov E; Lahini, Yoav; Silberberg, Yaron
2013-02-15
Topological insulators and topological superconductors are distinguished by their bulk phase transitions and gapless states at a sharp boundary with the vacuum. Quasicrystals have recently been found to be topologically nontrivial. In quasicrystals, the bulk phase transitions occur in the same manner as standard topological materials, but their boundary phenomena are more subtle. In this Letter we directly observe bulk phase transitions, using photonic quasicrystals, by constructing a smooth boundary between topologically distinct one-dimensional quasicrystals. Moreover, we use the same method to experimentally confirm the topological equivalence between the Harper and Fibonacci quasicrystals. PMID:25166388
Quantum algorithms for topological and geometric analysis of data.
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
Qin, Wei; Zhang, Zhenyu
2014-12-31
At the interface of an s-wave superconductor and a three-dimensional topological insulator, Majorana zero modes and Majorana helical states have been proposed to exist respectively around magnetic vortices and geometrical edges. Here we first show that randomly distributed magnetic impurities at such an interface will induce bound states that broaden into impurity bands inside (but near the edges of) the superconducting gap, which remains open unless the impurity concentration is too high. Next we find that an increase in the superconducting gap suppresses both the oscillation magnitude and the period of the Ruderman-Kittel-Kasuya-Yosida interaction between two magnetic impurities. Within a mean-field approximation, the ferromagnetic Curie temperature is found to be essentially independent of the superconducting gap, an intriguing phenomenon due to a compensation effect between the short-range ferromagnetic and long-range antiferromagnetic interactions. The existence of robust superconductivity and persistent ferromagnetism at the interface allows realization of a novel topological phase transition from a nonchiral to a chiral superconducting state at sufficiently low temperatures, providing a new platform for topological quantum computation.
Song, Zhigong; Artyukhov, Vasilii I; Wu, Jian; Yakobson, Boris I; Xu, Zhiping
2015-01-27
Defects in solids commonly limit mechanical performance of materials by reducing their rigidity and strength. However, topological defects also induce a prominent geometrical effect in addition to local stress buildup, which is especially pronounced in two-dimensional crystals. These dual roles of defects modulate mechanical responses of the material under local and global probes in very different ways. We demonstrate through atomistic simulations and theoretical analysis that local response of two-dimensional crystals can even be stiffened and strengthened by topological defects as the structure under indentation features a positive Gaussian curvature, while softened and weakened mechanical responses are measured at locations with negative Gaussian curvatures. These findings shed lights on mechanical characterization of two-dimensional materials in general. The geometrical effect of topological defects also adds a new dimension to material design, in the scenario of geometrical and topological engineering.
Photoinduced topological phase transition in epitaxial graphene
NASA Astrophysics Data System (ADS)
Zhai, Xuechao; Jin, Guojun
2014-06-01
In epitaxial graphene irradiated by an off-resonance circularly polarized light, we demonstrate a phase transition taking place between the band insulator and Floquet topological insulator. Considering the competition between staggered sublattice potential and photon dressing, we derive the dynamical energy gap and phase diagram in the tight-binding approximation. It is found that a threshold value of light intensity is necessary to realize a Floquet topological insulator. At the phase boundary, for each set of parameters, there is a special state with only one valley that is Dirac cone gapless, but the other remains gapped; in the band insulating phase, only one valley provides low-energy electrons, and it could be switched to the other by reversing the polarization direction of light. From these results, two electronic devices are designed: one is an optical-sensing np junction, where the photodriven unusual intervalley tunneling exhibits a stronger detectable signal than the intravalley tunneling, and the other is a topological field-effect transistor, where polarized light is used to turn on or turn off a nonequilibrium current.
Park, Byung Cheol; Kim, Tae-Hyeon; Sim, Kyung Ik; Kang, Boyoun; Kim, Jeong Won; Cho, Beongki; Jeong, Kwang-Ho; Cho, Mann-Ho; Kim, Jae Hoon
2015-03-16
Strong spin-orbit interaction and time-reversal symmetry in topological insulators generate novel quantum states called topological surface states. Their study provides unique opportunities to explore exotic phenomena such as spin Hall effects and topological phase transitions, relevant to the development of quantum devices for spintronics and quantum computation. Although ultrahigh-vacuum surface probes can identify individual topological surface states, standard electrical and optical experiments have so far been hampered by the interference of bulk and quantum well states. Here, with terahertz time-domain spectroscopy of ultrathin Bi₂Se₃ films, we give evidence for topological phase transitions, a single conductance quantum per topological surface state, and a quantized terahertz absorbance of 2.9% (four times the fine structure constant). Our experiment demonstrates the feasibility to isolate, detect and manipulate topological surface states in the ambient at room temperature for future fundamental research on the novel physics of topological insulators and their practical applications.
Topological phases and phase transitions on the honeycomb lattice
NASA Astrophysics Data System (ADS)
Yang, Yuan; Li, Xiaobing; Xing, Dingyu
2016-10-01
We investigate possible phase transitions among the different topological insulators in a honeycomb lattice under the combined influence of spin-orbit couplings and staggered magnetic flux. We observe a series of topological phase transitions when tuning the flux amplitude, and find topologically nontrivial phases with high Chern number or spin-Chern number. Through tuning the exchange field, we also find a new quantum state which exhibits the electronic properties of both the quantum spin Hall state and quantum anomalous Hall state. The topological characterization based on the Chern number and the spin-Chern number are in good agreement with the edge-state picture of various topological phases.
Geometrical and topological aspects of graphene and related materials
NASA Astrophysics Data System (ADS)
Cortijo, A.; Guinea, F.; Vozmediano, M. A. H.
2012-09-01
Graphene, a two-dimensional crystal made of carbon atoms, provides a new and unexpected bridge between low- and high-energy physics. The field has evolved very quickly and there are already a number of good reviews available in the literature. Graphene constitutes a condensed-matter realization of lower dimensional quantum field theory models that were proposed to confront important—still unresolved—puzzles in the area: chiral symmetry breaking and quark confinement. The new materials named topological insulators, closely related to graphene, are physical realizations of topological field theory. This article reviews some of these topics with the aim of bridging the gap and making these condensed-matter issues accessible to high-energy readers. The electronic interactions in the monolayer are analyzed with special emphasis on the recent experimental confirmation of some theoretical predictions. The issue of spontaneous chiral symmetry breaking in the model materials is also reviewed. Finally we give an extensive description of some recent topological properties of graphene that allow us to understand the main aspects of topological insulators.
Geometric and Topological Methods for Quantum Field Theory
NASA Astrophysics Data System (ADS)
Cardona, Alexander; Contreras, Iván.; Reyes-Lega, Andrés. F.
2013-05-01
Introduction; 1. A brief introduction to Dirac manifolds Henrique Bursztyn; 2. Differential geometry of holomorphic vector bundles on a curve Florent Schaffhauser; 3. Paths towards an extension of Chern-Weil calculus to a class of infinite dimensional vector bundles Sylvie Paycha; 4. Introduction to Feynman integrals Stefan Weinzierl; 5. Iterated integrals in quantum field theory Francis Brown; 6. Geometric issues in quantum field theory and string theory Luis J. Boya; 7. Geometric aspects of the standard model and the mysteries of matter Florian Scheck; 8. Absence of singular continuous spectrum for some geometric Laplacians Leonardo A. Cano García; 9. Models for formal groupoids Iván Contreras; 10. Elliptic PDEs and smoothness of weakly Einstein metrics of Hölder regularity Andrés Vargas; 11. Regularized traces and the index formula for manifolds with boundary Alexander Cardona and César Del Corral; Index.
Weyl semimetals and topological phase transitions
NASA Astrophysics Data System (ADS)
Murakami, Shuichi
Weyl semimetals are semimetals with nondegenerate 3D Dirac cones in the bulk. We showed that in a transition between different Z2 topological phases, i.e. between the normal insulator (NI) and topological insulator (TI), the Weyl semimetal phase necessarily appears when inversion symmetry is broken. In the presentation we show that this scenario holds for materials with any space groups without inversion symmetry. Namely, let us take any band insulator without inversion symmetry, and assume that the gap is closed by a change of an external parameter. In such cases we found that the system runs either into (i) a Weyl semimetal or (ii) a nodal-line semimetal, but no insulator-to-insulator transition happens. This is confirmed by classifying the gap closing in terms of the space groups and the wavevector. In the case (i), the number of Weyl nodes produced at the gap closing ranges from 2 to 12 depending on the symmetry. In (ii) the nodal line is protected by mirror symmetry. In the presentation, we explain some Weyl semimetal and nodal-line semimetals which we find by using this classification. As an example, we explain our result on ab initio calculation on tellurium (Te). Tellurium consists of helical chains, and therefore lacks inversion and mirror symmetries. At high pressure the band gap of Te decreases and finally it runs into a Weyl semimetal phase, as confirmed by our ab initio calculation. In such chiral systems as tellurium, we also theoretically propose chiral transport in systems with such helical structures; namely, an orbital magnetization is induced by a current along the chiral axis, in analogy with a solenoid.
Z2 Invariants of Topological Insulators as Geometric Obstructions
NASA Astrophysics Data System (ADS)
Fiorenza, Domenico; Monaco, Domenico; Panati, Gianluca
2016-05-01
We consider a gapped periodic quantum system with time-reversal symmetry of fermionic (or odd) type, i.e. the time-reversal operator squares to -1. We investigate the existence of periodic and time-reversal invariant Bloch frames in dimensions 2 and 3. In 2 d, the obstruction to the existence of such a frame is shown to be encoded in a Z_2-valued topological invariant, which can be computed by a simple algorithm. We prove that the latter agrees with the Fu-Kane index. In 3 d, instead, four Z_2 invariants emerge from the construction, again related to the Fu-Kane-Mele indices. When no topological obstruction is present, we provide a constructive algorithm yielding explicitly a periodic and time-reversal invariant Bloch frame. The result is formulated in an abstract setting, so that it applies both to discrete models and to continuous ones.
Topology Synthesis of Structures Using Parameter Relaxation and Geometric Refinement
NASA Technical Reports Server (NTRS)
Hull, P. V.; Tinker, M. L.
2007-01-01
Typically, structural topology optimization problems undergo relaxation of certain design parameters to allow the existence of intermediate variable optimum topologies. Relaxation permits the use of a variety of gradient-based search techniques and has been shown to guarantee the existence of optimal solutions and eliminate mesh dependencies. This Technical Publication (TP) will demonstrate the application of relaxation to a control point discretization of the design workspace for the structural topology optimization process. The control point parameterization with subdivision has been offered as an alternative to the traditional method of discretized finite element design domain. The principle of relaxation demonstrates the increased utility of the control point parameterization. One of the significant results of the relaxation process offered in this TP is that direct manufacturability of the optimized design will be maintained without the need for designer intervention or translation. In addition, it will be shown that relaxation of certain parameters may extend the range of problems that can be addressed; e.g., in permitting limited out-of-plane motion to be included in a path generation problem.
Exploring percolative landscapes: Infinite cascades of geometric phase transitions
NASA Astrophysics Data System (ADS)
Timonin, P. N.; Chitov, Gennady Y.
2016-01-01
The evolution of many kinetic processes in 1+1 (space-time) dimensions results in 2 D directed percolative landscapes. The active phases of these models possess numerous hidden geometric orders characterized by various types of large-scale and/or coarse-grained percolative backbones that we define. For the patterns originated in the classical directed percolation (DP) and contact process we show from the Monte Carlo simulation data that these percolative backbones emerge at specific critical points as a result of continuous phase transitions. These geometric transitions belong to the DP universality class and their nonlocal order parameters are the capacities of corresponding backbones. The multitude of conceivable percolative backbones implies the existence of infinite cascades of such geometric transitions in the kinetic processes considered. We present simple arguments to support the conjecture that such cascades of transitions are a generic feature of percolation as well as of many other transitions with nonlocal order parameters.
Orús, Román; Wei, Tzu-Chieh; Buerschaper, Oliver; García-Saez, Artur
2014-12-19
Topological order in two-dimensional (2D) quantum matter can be determined by the topological contribution to the entanglement Rényi entropies. However, when close to a quantum phase transition, its calculation becomes cumbersome. Here, we show how topological phase transitions in 2D systems can be much better assessed by multipartite entanglement, as measured by the topological geometric entanglement of blocks. Specifically, we present an efficient tensor network algorithm based on projected entangled pair states to compute this quantity for a torus partitioned into cylinders and then use this method to find sharp evidence of topological phase transitions in 2D systems with a string-tension perturbation. When compared to tensor network methods for Rényi entropies, our approach produces almost perfect accuracies close to criticality and, additionally, is orders of magnitude faster. The method can be adapted to deal with any topological state of the system, including minimally entangled ground states. It also allows us to extract the critical exponent of the correlation length and shows that there is no continuous entanglement loss along renormalization group flows in topological phases.
Blanco-Redondo, Andrea; Andonegui, Imanol; Collins, Matthew J; Harari, Gal; Lumer, Yaakov; Rechtsman, Mikael C; Eggleton, Benjamin J; Segev, Mordechai
2016-04-22
One-dimensional models with topological band structures represent a simple and versatile platform to demonstrate novel topological concepts. Here we experimentally study topologically protected states in silicon at the interface between two dimer chains with different Zak phases. Furthermore, we propose and demonstrate that, in a system where topological and trivial defect modes coexist, we can probe them independently. Tuning the configuration of the interface, we observe the transition between a single topological defect and a compound trivial defect state. These results provide a new paradigm for topologically protected waveguiding in a complementary metal-oxide-semiconductor compatible platform and highlight the novel concept of isolating topological and trivial defect modes in the same system that can have important implications in topological physics.
Quantum phase transitions of topological insulators without gap closing.
Rachel, Stephan
2016-10-12
We consider two-dimensional Chern insulators and time-reversal invariant topological insulators and discuss the effect of perturbations breaking either particle-number conservation or time-reversal symmetry. The appearance of trivial mass terms is expected to cause quantum phase transitions into trivial phases when such a perturbation overweighs the topological term. These phase transitions are usually associated with a bulk-gap closing. In contrast, the chiral Chern insulator is unaffected by particle-number breaking perturbations. Moreover, the [Formula: see text] topological insulator undergoes phase transitions into topologically trivial phases without bulk-gap closing in the presence of any of such perturbations. In certain cases, these phase transitions can be circumvented and the protection restored by another U(1) symmetry, e.g. due to spin conservation. These findings are discussed in the context of interacting topological insulators.
Quantum phase transitions of topological insulators without gap closing
NASA Astrophysics Data System (ADS)
Rachel, Stephan
2016-10-01
We consider two-dimensional Chern insulators and time-reversal invariant topological insulators and discuss the effect of perturbations breaking either particle-number conservation or time-reversal symmetry. The appearance of trivial mass terms is expected to cause quantum phase transitions into trivial phases when such a perturbation overweighs the topological term. These phase transitions are usually associated with a bulk-gap closing. In contrast, the chiral Chern insulator is unaffected by particle-number breaking perturbations. Moreover, the {{{Z}}2} topological insulator undergoes phase transitions into topologically trivial phases without bulk-gap closing in the presence of any of such perturbations. In certain cases, these phase transitions can be circumvented and the protection restored by another U(1) symmetry, e.g. due to spin conservation. These findings are discussed in the context of interacting topological insulators.
Quantum phase transitions of topological insulators without gap closing.
Rachel, Stephan
2016-10-12
We consider two-dimensional Chern insulators and time-reversal invariant topological insulators and discuss the effect of perturbations breaking either particle-number conservation or time-reversal symmetry. The appearance of trivial mass terms is expected to cause quantum phase transitions into trivial phases when such a perturbation overweighs the topological term. These phase transitions are usually associated with a bulk-gap closing. In contrast, the chiral Chern insulator is unaffected by particle-number breaking perturbations. Moreover, the [Formula: see text] topological insulator undergoes phase transitions into topologically trivial phases without bulk-gap closing in the presence of any of such perturbations. In certain cases, these phase transitions can be circumvented and the protection restored by another U(1) symmetry, e.g. due to spin conservation. These findings are discussed in the context of interacting topological insulators. PMID:27530509
Topological phase transition in quasi-one dimensional organic conductors.
Ye, Xiao-Shan; Liu, Yong-Jun; Zeng, Xiang-Hua; Wu, Guoqing
2015-01-01
We explore topological phase transition, which involves the energy spectra of field-induced spin-density-wave (FISDW) states in quasi-one dimensional (Q1D) organic conductors, using an extended Su-Schrieffer-Heeger (SSH) model. We show that, in presence of half magnetic-flux FISDW state, the system exhibits topologically nontrivial phases, which can be characterized by a nonzero Chern number. The nontrivial evolution of the bulk bands with chemical potential in a topological phase transition is discussed. We show that the system can have a similar phase diagram which is discussed in the Haldane's model. We suggest that the topological feature should be tested experimentally in this organic system. These studies enrich the theoretical research on topologically nontrivial phases in the Q1D lattice system as compared to the Haldane topological phase appearing in the two-dimensional lattices. PMID:26612317
Topological phase transition in quasi-one dimensional organic conductors
NASA Astrophysics Data System (ADS)
Ye, Xiao-Shan; Liu, Yong-Jun; Zeng, Xiang-Hua; Wu, Guoqing
2015-11-01
We explore topological phase transition, which involves the energy spectra of field-induced spin-density-wave (FISDW) states in quasi-one dimensional (Q1D) organic conductors, using an extended Su-Schrieffer-Heeger (SSH) model. We show that, in presence of half magnetic-flux FISDW state, the system exhibits topologically nontrivial phases, which can be characterized by a nonzero Chern number. The nontrivial evolution of the bulk bands with chemical potential in a topological phase transition is discussed. We show that the system can have a similar phase diagram which is discussed in the Haldane’s model. We suggest that the topological feature should be tested experimentally in this organic system. These studies enrich the theoretical research on topologically nontrivial phases in the Q1D lattice system as compared to the Haldane topological phase appearing in the two-dimensional lattices.
Topological phase transition in quasi-one dimensional organic conductors
Ye, Xiao-Shan; Liu, Yong-Jun; Zeng, Xiang-Hua; Wu, Guoqing
2015-01-01
We explore topological phase transition, which involves the energy spectra of field-induced spin-density-wave (FISDW) states in quasi-one dimensional (Q1D) organic conductors, using an extended Su-Schrieffer-Heeger (SSH) model. We show that, in presence of half magnetic-flux FISDW state, the system exhibits topologically nontrivial phases, which can be characterized by a nonzero Chern number. The nontrivial evolution of the bulk bands with chemical potential in a topological phase transition is discussed. We show that the system can have a similar phase diagram which is discussed in the Haldane’s model. We suggest that the topological feature should be tested experimentally in this organic system. These studies enrich the theoretical research on topologically nontrivial phases in the Q1D lattice system as compared to the Haldane topological phase appearing in the two-dimensional lattices. PMID:26612317
Geometric and Topological Methods for Quantum Field Theory
NASA Astrophysics Data System (ADS)
Ocampo, Hernan; Pariguan, Eddy; Paycha, Sylvie
2010-04-01
Introduction; 1. The impact of QFT on low-dimensional topology Paul Kirk; 2. Differential equations aspects of quantum cohomology Martin A. Guest; 3. Index theory and groupoids Claire Debord and Jean-Marie Lescure; 4. Renormalization Hopf algebras and combinatorial groups Alessandra Frabetti; 5. BRS invariance for massive boson fields José M. Gracia-Bondía; 6. Large N field theories and geometry David Berenstein; 7. Functional renormalization group equations, asymptotic safety, and quantum Einstein gravity Martin Reuter and Frank Saueressig; 8. When is a differentiable manifold the boundary of an orbifold? Andrés Angel; 9. Canonical group quantization, rotation generators and quantum indistinguishability Carlos Benavides and Andrés Reyes-Lega; 10. Conserved currents in Kähler manifolds Jaime R. Camacaro and Juan Carlos Moreno; 11. A symmetrized canonical determinant on odd-class pseudodifferential operators Marie-Françoise Ouedraogo; 12. Some remarks about cosymplectic metrics on maximal flag manifolds Marlio Paredes and Sofia Pinzón; 13. Heisenberg modules over real multiplication noncommutative tori and related algebraic structures Jorge Plazas; Index.
Topology, delocalization via average symmetry and the symplectic Anderson transition.
Fu, Liang; Kane, C L
2012-12-14
A field theory of the Anderson transition in two-dimensional disordered systems with spin-orbit interactions and time-reversal symmetry is developed, in which the proliferation of vortexlike topological defects is essential for localization. The sign of vortex fugacity determines the Z(2) topological class of the localized phase. There are two distinct fixed points with the same critical exponents, corresponding to transitions from a metal to an insulator and a topological insulator, respectively. The critical conductivity and correlation length exponent of these transitions are computed in an N=1-[symbol: see text] expansion in the number of replicas, where for small [symbol: see text] the critical points are perturbatively connected to the Kosterlitz-Thouless critical point. Delocalized states, which arise at the surface of weak topological insulators and topological crystalline insulators, occur because vortex proliferation is forbidden due to the presence of symmetries that are violated by disorder, but are restored by disorder averaging.
Topological and geometrical quantum computation in cohesive Khovanov homotopy type theory
NASA Astrophysics Data System (ADS)
Ospina, Juan
2015-05-01
The recently proposed Cohesive Homotopy Type Theory is exploited as a formal foundation for central concepts in Topological and Geometrical Quantum Computation. Specifically the Cohesive Homotopy Type Theory provides a formal, logical approach to concepts like smoothness, cohomology and Khovanov homology; and such approach permits to clarify the quantum algorithms in the context of Topological and Geometrical Quantum Computation. In particular we consider the so-called "open-closed stringy topological quantum computer" which is a theoretical topological quantum computer that employs a system of open-closed strings whose worldsheets are open-closed cobordisms. The open-closed stringy topological computer is able to compute the Khovanov homology for tangles and for hence it is a universal quantum computer given than any quantum computation is reduced to an instance of computation of the Khovanov homology for tangles. The universal algebra in this case is the Frobenius Algebra and the possible open-closed stringy topological quantum computers are forming a symmetric monoidal category which is equivalent to the category of knowledgeable Frobenius algebras. Then the mathematical design of an open-closed stringy topological quantum computer is involved with computations and theorem proving for generalized Frobenius algebras. Such computations and theorem proving can be performed automatically using the Automated Theorem Provers with the TPTP language and the SMT-solver Z3 with the SMT-LIB language. Some examples of application of ATPs and SMT-solvers in the mathematical setup of an open-closed stringy topological quantum computer will be provided.
NASA Astrophysics Data System (ADS)
Makhfudz, Imam
2016-04-01
Axion electrodynamics, first proposed in the context of particle physics, manifests itself in condensed matter physics in the topological field theory description of 3 d topological insulators and gives rise to magnetoelectric effect, where applying magnetic (electric) field B (E ) induces polarization (magnetization) p (m ) . We use linear response theory to study the associated topological current using the Fu-Kane-Mele model of 3 d topological insulators in the presence of time-dependent uniform weak magnetic field. By computing the dynamical current susceptibility χij jpjp(ω ) , we discover from its static limit an `order parameter' of the topological phase transition between weak topological (or ordinary) insulator and strong topological insulator, found to be continuous. The χij jpjp(ω ) shows a sign-changing singularity at a critical frequency with suppressed strength in the topological insulating state. Our results can be verified in current noise experiment on 3 d TI candidate materials for the detection of such topological phase transition.
Geometric transitions and D-term SUSY breaking
Aganagic, Mina; Aganagic, Mina; Beem, Christopher
2007-11-05
We propose a new way of using geometric transitions to study metastable vacua in string theory and certain confining gauge theories. The gauge theories in question are N=2 supersymmetric theories deformed to N=1 by superpotential terms. We first geometrically engineer supersymmetry-breaking vacua by wrapping D5 branes on rigid 2-cycles in noncompact Calabi-Yau geometries, such that the central charges of the branes are misaligned. In a limit of slightly misaligned charges, this has a gauge theory description, where supersymmetry is broken by Fayet-Iliopoulos D-terms. Geometric transitions relate these configurations to dual Calabi-Yaus with fluxes, where H_RR, H_NS and dJ are all nonvanishing. We argue that the dual geometry can be effectively used to study the resulting non-supersymmetric, confining vacua
NASA Astrophysics Data System (ADS)
Tung, J. C.; Tuan, P. H.; Liang, H. C.; Huang, K. F.; Chen, Y. F.
2016-08-01
We theoretically verify that the symmetry breaking in spherical resonators can result in a fractal frequency spectrum that is full of numerous new accidental degeneracies to cluster around the unperturbed degenerate cavity. We further experimentally discover that the fractal frequency spectrum excellently reflects the intimate connection between the emission power and the degenerate mode numbers. It is observed that the wave distributions of lasing modes at the accidental degeneracies are strongly concentrated on three-dimensional (3D) geometric topology. Considering the overlapping effect, the wave representation of the coherent states is analytically derived to manifest the observed 3D geometric surfaces.
Topological and unconventional magnetic states in transition metal oxides
NASA Astrophysics Data System (ADS)
Fiete, Gregory
In this talk I describe some recent work on unusual correlated phases that may be found in bulk transition metal oxides with strong spin-orbit coupling. I will focus on model Hamiltonian studies that are motivated by the pyrocholore iridates, though the correlated topological phases described may appear in a much broader class of materials. I will describe a variety of fractionalized topological phases protected by time-reversal and crystalline symmetries: The weak topological Mott insulator (WTMI), the TI* phase, and the topological crystalline Mott insulator (TCMI). If time permits, I will also discuss closely related heterostructures of pyrochlore iridates in a bilayer and trilayer film geometry. These quasi-two dimensional systems may exhibit a number of interesting topological and magnetic phases. This work is generously funded by the ARO, DARPA, and the NSF.
NASA Astrophysics Data System (ADS)
He, Yuan-Yao; Wu, Han-Qing; You, Yi-Zhuang; Xu, Cenke; Meng, Zi Yang; Lu, Zhong-Yi
2016-03-01
It is expected that the interplay between nontrivial band topology and strong electron correlation will lead to very rich physics. Thus a controlled study of the competition between topology and correlation is of great interest. Here, employing large-scale quantum Monte Carlo simulations, we provide a concrete example of the Kane-Mele-Hubbard model on an AA-stacking bilayer honeycomb lattice with interlayer antiferromagnetic interaction. Our simulation identified several different phases: a quantum spin Hall insulator (QSH), an x y -plane antiferromagnetic Mott insulator, and an interlayer dimer-singlet insulator. Most importantly, a bona fide topological phase transition between the QSH and the dimer-singlet insulators, purely driven by the interlayer antiferromagnetic interaction, is found. At the transition, the spin and charge gap of the system close while the single-particle excitations remain gapped, which means that this transition has no mean-field analog and it can be viewed as a transition between bosonic symmetry-protected topological (SPT) states. At one special point, this transition is described by a (2 +1 )d O (4 ) nonlinear sigma model with exact S O (4 ) symmetry and a topological term at exactly Θ =π . The relevance of this work towards more general interacting SPT states is discussed.
Universal Finite-Size Scaling around Topological Quantum Phase Transitions
NASA Astrophysics Data System (ADS)
Gulden, Tobias; Janas, Michael; Wang, Yuting; Kamenev, Alex
The critical point of a topological phase transition is described by a conformal field theory, where finite-size corrections to energy are uniquely related to its central charge. We investigate the behavior away from criticality and obtain a scaling function. In contrast to scaling functions for entanglement entropy it discriminates between phases with different topological indexes. This function appears to be universal for all five Altland-Zirnbauer symmetry classes with non-trivial topology in one spatial dimension. We obtain an analytic form of the scaling function and compare it with numerical results.
Universal Finite-Size Scaling around Topological Quantum Phase Transitions
NASA Astrophysics Data System (ADS)
Gulden, Tobias; Janas, Michael; Wang, Yuting; Kamenev, Alex
2016-01-01
The critical point of a topological phase transition is described by a conformal field theory, where finite-size corrections to energy are uniquely related to its central charge. We investigate the finite-size scaling away from criticality and find a scaling function, which discriminates between phases with different topological indices. This function appears to be universal for all five Altland-Zirnbauer symmetry classes with nontrivial topology in one spatial dimension. We obtain an analytic form of the scaling function and compare it with numerical results.
Universal Finite-Size Scaling around Topological Quantum Phase Transitions.
Gulden, Tobias; Janas, Michael; Wang, Yuting; Kamenev, Alex
2016-01-15
The critical point of a topological phase transition is described by a conformal field theory, where finite-size corrections to energy are uniquely related to its central charge. We investigate the finite-size scaling away from criticality and find a scaling function, which discriminates between phases with different topological indices. This function appears to be universal for all five Altland-Zirnbauer symmetry classes with nontrivial topology in one spatial dimension. We obtain an analytic form of the scaling function and compare it with numerical results.
Interaction effects and quantum phase transitions in topological insulators
Varney, Christopher N.; Sun Kai; Galitski, Victor; Rigol, Marcos
2010-09-15
We study strong correlation effects in topological insulators via the Lanczos algorithm, which we utilize to calculate the exact many-particle ground-state wave function and its topological properties. We analyze the simple, noninteracting Haldane model on a honeycomb lattice with known topological properties and demonstrate that these properties are already evident in small clusters. Next, we consider interacting fermions by introducing repulsive nearest-neighbor interactions. A first-order quantum phase transition was discovered at finite interaction strength between the topological band insulator and a topologically trivial Mott insulating phase by use of the fidelity metric and the charge-density-wave structure factor. We construct the phase diagram at T=0 as a function of the interaction strength and the complex phase for the next-nearest-neighbor hoppings. Finally, we consider the Haldane model with interacting hard-core bosons, where no evidence for a topological phase is observed. An important general conclusion of our work is that despite the intrinsic nonlocality of topological phases their key topological properties manifest themselves already in small systems and therefore can be studied numerically via exact diagonalization and observed experimentally, e.g., with trapped ions and cold atoms in optical lattices.
NASA Astrophysics Data System (ADS)
Wu, Wei; Xu, Jing-Bo
2016-09-01
We investigate the quantum phase transition of an atomic ensemble trapped in a single-mode optical cavity via the geometric phase and quantum Fisher information of an extra probe atom which is injected into the optical cavity and interacts with the cavity field. We also find that the geometric quantum correlation between two probe atoms exhibits a double sudden transition phenomenon and show this double sudden transition phenomenon is closely associated with the quantum phase transition of the atomic ensemble. Furthermore, we propose a theoretical scheme to prolong the frozen time during which the geometric quantum correlation remains constant by applying time-dependent electromagnetic field.
Topological transitions in multi-band superconductors
Continentino, Mucio A.; Deus, Fernanda; Padilha, Igor T.; Caldas, Heron
2014-09-15
The search for Majorana fermions has been concentrated in topological insulators or superconductors. In general, the existence of these modes requires the presence of spin–orbit interactions and of an external magnetic field. The former implies in having systems with broken inversion symmetry, while the latter breaks time reversal invariance. In a recent paper, we have shown that a two-band metal with an attractive inter-band interaction has non-trivial superconducting properties, if the k-dependent hybridization is anti-symmetric in the wave-vector. This is the case, if the crystalline potential mixes states with different parities as for orbitals with angular momentum l and l+1. In this paper we take into account the effect of an external magnetic field, not considered in the previous investigation, in a two-band metal and show how it modifies the topological properties of its superconducting state. We also discuss the conditions for the appearance of Majorana fermions in this system.
Geometric phase for a neutral particle in the presence of a topological defect
Bakke, K.; Nascimento, J. R.; Furtado, C.
2008-09-15
In this paper we study the quantum dynamics of a neutral particle in the presence of a topological defect. We investigate the appearance of a geometric phase in the relativistic quantum dynamics of a neutral particle which possesses permanent magnetic and electric dipole moments in the presence of an electromagnetic field in this curved space-time. The nonrelativistic quantum dynamics are investigated using the Foldy-Wouthuysen expansion. The gravitational Aharonov-Casher and He-McKellar-Wilkens effects are investigated for a series of electric and magnetic field configurations.
Multifarious topological quantum phase transitions in two-dimensional topological superconductors
NASA Astrophysics Data System (ADS)
Liu, Xiao-Ping; Zhou, Yuan; Wang, Yi-Fei; Gong, Chang-De
2016-06-01
We study the two-dimensional topological superconductors of spinless fermions in a checkerboard-lattice Chern-insulator model. With the short-range p-wave superconducting pairing, multifarious topological quantum phase transitions have been found and several phases with high Chern numbers have been observed. We have established a rich phase diagram for these topological superconducting states. A finite-size checkerboard-lattice cylinder with a harmonic trap potential has been further investigated. Based upon the self-consistent numerical calculations of the Bogoliubov-de Gennes equations, various phase transitions have also been identified at different regions of the system. Multiple pairs of Majorana fermions are found to be well-separated and localized at the phase boundaries between the phases characterized by different Chern numbers.
Multifarious topological quantum phase transitions in two-dimensional topological superconductors
Liu, Xiao-Ping; Zhou, Yuan; Wang, Yi-Fei; Gong, Chang-De
2016-01-01
We study the two-dimensional topological superconductors of spinless fermions in a checkerboard-lattice Chern-insulator model. With the short-range p-wave superconducting pairing, multifarious topological quantum phase transitions have been found and several phases with high Chern numbers have been observed. We have established a rich phase diagram for these topological superconducting states. A finite-size checkerboard-lattice cylinder with a harmonic trap potential has been further investigated. Based upon the self-consistent numerical calculations of the Bogoliubov-de Gennes equations, various phase transitions have also been identified at different regions of the system. Multiple pairs of Majorana fermions are found to be well-separated and localized at the phase boundaries between the phases characterized by different Chern numbers. PMID:27329219
Laser-induced topological transitions in phosphorene with inversion symmetry
NASA Astrophysics Data System (ADS)
Dutreix, C.; Stepanov, E. A.; Katsnelson, M. I.
2016-06-01
Recent ab initio calculations and experiments reported insulating-semimetallic phase transitions in multilayer phosphorene under a perpendicular dc field, pressure, or doping, as a possible route to realize topological phases. In this work, we show that even a monolayer phosphorene may undergo Lifshitz transitions toward semimetallic and topological insulating phases, provided it is rapidly driven by in-plane time-periodic laser fields. Based on a four-orbital tight-binding description, we give an inversion-symmetry-based prescription in order to apprehend the topology of the photon-renormalized band structure, up to the second order in the high-frequency limit. Apart from the initial band insulating behavior, two additional phases are thus identified. A semimetallic phase with massless Dirac electrons may be induced by linear polarized fields, whereas elliptic polarized fields are likely to drive the material into an anomalous quantum Hall phase.
Statistical mechanics of topological phase transitions in networks
NASA Astrophysics Data System (ADS)
Palla, Gergely; Derényi, Imre; Farkas, Illés; Vicsek, Tamás
2004-04-01
We provide a phenomenological theory for topological transitions in restructuring networks. In this statistical mechanical approach energy is assigned to the different network topologies and temperature is used as a quantity referring to the level of noise during the rewiring of the edges. The associated microscopic dynamics satisfies the detailed balance condition and is equivalent to a lattice gas model on the edge-dual graph of a fully connected network. In our studies—based on an exact enumeration method, Monte Carlo simulations, and theoretical considerations—we find a rich variety of topological phase transitions when the temperature is varied. These transitions signal singular changes in the essential features of the global structure of the network. Depending on the energy function chosen, the observed transitions can be best monitored using the order parameters Φs=smax/M, i.e., the size of the largest connected component divided by the number of edges, or Φk=kmax/M, the largest degree in the network divided by the number of edges. If, for example, the energy is chosen to be E=-smax, the observed transition is analogous to the percolation phase transition of random graphs. For this choice of the energy, the phase diagram in the (
Structural and topological phase transitions on the German Stock Exchange
NASA Astrophysics Data System (ADS)
Wiliński, M.; Sienkiewicz, A.; Gubiec, T.; Kutner, R.; Struzik, Z. R.
2013-12-01
We find numerical and empirical evidence for dynamical, structural and topological phase transitions on the (German) Frankfurt Stock Exchange (FSE) in the temporal vicinity of the worldwide financial crash. Using the Minimal Spanning Tree (MST) technique, a particularly useful canonical tool of the graph theory, two transitions of the topology of a complex network representing the FSE were found. The first transition is from a hierarchical scale-free MST representing the stock market before the recent worldwide financial crash, to a superstar-like MST decorated by a scale-free hierarchy of trees representing the market’s state for the period containing the crash. Subsequently, a transition is observed from this transient, (meta)stable state of the crash to a hierarchical scale-free MST decorated by several star-like trees after the worldwide financial crash. The phase transitions observed are analogous to the ones we obtained earlier for the Warsaw Stock Exchange and more pronounced than those found by Onnela-Chakraborti-Kaski-Kertész for the S&P 500 index in the vicinity of Black Monday (October 19, 1987) and also in the vicinity of January 1, 1998. Our results provide an empirical foundation for the future theory of dynamical, structural and topological phase transitions on financial markets.
Geometrical guidance and trapping transition of human sperm cells
NASA Astrophysics Data System (ADS)
Guidobaldi, A.; Jeyaram, Y.; Berdakin, I.; Moshchalkov, V. V.; Condat, C. A.; Marconi, V. I.; Giojalas, L.; Silhanek, A. V.
2014-03-01
The guidance of human sperm cells under confinement in quasi-2D microchambers is investigated using a purely physical method to control their distribution. Transport property measurements and simulations are performed with diluted sperm populations, for which effects of geometrical guidance and concentration are studied in detail. In particular, a trapping transition at convex angular wall features is identified and analyzed. We also show that highly efficient microratchets can be fabricated by using curved asymmetric obstacles to take advantage of the spermatozoa specific swimming strategy.
NASA Astrophysics Data System (ADS)
Jauregui, Luis A.; Pettes, Michael T.; Rokhinson, Leonid P.; Shi, Li; Chen, Yong P.
2016-04-01
The spin-helical Dirac fermion topological surface states in a topological insulator nanowire or nanoribbon promise novel topological devices and exotic physics such as Majorana fermions. Here, we report local and non-local transport measurements in Bi2Te3 topological insulator nanoribbons that exhibit quasi-ballistic transport over ˜2 μm. The conductance versus axial magnetic flux Φ exhibits Aharonov-Bohm oscillations with maxima occurring alternately at half-integer or integer flux quanta (Φ0 = h/e, where h is Planck's constant and e is the electron charge) depending periodically on the gate-tuned Fermi wavevector (kF) with period 2π/C (where C is the nanoribbon circumference). The conductance versus gate voltage also exhibits kF-periodic oscillations, anti-correlated between Φ = 0 and Φ0/2. These oscillations enable us to probe the Bi2Te3 band structure, and are consistent with the circumferentially quantized topological surface states forming a series of one-dimensional subbands, which undergo periodic magnetic field-induced topological transitions with the disappearance/appearance of the gapless Dirac point with a one-dimensional spin helical mode.
Jauregui, Luis A; Pettes, Michael T; Rokhinson, Leonid P; Shi, Li; Chen, Yong P
2016-04-01
The spin-helical Dirac fermion topological surface states in a topological insulator nanowire or nanoribbon promise novel topological devices and exotic physics such as Majorana fermions. Here, we report local and non-local transport measurements in Bi2Te3 topological insulator nanoribbons that exhibit quasi-ballistic transport over ∼2 μm. The conductance versus axial magnetic flux Φ exhibits Aharonov-Bohm oscillations with maxima occurring alternately at half-integer or integer flux quanta (Φ0 = h/e, where h is Planck's constant and e is the electron charge) depending periodically on the gate-tuned Fermi wavevector (kF) with period 2π/C (where C is the nanoribbon circumference). The conductance versus gate voltage also exhibits kF-periodic oscillations, anti-correlated between Φ = 0 and Φ0/2. These oscillations enable us to probe the Bi2Te3 band structure, and are consistent with the circumferentially quantized topological surface states forming a series of one-dimensional subbands, which undergo periodic magnetic field-induced topological transitions with the disappearance/appearance of the gapless Dirac point with a one-dimensional spin helical mode.
NASA Astrophysics Data System (ADS)
Jauregui, Luis A.; Pettes, Michael T.; Rokhinson, Leonid P.; Shi, Li; Chen, Yong P.
2016-04-01
The spin-helical Dirac fermion topological surface states in a topological insulator nanowire or nanoribbon promise novel topological devices and exotic physics such as Majorana fermions. Here, we report local and non-local transport measurements in Bi2Te3 topological insulator nanoribbons that exhibit quasi-ballistic transport over ∼2 μm. The conductance versus axial magnetic flux Φ exhibits Aharonov–Bohm oscillations with maxima occurring alternately at half-integer or integer flux quanta (Φ0 = h/e, where h is Planck's constant and e is the electron charge) depending periodically on the gate-tuned Fermi wavevector (kF) with period 2π/C (where C is the nanoribbon circumference). The conductance versus gate voltage also exhibits kF-periodic oscillations, anti-correlated between Φ = 0 and Φ0/2. These oscillations enable us to probe the Bi2Te3 band structure, and are consistent with the circumferentially quantized topological surface states forming a series of one-dimensional subbands, which undergo periodic magnetic field-induced topological transitions with the disappearance/appearance of the gapless Dirac point with a one-dimensional spin helical mode.
Chern-Simons-Higgs transitions out of topological superconducting phases
NASA Astrophysics Data System (ADS)
Clarke, David J.; Nayak, Chetan
2015-10-01
In this study, we examine effective field theories of superconducting phases with topological order, making a connection to proposed realizations of exotic topological phases (including those hosting Ising and Fibonacci anyons) in superconductor-quantum Hall heterostructures. Our effective field theories for the non-Abelian superconducting states are non-Abelian Chern-Simons theories in which the condensation of vortices carrying non-Abelian gauge flux leads to the associated Abelian quantum Hall states. This Chern-Simons-Higgs condensation process is dual to the emergence of superconducting non-Abelian topological phases in coupled chain constructions. In such transitions, the chiral central charge of the system generally changes, so they fall outside the description of bosonic condensation transitions put forth by Bais and Slingerland [F. A. Bais and J. K. Slingerland, Phys. Rev. B 79, 045316 (2009), 10.1103/PhysRevB.79.045316] (though the two approaches agree when the described transitions coincide). Our condensation process may be generalized to Chern-Simons theories based on arbitrary Lie groups, always describing a transition from a Lie algebra to its Cartan subalgebra. We include several instructive examples of such transitions.
Reentrant topological phase transitions in a disordered spinless superconducting wire
NASA Astrophysics Data System (ADS)
Rieder, Maria-Theresa; Brouwer, Piet W.; Adagideli, İnanç
2013-08-01
In a one-dimensional spinless p-wave superconductor with coherence length ξ, disorder induces a phase transition between a topologically nontrivial phase and a trivial insulating phase at the critical mean-free path l=ξ/2. Here, we show that a multichannel spinless p-wave superconductor goes through an alternation of topologically trivial and nontrivial phases upon increasing the disorder strength, the number of phase transitions being equal to the channel number N. The last phase transition, from a nontrivial phase into the trivial phase, takes place at a mean-free path l=ξ/(N+1), parametrically smaller than the critical mean-free path in one dimension. Our result is valid in the limit that the wire width W is much smaller than the superconducting coherence length ξ.
Coherence-Driven Topological Transition in Quantum Metamaterials.
Jha, Pankaj K; Mrejen, Michael; Kim, Jeongmin; Wu, Chihhui; Wang, Yuan; Rostovtsev, Yuri V; Zhang, Xiang
2016-04-22
We introduce and theoretically demonstrate a quantum metamaterial made of dense ultracold neutral atoms loaded into an inherently defect-free artificial crystal of light, immune to well-known critical challenges inevitable in conventional solid-state platforms. We demonstrate an all-optical control, on ultrafast time scales, over the photonic topological transition of the isofrequency contour from an open to closed topology at the same frequency. This atomic lattice quantum metamaterial enables a dynamic manipulation of the decay rate branching ratio of a probe quantum emitter by more than an order of magnitude. Our proposal may lead to practically lossless, tunable, and topologically reconfigurable quantum metamaterials, for single or few-photon-level applications as varied as quantum sensing, quantum information processing, and quantum simulations using metamaterials. PMID:27152810
Coherence-Driven Topological Transition in Quantum Metamaterials
NASA Astrophysics Data System (ADS)
Jha, Pankaj K.; Mrejen, Michael; Kim, Jeongmin; Wu, Chihhui; Wang, Yuan; Rostovtsev, Yuri V.; Zhang, Xiang
2016-04-01
We introduce and theoretically demonstrate a quantum metamaterial made of dense ultracold neutral atoms loaded into an inherently defect-free artificial crystal of light, immune to well-known critical challenges inevitable in conventional solid-state platforms. We demonstrate an all-optical control, on ultrafast time scales, over the photonic topological transition of the isofrequency contour from an open to closed topology at the same frequency. This atomic lattice quantum metamaterial enables a dynamic manipulation of the decay rate branching ratio of a probe quantum emitter by more than an order of magnitude. Our proposal may lead to practically lossless, tunable, and topologically reconfigurable quantum metamaterials, for single or few-photon-level applications as varied as quantum sensing, quantum information processing, and quantum simulations using metamaterials.
Coherence-Driven Topological Transition in Quantum Metamaterials.
Jha, Pankaj K; Mrejen, Michael; Kim, Jeongmin; Wu, Chihhui; Wang, Yuan; Rostovtsev, Yuri V; Zhang, Xiang
2016-04-22
We introduce and theoretically demonstrate a quantum metamaterial made of dense ultracold neutral atoms loaded into an inherently defect-free artificial crystal of light, immune to well-known critical challenges inevitable in conventional solid-state platforms. We demonstrate an all-optical control, on ultrafast time scales, over the photonic topological transition of the isofrequency contour from an open to closed topology at the same frequency. This atomic lattice quantum metamaterial enables a dynamic manipulation of the decay rate branching ratio of a probe quantum emitter by more than an order of magnitude. Our proposal may lead to practically lossless, tunable, and topologically reconfigurable quantum metamaterials, for single or few-photon-level applications as varied as quantum sensing, quantum information processing, and quantum simulations using metamaterials.
Thermally Driven Electronic Topological Transition in FeTi.
Yang, F C; Muñoz, J A; Hellman, O; Mauger, L; Lucas, M S; Tracy, S J; Stone, M B; Abernathy, D L; Xiao, Yuming; Fultz, B
2016-08-12
Ab initio molecular dynamics, supported by inelastic neutron scattering and nuclear resonant inelastic x-ray scattering, showed an anomalous thermal softening of the M_{5}^{-} phonon mode in B2-ordered FeTi that could not be explained by phonon-phonon interactions or electron-phonon interactions calculated at low temperatures. A computational investigation showed that the Fermi surface undergoes a novel thermally driven electronic topological transition, in which new features of the Fermi surface arise at elevated temperatures. The thermally induced electronic topological transition causes an increased electronic screening for the atom displacements in the M_{5}^{-} phonon mode and an adiabatic electron-phonon interaction with an unusual temperature dependence. PMID:27563978
Thermally Driven Electronic Topological Transition in FeTi
Yang, F. C.; Muñoz, J. A.; Hellman, O.; Mauger, L.; Lucas, M. S.; Tracy, S. J.; Stone, M. B.; Abernathy, D. L.; Xiao, Yuming; Fultz, B.
2016-08-08
In this paper, ab initio molecular dynamics, supported by inelastic neutron scattering and nuclear resonant inelastic x-ray scattering, showed an anomalous thermal softening of the M5- phonon mode in B2-ordered FeTi that could not be explained by phonon-phonon interactions or electron-phonon interactions calculated at low temperatures. A computational investigation showed that the Fermi surface undergoes a novel thermally driven electronic topological transition, in which new features of the Fermi surface arise at elevated temperatures. Finally, the thermally induced electronic topological transition causes an increased electronic screening for the atom displacements in the M5- phonon mode and an adiabatic electron-phonon interactionmore » with an unusual temperature dependence.« less
Thermally Driven Electronic Topological Transition in FeTi
NASA Astrophysics Data System (ADS)
Yang, F. C.; Muñoz, J. A.; Hellman, O.; Mauger, L.; Lucas, M. S.; Tracy, S. J.; Stone, M. B.; Abernathy, D. L.; Xiao, Yuming; Fultz, B.
2016-08-01
Ab initio molecular dynamics, supported by inelastic neutron scattering and nuclear resonant inelastic x-ray scattering, showed an anomalous thermal softening of the M5- phonon mode in B 2 -ordered FeTi that could not be explained by phonon-phonon interactions or electron-phonon interactions calculated at low temperatures. A computational investigation showed that the Fermi surface undergoes a novel thermally driven electronic topological transition, in which new features of the Fermi surface arise at elevated temperatures. The thermally induced electronic topological transition causes an increased electronic screening for the atom displacements in the M5- phonon mode and an adiabatic electron-phonon interaction with an unusual temperature dependence.
Formation of geometrically complex lipid nanotube-vesicle networks of higher-order topologies
Karlsson, Mattias; Sott, Kristin; Davidson, Maximillian; Cans, Ann-Sofie; Linderholm, Pontus; Chiu, Daniel; Orwar, Owe
2002-01-01
We present a microelectrofusion method for construction of fluid-state lipid bilayer networks of high geometrical complexity up to fully connected networks with genus = 3 topology. Within networks, self-organizing branching nanotube architectures could be produced where intersections spontaneously arrange themselves into three-way junctions with an angle of 120° between each nanotube. Formation of branching nanotube networks appears to follow a minimum-bending energy algorithm that solves for pathway minimization. It is also demonstrated that materials can be injected into specific containers within a network by nanotube-mediated transport of satellite vesicles having defined contents. Using a combination of microelectrofusion, spontaneous nanotube pattern formation, and satellite-vesicle injection, complex networks of containers and nanotubes can be produced for a range of applications in, for example, nanofluidics and artificial cell design. In addition, this electrofusion method allows integration of biological cells into lipid nanotube-vesicle networks. PMID:12185244
Detection of topological transitions by transport through molecules and nanodevices.
Aligia, A A; Hallberg, K; Normand, B; Kampf, A P
2004-08-13
We analyze the phase transitions of an interacting electronic system weakly coupled to free-electron leads by considering its zero-bias conductance. This is expressed in terms of two effective impurity models for the cases with and without spin degeneracy. Using the half-filled ionic Hubbard ring, we demonstrate that the weight of the first conductance peak as a function of external flux or of the difference in gate voltages between even and odd sites allows one to identify the topological charge transition between a correlated insulator and a band insulator.
Structural phase transitions and topological defects in ion Coulomb crystals
Partner, Heather L.; Nigmatullin, Ramil; Burgermeister, Tobias; Keller, Jonas; Pyka, Karsten; Plenio, Martin B.; Retzker, Alex; Zurek, Wojciech Hubert; del Campo, Adolfo; Mehlstaubler, Tanja E.
2014-11-19
We use laser-cooled ion Coulomb crystals in the well-controlled environment of a harmonic radiofrequency ion trap to investigate phase transitions and defect formation. Topological defects in ion Coulomb crystals (kinks) have been recently proposed for studies of nonlinear physics with solitons and as carriers of quantum information. Defects form when a symmetry breaking phase transition is crossed non-adiabatically. For a second order phase transition, the Kibble-Zurek mechanism predicts that the formation of these defects follows a power law scaling in the rate of the transition. We demonstrate a scaling of defect density and describe kink dynamics and stability. We further discuss the implementation of mass defects and electric fields as first steps toward controlled kink preparation and manipulation.
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.
Geometrically controlled snapping transitions in shells with curved creases
Bende, Nakul Prabhakar; Evans, Arthur A.; Innes-Gold, Sarah; Marin, Luis A.; Cohen, Itai; Hayward, Ryan C.; Santangelo, Christian D.
2015-01-01
Curvature and mechanics are intimately connected for thin materials, and this coupling between geometry and physical properties is readily seen in folded structures from intestinal villi and pollen grains to wrinkled membranes and programmable metamaterials. While the well-known rules and mechanisms behind folding a flat surface have been used to create deployable structures and shape transformable materials, folding of curved shells is still not fundamentally understood. Shells naturally deform by simultaneously bending and stretching, and while this coupling gives them great stability for engineering applications, it makes folding a surface of arbitrary curvature a nontrivial task. Here we discuss the geometry of folding a creased shell, and demonstrate theoretically the conditions under which it may fold smoothly. When these conditions are violated we show, using experiments and simulations, that shells undergo rapid snapping motion to fold from one stable configuration to another. Although material asymmetry is a proven mechanism for creating this bifurcation of stability, for the case of a creased shell, the inherent geometry itself serves as a barrier to folding. We discuss here how two fundamental geometric concepts, creases and curvature, combine to allow rapid transitions from one stable state to another. Independent of material system and length scale, the design rule that we introduce here explains how to generate snapping transitions in arbitrary surfaces, thus facilitating the creation of programmable multistable materials with fast actuation capabilities. PMID:26294253
Electronic topological transition in LaSn3 under pressure
NASA Astrophysics Data System (ADS)
Ram, Swetarekha; Kanchana, V.; Vaitheeswaran, G.; Svane, A.; Dugdale, S. B.; Christensen, N. E.
2012-05-01
The electronic structure, Fermi surface, and elastic properties of the isostructural and isoelectronic LaSn3 and YSn3 intermetallic compounds are studied under pressure within the framework of density functional theory including spin-orbit coupling. The LaSn3 Fermi surface consists of two sheets, of which the second is very complex. Under pressure a third sheet appears around compression V/V0=0.94, while a small topology change in the second sheet is seen at compression V/V0=0.90. This may be in accordance with the anomalous behavior in the superconducting transition temperature observed in LaSn3, which has been suggested to reflect a Fermi surface topological transition, along with a nonmonotonic pressure dependence of the density of states at the Fermi level. The same behavior is not observed in YSn3, the Fermi surface of which already includes three sheets at ambient conditions, and the topology remains unchanged under pressure. The reason for the difference in behavior between LaSn3 and YSn3 is the role of spin-orbit coupling and the hybridization of La 4f states with the Sn p states in the vicinity of the Fermi level, which is well explained using the band structure calculation. The elastic constants and related mechanical properties are calculated at ambient as well as at elevated pressures. The elastic constants increase with pressure for both compounds and satisfy the conditions for mechanical stability under pressure.
Topological-distance-dependent transition in flocks with binary interactions.
Bhattacherjee, Biplab; Mishra, Shradha; Manna, S S
2015-12-01
We have studied a flocking model with binary interactions (binary flock), where the velocity of an agent depends on the velocity of only another agent and its own velocity, topped by the angular noise. The other agent is selected as the nth topological neighbor; the specific value of n being a fixed parameter of the problem. On the basis of extensive numerical simulation results, we argue that for n = 1, the phase transition from the ordered to the disordered phase of the flock is a special kind of discontinuous transition. Here, the order parameter does not flip-flop between multiple metastable states. It continues its initial disordered state for a period t(c), then switches over to the ordered state and remains in this state ever after. For n = 2, it is the usual discontinuous transition between two metastable states. Beyond this range, the continuous transitions are observed for n≥3. Such a system of binary flocks has been further studied using the hydrodynamic equations of motion. Linear stability analysis of the homogeneous polarized state shows that such a state is unstable close to the critical point and above some critical speed, which increases as we increase n. The critical noise strengths, which depend on the average correlation between a pair of topological neighbors, are estimated for five different values of n, which match well with their simulated values. PMID:26764659
Novel Quantum Criticality in Two Dimensional Topological Phase transitions
Cho, Gil Young; Moon, Eun-Gook
2016-01-01
Topological quantum phase transitions intrinsically intertwine self-similarity and topology of many-electron wave-functions, and divining them is one of the most significant ways to advance understanding in condensed matter physics. Our focus is to investigate an unconventional class of the transitions between insulators and Dirac semimetals whose description is beyond conventional pseudo relativistic Dirac Hamiltonian. At the transition without the long-range Coulomb interaction, the electronic energy dispersion along one direction behaves like a relativistic particle, linear in momentum, but along the other direction it behaves like a non-relativistic particle, quadratic in momentum. Various physical systems ranging from TiO2-VO2 heterostructure to organic material α-(BEDT-TTF)2I3 under pressure have been proposed to have such anisotropic dispersion relation. Here, we discover a novel quantum criticality at the phase transition by incorporating the long range Coulomb interaction. Unique interplay between the Coulomb interaction and electronic critical modes enforces not only the anisotropic renormalization of the Coulomb interaction but also marginally modified electronic excitation. In connection with experiments, we investigate several striking effects in physical observables of our novel criticality. PMID:26791803
Abundant topological states in silicene with transition metal adatoms
NASA Astrophysics Data System (ADS)
Zhang, Jiayong; Zhao, Bao; Yang, Zhongqin
2013-10-01
Electronic and topological properties of silicene adsorbed with 4d transition metal (TM) atoms are investigated by using ab initio methods together with tight-binding models. All six kinds of TM adatoms (Y to Ru) we studied prefer hollow sites of silicene. The interplay of TM-induced exchange interactions, spin-orbit coupling, and staggered AB-sublattice potential triggers abundant topological states, including quantum anomalous Hall (QAH) states, valley Hall states, and valley-polarized metallic states. Particularly, QAH states with different Chern numbers are obtained, which is -2 in the Nb/Ru doped system and 1 in the Y doped system. Our results indicate that great potential for information processing applications exists in these systems of silicene adsorbed with TM atoms.
Topological catastrophe and isostructural phase transition in calcium.
Jones, Travis E; Eberhart, Mark E; Clougherty, Dennis P
2010-12-31
We predict a quantum phase transition in fcc Ca under hydrostatic pressure. Using density functional theory, we find, at pressures below 80 kbar, the topology of the electron charge density is characterized by nearest neighbor atoms connected through bifurcated bond paths and deep minima in the octahedral holes. At pressures above 80 kbar, the atoms bond through non-nuclear maxima that form in the octahedral holes. This topological change in the charge density softens the C' elastic modulus of fcc Ca, while C44 remains unchanged. We propose an order parameter based on applying Morse theory to the charge density, and we show that near the critical point it follows the expected mean-field scaling law with reduced pressure. PMID:21231679
Topological Catastrophe and Isostructural Phase Transition in Calcium
NASA Astrophysics Data System (ADS)
Jones, Travis E.; Eberhart, Mark E.; Clougherty, Dennis P.
2010-12-01
We predict a quantum phase transition in fcc Ca under hydrostatic pressure. Using density functional theory, we find, at pressures below 80 kbar, the topology of the electron charge density is characterized by nearest neighbor atoms connected through bifurcated bond paths and deep minima in the octahedral holes. At pressures above 80 kbar, the atoms bond through non-nuclear maxima that form in the octahedral holes. This topological change in the charge density softens the C' elastic modulus of fcc Ca, while C44 remains unchanged. We propose an order parameter based on applying Morse theory to the charge density, and we show that near the critical point it follows the expected mean-field scaling law with reduced pressure.
UNIVERSALITY OF PHASE TRANSITION DYNAMICS: TOPOLOGICAL DEFECTS FROM SYMMETRY BREAKING
Zurek, Wojciech H.; Del Campo, Adolfo
2014-02-13
In the course of a non-equilibrium continuous phase transition, the dynamics ceases to be adiabatic in the vicinity of the critical point as a result of the critical slowing down (the divergence of the relaxation time in the neighborhood of the critical point). This enforces a local choice of the broken symmetry and can lead to the formation of topological defects. The Kibble-Zurek mechanism (KZM) was developed to describe the associated nonequilibrium dynamics and to estimate the density of defects as a function of the quench rate through the transition. During recent years, several new experiments investigating formation of defects in phase transitions induced by a quench both in classical and quantum mechanical systems were carried out. At the same time, some established results were called into question. We review and analyze the Kibble-Zurek mechanism focusing in particular on this surge of activity, and suggest possible directions for further progress.
Eon, Jean-Guillaume
2011-01-01
Crystal-structure topologies, represented by periodic nets, are described by labelled quotient graphs (or voltage graphs). Because the edge space of a finite graph is the direct sum of its cycle and co-cycle spaces, a Euclidian representation of the derived periodic net is provided by mapping a basis of the cycle and co-cycle spaces to a set of real vectors. The mapping is consistent if every cycle of the basis is mapped on its own net voltage. The sum of all outgoing edges at every vertex may be chosen as a generating set of the co-cycle space. The embedding maps the cycle space onto the lattice L. By analogy, the concept of the co-lattice L* is defined as the image of the generators of the co-cycle space; a co-lattice vector is proportional to the distance vector between an atom and the centre of gravity of its neighbours. The pair (L, L*) forms a complete geometric descriptor of the embedding, generalizing the concept of barycentric embedding. An algebraic expression permits the direct calculation of fractional coordinates. Non-zero co-lattice vectors allow nets with collisions, displacive transitions etc. to be dealt with. The method applies to nets of any periodicity and dimension, be they crystallographic nets or not. Examples are analyzed: α-cristobalite, the seven unstable 3-periodic minimal nets etc.
Phase Transitions on Random Lattices: How Random is Topological Disorder?
NASA Astrophysics Data System (ADS)
Barghathi, Hatem; Vojta, Thomas
2015-03-01
We study the effects of topological (connectivity) disorder on phase transitions. We identify a broad class of random lattices whose disorder fluctuations decay much faster with increasing length scale than those of generic random systems, yielding a wandering exponent of ω = (d - 1) / (2 d) in d dimensions. The stability of clean critical points is thus governed by the criterion (d + 1) ν > 2 rather than the usual Harris criterion dν > 2 , making topological disorder less relevant than generic randomness. The Imry-Ma criterion is also modified, allowing first-order transitions to survive in all dimensions d > 1 . These results explain a host of puzzling violations of the original criteria for equilibrium and nonequilibrium phase transitions on random lattices. We discuss applications, and we illustrate our theory by computer simulations of random Voronoi and other lattices. This work was supported by the NSF under Grant Nos. DMR-1205803 and PHYS-1066293. We acknowledge the hospitality of the Aspen Center for Physics.
Topology of optimally controlled quantum mechanical transition probability landscapes
Rabitz, H.; Ho, T.-S.; Hsieh, M.; Kosut, R.; Demiralp, M.
2006-07-15
An optimally controlled quantum system possesses a search landscape defined by the physical objective as a functional of the control field. This paper particularly explores the topological structure of quantum mechanical transition probability landscapes. The quantum system is assumed to be controllable and the analysis is based on the Euler-Lagrange variational equations derived from a cost function only requiring extremizing the transition probability. It is shown that the latter variational equations are automatically satisfied as a mathematical identity for control fields that either produce transition probabilities of zero or unit value. Similarly, the variational equations are shown to be inconsistent (i.e., they have no solution) for any control field that produces a transition probability different from either of these two extreme values. An upper bound is shown to exist on the norm of the functional derivative of the transition probability with respect to the control field anywhere over the landscape. The trace of the Hessian, evaluated for a control field producing a transition probability of a unit value, is shown to be bounded from below. Furthermore, the Hessian at a transition probability of unit value is shown to have an extensive null space and only a finite number of negative eigenvalues. Collectively, these findings show that (a) the transition probability landscape extrema consists of values corresponding to no control or full control, (b) approaching full control involves climbing a gentle slope with no false traps in the control space and (c) an inherent degree of robustness exists around any full control solution. Although full controllability may not exist in some applications, the analysis provides a basis to understand the evident ease of finding controls that produce excellent yields in simulations and in the laboratory.
Geometric and topological properties of the canonical grain-growth microstructure
NASA Astrophysics Data System (ADS)
Mason, Jeremy K.; Lazar, Emanuel A.; MacPherson, Robert D.; Srolovitz, David J.
2015-12-01
Many physical systems can be modeled as large sets of domains "glued" together along boundaries—biological cells meet along cell membranes, soap bubbles meet along thin films, countries meet along geopolitical boundaries, and metallic crystals meet along grain interfaces. Each class of microstructures results from a complex interplay of initial conditions and particular evolutionary dynamics. The statistical steady-state microstructure resulting from isotropic grain growth of a polycrystalline material is canonical in that it is the simplest example of a cellular microstructure resulting from a gradient flow of an energy that is directly proportional to the total length or area of all cell boundaries. As many properties of polycrystalline materials depend on their underlying microstructure, a more complete understanding of the grain growth steady state can provide insight into the physics of a broad range of everyday materials. In this paper we report geometric and topological features of these canonical two- and three-dimensional steady-state microstructures obtained through extensive simulations of isotropic grain growth.
Geometric and topological properties of the canonical grain-growth microstructure.
Mason, Jeremy K; Lazar, Emanuel A; MacPherson, Robert D; Srolovitz, David J
2015-12-01
Many physical systems can be modeled as large sets of domains "glued" together along boundaries-biological cells meet along cell membranes, soap bubbles meet along thin films, countries meet along geopolitical boundaries, and metallic crystals meet along grain interfaces. Each class of microstructures results from a complex interplay of initial conditions and particular evolutionary dynamics. The statistical steady-state microstructure resulting from isotropic grain growth of a polycrystalline material is canonical in that it is the simplest example of a cellular microstructure resulting from a gradient flow of an energy that is directly proportional to the total length or area of all cell boundaries. As many properties of polycrystalline materials depend on their underlying microstructure, a more complete understanding of the grain growth steady state can provide insight into the physics of a broad range of everyday materials. In this paper we report geometric and topological features of these canonical two- and three-dimensional steady-state microstructures obtained through extensive simulations of isotropic grain growth. PMID:26764854
Topological phase transitions in the gauged BPS baby Skyrme model
NASA Astrophysics Data System (ADS)
Adam, C.; Naya, C.; Romanczukiewicz, T.; Sanchez-Guillen, J.; Wereszczynski, A.
2015-05-01
We demonstrate that the gauged BPS baby Skyrme model with a double vacuum potential allows for phase transitions from a non-solitonic to a solitonic phase, where the latter corresponds to a ferromagnetic liquid. Such a transition can be generated by increasing the external pressure P or by turning on an external magnetic field H. As a consequence, the topological phase where gauged BPS baby skyrmions exist, is a higher density phase. For smaller densities, obtained for smaller values of P and H, a phase without solitons is reached. We find the critical line in the P, H parameter space. Furthermore, in the soliton phase, we find the equation of state for the baby skyrmion matter V = V( P,H) at zero temperature, where V is the "volume", i.e., area of the solitons.
Quantum Anomalous Hall Effects and Topological Phase Transitions in Silicene
NASA Astrophysics Data System (ADS)
Ezawa, Motohiko
2013-03-01
Silicene is a monolayer of silicon atoms forming a two-dimensional honeycomb lattice, which is experimentally manufactured this year. The low energy theory is described by Dirac electrons, but they are massive due to a relatively large spin-orbit interaction. I will explain the following properties of silicene: 1) The band structure is controllable by applying an electric field. Silicene undergoes a phase transition from a topological insulator to a band insulator by applying external electric field. 2) The topological phase transition can be detected experimentally by way of diamagnetism. 3) There is a novel circular dichroism and spinvalley selection rules by way of photon absorption. 4) Silicene shows a quantum anomalous Hall effects when ferromagnet is attached onto silicone. 5) Silicene shows a photo-induced quantum Hall effects when we apply strong laser onto silicene. 6) Single Dirac cone state emerges when we apply photo-irradiation and electric field, where the gap is open at the K point and closed at the K' point.
NASA Astrophysics Data System (ADS)
Kaden, R.; Kolbe, T. H.
2012-07-01
Virtual 3D city models are integrated complex compositions of spatial data of different themes, origin, quality, scale, and dimensions. Within this paper, we address the problem of spatial compatibility of geodata aiming to provide support for ad-hoc integration of virtual 3D city models including geodata of different sources and themes like buildings, terrain, and city furniture. In contrast to related work which is dealing with the integration of redundant geodata structured according to different data models and ontologies, we focus on the integration of complex 3D models of the same representation (here: CityGML) but regarding to the geometric-topological consistent matching of non-homologous objects, e.g. a building is connected to a road, and their geometric homogenisation. Therefore, we present an approach including a data model for a Geodata Join and the general concept of an integration procedure using the join information. The Geodata Join aims to bridge the lack of information between fragmented geodata by describing the relationship between adjacent objects from different datasets. The join information includes the geometrical representation of those parts of an object, which have a specific/known topological or geometrical relationship to another object. This part is referred to as a Connector and is either described by points, lines, or surfaces of the existing object geometry or by additional join geometry. In addition, the join information includes the specification of the connected object in the other dataset and the description of the topological and geometrical relationship between both objects, which is used to aid the matching process. Furthermore, the Geodata Join contains object-related information like accuracy values and restrictions of movement and deformation which are used to optimize the integration process. Based on these parameters, a functional model including a matching algorithm, transformation methods, and conditioned adjustment
Dan Maljovec; Bei Wang; Valerio Pascucci; Peer-Timo Bremer; Diego Mandelli; Michael Pernice; Robert Nourgaliev
2013-10-01
and 2) topology-based methodologies to interactively visualize multidimensional data and extract risk-informed insights. Regarding item 1) we employ learning algorithms that aim to infer/predict simulation outcome and decide the coordinate in the input space of the next sample that maximize the amount of information that can be gained from it. Such methodologies can be used to both explore and exploit the input space. The later one is especially used for safety analysis scopes to focus samples along the limit surface, i.e. the boundaries in the input space between system failure and system success. Regarding item 2) we present a software tool that is designed to analyze multi-dimensional data. We model a large-scale nuclear simulation dataset as a high-dimensional scalar function defined over a discrete sample of the domain. First, we provide structural analysis of such a function at multiple scales and provide insight into the relationship between the input parameters and the output. Second, we enable exploratory analysis for users, where we help the users to differentiate features from noise through multi-scale analysis on an interactive platform, based on domain knowledge and data characterization. Our analysis is performed by exploiting the topological and geometric properties of the domain, building statistical models based on its topological segmentations and providing interactive visual interfaces to facilitate such explorations.
The formation of topological defects in phase transitions
NASA Technical Reports Server (NTRS)
Hodges, Hardy M.
1989-01-01
It was argued, and fought through numerical work that the results of non-dynamical Monte Carlo computer simulations cannot be applied to describe the formation of topological defects when the correlation length at the Ginzburg temperature is significantly smaller than the horizon size. To test the current hypothesis that infinite strings at formation are essentially described by Brownian walks of size the correlation length at the Ginzburg temperature, fields at the Ginzburg temperature were equilibrated. Infinite structure do not exist in equilibrium for reasonable definitions of the Ginzburg temperature, and horizons must be included in a proper treatment. A phase transition, from small-scale to large-scale string or domain wall structure, is found to occur very close to the Ginzburg temperature, in agreement with recent work. The formation process of domain walls and global strings were investigated through the breaking of initially ordered states. To mimic conditions in the early Universe, cooling times are chosen so that horizons exist in the sample volume when topological structure formation occurs. The classical fields are evolved in real-time by the numerical solution of Langevin equations of motion on a three dimensional spatial lattice. The results indicate that it is possible for most of the string energy to be in small loops, rather than in long strings, at formation.
Two-dimensional topological insulator state and topological phase transition in bilayer graphene.
Qiao, Zhenhua; Tse, Wang-Kong; Jiang, Hua; Yao, Yugui; Niu, Qian
2011-12-16
We show that gated bilayer graphene hosts a strong topological insulator (TI) phase in the presence of Rashba spin-orbit (SO) coupling. We find that gated bilayer graphene under preserved time-reversal symmetry is a quantum valley Hall insulator for small Rashba SO coupling λ(R), and transitions to a strong TI when λ(R)>√[U(2)+t(⊥)(2)], where U and t(⊥) are, respectively, the interlayer potential and tunneling energy. Different from a conventional quantum spin Hall state, the edge modes of our strong TI phase exhibit both spin and valley filtering, and thus share the properties of both quantum spin Hall and quantum valley Hall insulators. The strong TI phase remains robust in the presence of weak graphene intrinsic SO coupling.
NASA Astrophysics Data System (ADS)
Nagarajan, Mahesh B.; Coan, Paola; Huber, Markus B.; Diemoz, Paul C.; Wismüller, Axel
2014-03-01
Current assessment of cartilage is primarily based on identification of indirect markers such as joint space narrowing and increased subchondral bone density on x-ray images. In this context, phase contrast CT imaging (PCI-CT) has recently emerged as a novel imaging technique that allows a direct examination of chondrocyte patterns and their correlation to osteoarthritis through visualization of cartilage soft tissue. This study investigates the use of topological and geometrical approaches for characterizing chondrocyte patterns in the radial zone of the knee cartilage matrix in the presence and absence of osteoarthritic damage. For this purpose, topological features derived from Minkowski Functionals and geometric features derived from the Scaling Index Method (SIM) were extracted from 842 regions of interest (ROI) annotated on PCI-CT images of healthy and osteoarthritic specimens of human patellar cartilage. The extracted features were then used in a machine learning task involving support vector regression to classify ROIs as healthy or osteoarthritic. Classification performance was evaluated using the area under the receiver operating characteristic (ROC) curve (AUC). The best classification performance was observed with high-dimensional geometrical feature vectors derived from SIM (0.95 ± 0.06) which outperformed all Minkowski Functionals (p < 0.001). These results suggest that such quantitative analysis of chondrocyte patterns in human patellar cartilage matrix involving SIM-derived geometrical features can distinguish between healthy and osteoarthritic tissue with high accuracy.
Topological transition in disordered planar matching: combinatorial arcs expansion
NASA Astrophysics Data System (ADS)
Lokhov, Andrey Y.; Valba, Olga V.; Nechaev, Sergei K.; Tamm, Mikhail V.
2014-12-01
In this paper, we investigate analytically the properties of the disordered Bernoulli model of planar matching. This model is characterized by a topological phase transition, yielding complete planar matching solutions only above a critical density threshold. We develop a combinatorial procedure of arcs expansion that explicitly takes into account the contribution of short arcs and allows us to obtain an accurate analytical estimation of the critical value by reducing the global constrained problem to a set of local ones. As an application to a toy representation of the RNA secondary structures, we suggest generalized models that incorporate a one-to-one correspondence between the contact matrix and the RNA-type sequence, thus giving sense to the notion of effective non-integer alphabets.
Anomalous thermodynamic power laws near topological transitions in nodal superconductors
NASA Astrophysics Data System (ADS)
Mazidian, B.; Quintanilla, J.; Hillier, A. D.; Annett, J. F.
2013-12-01
Unconventional superconductors are most frequently identified by the observation of power-law behavior on low-temperature thermodynamic or transport properties, such as specific heat. Here, we show that, in addition to the usual point and line nodes, a much wider class of different nodal types can occur. These new types of nodes typically occur when there are transitions between different types of gap node topology, for example, when point or line nodes first appear as a function of some physical parameter. We identify anomalous, noninteger thermodynamic power laws associated with these new nodal types, and give physical examples of superconductors in which they might be observed experimentally, including the noncentrosymmetric superconductor Li2Pd3-xPtxB.
Topological phase transitions in the golden string-net model.
Schulz, Marc Daniel; Dusuel, Sébastien; Schmidt, Kai Phillip; Vidal, Julien
2013-04-01
We examine the zero-temperature phase diagram of the two-dimensional Levin-Wen string-net model with Fibonacci anyons in the presence of competing interactions. Combining high-order series expansions around three exactly solvable points and exact diagonalizations, we find that the non-Abelian doubled Fibonacci topological phase is separated from two nontopological phases by different second-order quantum critical points, the positions of which are computed accurately. These trivial phases are separated by a first-order transition occurring at a fourth exactly solvable point where the ground-state manifold is infinitely many degenerate. The evaluation of critical exponents suggests unusual universality classes. PMID:25167030
Quantum phase transitions and topological proximity effects in graphene nanoribbon heterostructures.
Zhang, Gufeng; Li, Xiaoguang; Wu, Guangfen; Wang, Jie; Culcer, Dimitrie; Kaxiras, Efthimios; Zhang, Zhenyu
2014-03-21
Topological insulators are bulk insulators that possess robust chiral conducting states along their interfaces with normal insulators. A tremendous research effort has recently been devoted to topological insulator-based heterostructures, in which conventional proximity effects give rise to a series of exotic physical phenomena. Here we establish the potential existence of topological proximity effects at the interface between a topological insulator and a normal insulator, using graphene-based heterostructures as prototypical systems. Unlike conventional proximity effects in topological insulator based heterostructures, which refer to various phase transitions associated with the symmetry breaking of specific local order parameters, topological proximity effects describe the rich variety of quantum phase transitions associated with the global properties of the system measured by the location of the topological edge states. Specifically, we show that the location of the topological edge states exhibits a versatile tunability as a function of the interface orientation, the strength of the interface tunnel coupling between a topological graphene nanoribbon and a normal graphene nanoribbon, the spin-orbit coupling strength in the normal graphene nanoribbon, and the width of the system. For zigzag and bearded graphene nanoribbons, the topological edge states can be tuned to be either at the interface or outer edge of the normal ribbon. For armchair graphene nanoribbons, the potential location of the topological edge state can be further shifted to the edge of or within the normal ribbon, to the interface, or diving into the topological graphene nanoribbon. We further show that the topological phase diagram established for the prototypical graphene heterostructures can also explain the intriguing quantum phase transition reported recently in other topological-insulator heterostructures. We also discuss potential experimental realizations of the predicted topological
Signature of topological transition in InAs nanowire Josephson junctions
NASA Astrophysics Data System (ADS)
Strambini, Elia; Paajaste, J.; Amado, M.; Roddaro, S.; San-Jose, P.; Aguado, R.; Bergeret, S.; Ercolani, D.; Sorba, L.; Giazotto, F.
The coupling of a conventional s-wave superconductors to semiconductors with strong spin-orbit (SO) coupling, like e. g. InAs or InSb nanowires (NWs), gives rise to unconventional p-wave superconductivity that may become a topological superconductor (TS), which is a natural host for exotic edge modes with Majorana character. Recently the enhancement of the critical supercurrent Ic in a strong SO semiconducting Josephson junction (JJ) have been proposed as a new evidence of the sought-after Majorana bound states. Here we report on the first observation of the colossal Ic enhancement induced by an external magnetic field on a mesoscopic JJ formed by InAs NWs and Ti/Al leads. This anomalous enhancement appears precisely above a threshold magnetic field Bth orthogonal to the substrate and in junctions of different lengths, suggesting that the origin of the enhancement is intrinsic, i.e. it is not related to geometrical resonances in the junction. None of the standard phenomenon known in JJ, including e. g. Fraunhofer patterns or π-junction behavior, can explain this colossal enhancement while a topological transition at Bth is qualitatively compatible with the observed phenomenology.
Real-time observation of nanoscale topological transitions in epitaxial PbTe/CdTe heterostructures
Groiss, H. E-mail: istvan.daruka@jku.at; Daruka, I. E-mail: istvan.daruka@jku.at; Springholz, G.; Schäffler, F.; Koike, K.; Yano, M.; Hesser, G.; Zakharov, N.; Werner, P.
2014-01-01
The almost completely immiscible PbTe/CdTe heterostructure has recently become a prototype system for self-organized quantum dot formation based on solid-state phase separation. Here, we study by real-time transmission electron microscopy the topological transformations of two-dimensional PbTe-epilayers into, first, a quasi-one-dimensional percolation network and subsequently into zero-dimensional quantum dots. Finally, the dot size distribution coarsens by Ostwald ripening. The whole transformation sequence occurs during all stages in the fully coherent solid state by bulk diffusion. A model based on the numerical solution of the Cahn-Hilliard equation reproduces all relevant morphological and dynamic aspects of the experiments, demonstrating that this standard continuum approach applies to coherent solids down to nanometer dimensions. As the Cahn-Hilliard equation does not depend on atomistic details, the observed morphological transformations are general features of the model. To confirm the topological nature of the observed shape transitions, we developed a parameter-free geometric model. This, together with the Cahn-Hilliard approach, is in qualitative agreement with the experiments.
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.
NASA Astrophysics Data System (ADS)
Faulkner, Michael F.; Bramwell, Steven T.; Holdsworth, Peter C. W.
2015-04-01
The Berezinskii-Kosterlitz-Thouless (BKT) phase transition drives the unbinding of topological defects in many two-dimensional systems. In the two-dimensional Coulomb gas, it corresponds to an insulator-conductor transition driven by charge deconfinement. We investigate the global topological properties of this transition, both analytically and by numerical simulation, using a lattice-field description of the two-dimensional Coulomb gas on a torus. The BKT transition is shown to be an ergodicity breaking between the topological sectors of the electric field, which implies a definition of topological order in terms of broken ergodicity. The breakdown of local topological order at the BKT transition leads to the excitation of global topological defects in the electric field, corresponding to different topological sectors. The quantized nature of these classical excitations, and their strict suppression by ergodicity breaking in the low-temperature phase, afford striking global signatures of topological-sector fluctuations at the BKT transition. We discuss how these signatures could be detected in experiments on, for example, magnetic films and cold-atom systems.
NASA Astrophysics Data System (ADS)
Parrikar, Onkar; Cho, Gil Young; Leigh, Robert; Hughes, Taylor
2014-03-01
Motivated by recent progress in understanding the interplay between the lattice and electronic topological phases, we consider quantum-melting transitions of liquid crystalline order that coexists with electronic topological phases. In certain classes of Chern band insulators, it has been previously demonstrated that there are topological Chern-Simons terms for local lattice deformations such as a Hall viscosity term. The Chern-Simons terms can induce non-trivial statistics for the topological lattice defects and furthermore dress the defects with certain symmetry quantum numbers. On the other hand, the melting transitions of such liquid-crystalline orders are driven by the condensation of lattice defects. Based on these observations, we show how the topological terms can change the nature of the proximate phases of the quantum liquid crystalline phases. We derive and study the effective field theories for the quantum phase transitions, and demonstrate some concrete examples. The authors are supported by the ICMT postdoctoral fellowship at UIUC (GYC) and by the US Department of Energy under contracts DE-FG02-07ER46453 (TLH) and DE-SC0009932 (RGL).
Unconventional transformation of spin Dirac phase across a topological quantum phase transition
Xu, Su -Yang; Neupane, Madhab; Belopolski, Ilya; Liu, Chang; Alidoust, Nasser; Bian, Guang; Jia, Shuang; Landolt, Gabriel; Slomski, Batosz; Dil, J. Hugo; Shibayev, Pavel P.; Basak, Susmita; Chang, Tay -Rong; Jeng, Horng -Tay; Cava, Robert J.; Lin, Hsin; Bansil, Arun; Hasan, M. Zahid
2015-04-17
The topology of a topological material can be encoded in its surface states. These surface states can only be removed by a bulk topological quantum phase transition into a trivial phase. Here we use photoemission spectroscopy to image the formation of protected surface states in a topological insulator as we chemically tune the system through a topological transition. Surprisingly, we discover an exotic spin-momentum locked, gapped surface state in the trivial phase that shares many important properties with the actual topological surface state in anticipation of the change of topology. Using a spin-resolved measurement, we show that apart from a surface bandgap these states develop spin textures similar to the topological surface states well before the transition. Our results provide a general paradigm for understanding how surface states in topological phases arise from a quantum phase transition and are suggestive for the future realization of Weyl arcs, condensed matter supersymmetry and other fascinating phenomena in the vicinity of a quantum criticality.
Unconventional transformation of spin Dirac phase across a topological quantum phase transition
Xu, Su -Yang; Neupane, Madhab; Belopolski, Ilya; Liu, Chang; Alidoust, Nasser; Bian, Guang; Jia, Shuang; Landolt, Gabriel; Slomski, Batosz; Dil, J. Hugo; et al
2015-04-17
The topology of a topological material can be encoded in its surface states. These surface states can only be removed by a bulk topological quantum phase transition into a trivial phase. Here we use photoemission spectroscopy to image the formation of protected surface states in a topological insulator as we chemically tune the system through a topological transition. Surprisingly, we discover an exotic spin-momentum locked, gapped surface state in the trivial phase that shares many important properties with the actual topological surface state in anticipation of the change of topology. Using a spin-resolved measurement, we show that apart from amore » surface bandgap these states develop spin textures similar to the topological surface states well before the transition. Our results provide a general paradigm for understanding how surface states in topological phases arise from a quantum phase transition and are suggestive for the future realization of Weyl arcs, condensed matter supersymmetry and other fascinating phenomena in the vicinity of a quantum criticality.« less
Unconventional transformation of spin Dirac phase across a topological quantum phase transition
NASA Astrophysics Data System (ADS)
Xu, Su-Yang; Neupane, Madhab; Belopolski, Ilya; Liu, Chang; Alidoust, Nasser; Bian, Guang; Jia, Shuang; Landolt, Gabriel; Slomski, Batosz; Dil, J. Hugo; Shibayev, Pavel P.; Basak, Susmita; Chang, Tay-Rong; Jeng, Horng-Tay; Cava, Robert J.; Lin, Hsin; Bansil, Arun; Hasan, M. Zahid
2015-04-01
The topology of a topological material can be encoded in its surface states. These surface states can only be removed by a bulk topological quantum phase transition into a trivial phase. Here we use photoemission spectroscopy to image the formation of protected surface states in a topological insulator as we chemically tune the system through a topological transition. Surprisingly, we discover an exotic spin-momentum locked, gapped surface state in the trivial phase that shares many important properties with the actual topological surface state in anticipation of the change of topology. Using a spin-resolved measurement, we show that apart from a surface bandgap these states develop spin textures similar to the topological surface states well before the transition. Our results offer a general paradigm for understanding how surface states in topological phases arise from a quantum phase transition and are suggestive for the future realization of Weyl arcs, condensed matter supersymmetry and other fascinating phenomena in the vicinity of a quantum criticality.
Unconventional transformation of spin Dirac phase across a topological quantum phase transition.
Xu, Su-Yang; Neupane, Madhab; Belopolski, Ilya; Liu, Chang; Alidoust, Nasser; Bian, Guang; Jia, Shuang; Landolt, Gabriel; Slomski, Batosz; Dil, J Hugo; Shibayev, Pavel P; Basak, Susmita; Chang, Tay-Rong; Jeng, Horng-Tay; Cava, Robert J; Lin, Hsin; Bansil, Arun; Hasan, M Zahid
2015-04-17
The topology of a topological material can be encoded in its surface states. These surface states can only be removed by a bulk topological quantum phase transition into a trivial phase. Here we use photoemission spectroscopy to image the formation of protected surface states in a topological insulator as we chemically tune the system through a topological transition. Surprisingly, we discover an exotic spin-momentum locked, gapped surface state in the trivial phase that shares many important properties with the actual topological surface state in anticipation of the change of topology. Using a spin-resolved measurement, we show that apart from a surface bandgap these states develop spin textures similar to the topological surface states well before the transition. Our results offer a general paradigm for understanding how surface states in topological phases arise from a quantum phase transition and are suggestive for the future realization of Weyl arcs, condensed matter supersymmetry and other fascinating phenomena in the vicinity of a quantum criticality.
Electronic, magnetic and topological properties of transition metal oxides
NASA Astrophysics Data System (ADS)
Quan, Yundi
III in AgO. Another interesting aspect of transition metal oxides is their topological properties that are attracting much attention in recent years. The semi-Dirac point, first discovered by Pardo et al and later modeled by Banerjee et al, has linear dispersion along the diagonal and quadratic dispersion perpendicular to the diagonal. In this thesis, we revisit the tight-binding Hamiltonian proposed by Banerjee and extend it to include the effects of external magnetic field on the energy spectrum and topological properties. We also discuss the forms of effective model Hamiltonians that can generate non-zero Berry phase. First principles calculations have been successful in guiding the experimental search for high Tc superconductors, the most recent example being high Tc (203K) superconductor H 3S under pressure (200GPa). The superconductivity of H3S was first predicted by Duan et al using DFT combined with structure optimization algorithms and validated soon after. Though elemental hydrogen was predicted to metallize under pressure in 1930, it was not realized until recently that hydrogen based compounds rather than pure hydrogen atoms are better candidates for high Tc superconductors. In this thesis, we carried out first principle calculations to study the unusual van Hove singularities located near the Fermi level that lead to a sharp peak, and analyzed the hybridization between sulfur and hydrogen states by constructing a tight-binding model.
Topological quantum phase transitions driven by external electric fields in Sb2Te3 thin films
Kim, Minsung; Kim, Choong H.; Kim, Heung-Sik; Ihm, Jisoon
2012-01-01
Using first-principles calculations, we show that topological quantum phase transitions are driven by external electric fields in thin films of Sb2Te3. The film, as the applied electric field normal to its surface increases, is transformed from a normal insulator to a topological insulator or vice versa depending on the film thickness. We identify the band topology by directly calculating the invariant from electronic wave functions. The dispersion of edge states is also found to be consistent with the bulk band topology in view of the bulk-boundary correspondence. We present possible applications of the topological phase transition as an on/off switch of the topologically protected edge states in nano-scale devices. PMID:22203972
Statistical moments of quantum-walk dynamics reveal topological quantum transitions
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
Statistical moments of quantum-walk dynamics reveal topological quantum transitions
NASA Astrophysics Data System (ADS)
Cardano, Filippo; Maffei, Maria; Massa, Francesco; Piccirillo, Bruno; de Lisio, Corrado; de Filippis, Giulio; Cataudella, Vittorio; Santamato, Enrico; Marrucci, Lorenzo
2016-04-01
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.
Topological phase transition induced by spin-orbit coupling in bilayer graphene.
Xu, Lei; Zhou, Yuan; Gong, Chang-De
2013-08-21
We study the topological phase transition in biased bilayer graphene in the presence of intrinsic and Rashba spin-orbit couplings. The system exhibits a complicated topological phase transition depending on the given parameters. The topological phase transition between these phases is always accompanied by the bulk gap closing and reopening, and can be realized by tuning the bias voltage. The stability of these topological phases are also investigated. We find that the weak (strong) topological insulator phase remains stable under a finite exchange field provided that the effect of intrinsic (Rashba) spin-orbit coupling is dominant, and this also holds for the quantum valley Hall phase if the spatial inversion symmetry breaking overcomes the time-reversal symmetry breaking.
CORBITS: Efficient Geometric Probabilities of Multi-Transiting Exoplanetary Systems
NASA Astrophysics Data System (ADS)
Brakensiek, Joshua; Ragozzine, Darin
2016-03-01
CORBITS (Computed Occurrence of Revolving Bodies for the Investigation of Transiting Systems) computes the probability that any particular group of exoplanets can be observed to transit from a collection of conjectured exoplanets orbiting a star. The efficient, semi-analytical code computes the areas bounded by circular curves on the surface of a sphere by applying elementary differential geometry. CORBITS is faster than previous algorithms, based on comparisons with Monte Carlo simulations, and tests show that it is extremely accurate even for highly eccentric planets.
Calculation of a volume effect accompanying an electronic topological transition in pure cerium
NASA Astrophysics Data System (ADS)
Ponomaryova, S. O.; Koval', Yu. M.; Ponomaryov, O. P.
2012-10-01
An analytic expression for estimating the volume effect accompanying an electronic topological transition (ETT) in pure cerium is derived on the basis of the microscopic Falikov-Ramirez-Kimball model.
Topological phases in oxide heterostructures with light and heavy transition metal ions (invited)
Fiete, Gregory A.; Rüegg, Andreas
2015-05-07
Using a combination of density functional theory, tight-binding models, and Hartree-Fock theory, we predict topological phases with and without time-reversal symmetry breaking in oxide heterostructures. We consider both heterostructures containing light transition metal ions and those containing heavy transition metal ions. We find that the (111) growth direction naturally leads to favorable conditions for topological phases in both perovskite structures and pyrochlore structures. For the case of light transition metal elements, Hartree-Fock theory predicts the spin-orbit coupling is effectively enhanced by on-site multiple-orbital interactions and may drive the system through a topological phase transition, while heavy elements with intrinsically large spin-orbit coupling require much weaker or even vanishing electron interactions to bring about a topological phase.
Nucleation in finite topological systems during continuous metastable quantum phase transitions.
Fialko, Oleksandr; Delattre, Marie-Coralie; Brand, Joachim; Kolovsky, Andrey R
2012-06-22
Finite topological quantum systems can undergo continuous metastable quantum phase transitions to change their topological nature. Here we show how to nucleate the transition between ring currents and dark soliton states in a toroidally trapped Bose-Einstein condensate. An adiabatic passage to wind and unwind its phase is achieved by explicit global breaking of the rotational symmetry. This could be realized with current experimental technology.
Exploration of Geometric Noise Suppression in Transition Edge Sensors
NASA Technical Reports Server (NTRS)
Chervenak, J. A.; Allen, C. A.; Abrahams, J. A.; Miller, T. M.; Talley, D. J.; Staguhn, J. G.; Benford, D. J.; Mosely, S. H.; Finkbeiner, F. M.; Brekosky, R. G.
2004-01-01
We present noise data on Mo/Au superconducting transition edge sensors featuring the noise suppression geometry using normal metal bars transverse to the bias current. The effectiveness of the bars in far-infrared bolometers and x-ray microcalorimeters is evaluated. We have examined the effect of the resistivity of the superconducting bilayer on excess noise in bolometer devices. We have also studied the effect of bar density on energy resolution in x-ray devices. We address the question of whether the reduction is noise is necessarily coupled to a reduction in the effective transition sharpness. We propose a fabrication technique experiment to examine the dependence of alpha and noise suppression in similar transverse bar densities.
Niu, Chengwang; Buhl, Patrick M; Bihlmayer, Gustav; Wortmann, Daniel; Blügel, Stefan; Mokrousov, Yuriy
2015-09-01
The properties that distinguish topological crystalline insulator (TCI) and topological insulator (TI) rely on crystalline symmetry and time-reversal symmetry, respectively, which encodes different bulk and surface/edge properties. Here, we predict theoretically that electron-doped TlM (M = S and Se) (110) monolayers realize a family of two-dimensional (2D) TCIs characterized by mirror Chern number CM = -2. Remarkably, under uniaxial strain (≈ 1%), a topological phase transition between 2D TCI and 2D TI is revealed with the calculated spin Chern number CS = -1 for the 2D TI. Using spin-resolved edge states analysis, we show different edge-state behaviors, especially at the time reversal invariant points. Finally, a TlBiSe2/NaCl quantum well is proposed to realize an undoped 2D TCI with inverted gap as large as 0.37 eV, indicating the high possibility for room-temperature observation.
Zeeman-Field-Tuned Topological Phase Transitions in a Two-Dimensional Class-DIII Superconductor
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
Fermi points and topological quantum phase transitions in a multi-band superconductor.
Puel, T O; Sacramento, P D; Continentino, M A
2015-10-28
The importance of models with an exact solution for the study of materials with non-trivial topological properties has been extensively demonstrated. The Kitaev model plays a guiding role in the search for Majorana modes in condensed matter systems. Also, the sp-chain with an anti-symmetric mixing among the s and p bands is a paradigmatic example of a topological insulator with well understood properties. Interestingly, these models share the same universality class for their topological quantum phase transitions. In this work we study a two-band model of spinless fermions with attractive inter-band interactions. We obtain its zero temperature phase diagram, which presents a rich variety of phases including a Weyl superconductor and a topological insulator. The transition from the topological to the trivial superconducting phase has critical exponents different from those of Kitaev's model.
Zeeman-Field-Tuned Topological Phase Transitions in a Two-Dimensional Class-DIII Superconductor.
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.
Non-local Optical Topological Transitions and Critical States in Electromagnetic Metamaterials
Ishii, Satoshi; Narimanov, Evgenii
2015-01-01
Just as the topology of the Fermi surface defines the properties of the free electrons in metals and semiconductors, the geometry of the iso-frequency surface in the phase space of the propagating electromagnetic waves, determines the optical properties of the corresponding optical materials. Furthermore, in the direct analog to the Lifshitz transition in condensed matter physics, a change in the topology of iso-frequency surface has a dramatic effect on the emission, propagation and scattering of the electromagnetic waves. Here, we uncover a new class of such optical topological transitions in metamaterials, induced by the non-locality of the electromagnetic response inherent to these composites. PMID:26670600
Non-local Optical Topological Transitions and Critical States in Electromagnetic Metamaterials.
Ishii, Satoshi; Narimanov, Evgenii
2015-01-01
Just as the topology of the Fermi surface defines the properties of the free electrons in metals and semiconductors, the geometry of the iso-frequency surface in the phase space of the propagating electromagnetic waves, determines the optical properties of the corresponding optical materials. Furthermore, in the direct analog to the Lifshitz transition in condensed matter physics, a change in the topology of iso-frequency surface has a dramatic effect on the emission, propagation and scattering of the electromagnetic waves. Here, we uncover a new class of such optical topological transitions in metamaterials, induced by the non-locality of the electromagnetic response inherent to these composites. PMID:26670600
Quantum phase transition from Z2×Z2 to Z2 topological order
NASA Astrophysics Data System (ADS)
Zarei, Mohammad Hossein
2016-04-01
Although the topological order is known as a quantum order in quantum many-body systems, it seems that there is not a one-to-one correspondence between topological phases and quantum phases. As a well-known example, it has been shown that all one-dimensional (1D) quantum phases are topologically trivial [X. Chen et al., Phys. Rev. B 90, 035117 (2014), 10.1103/PhysRevB.90.035117]. By such facts, it seems a challenging task to understand when a quantum phase transition between different topological models necessarily reveals different topological classes of them. In this paper, we make an attempt to consider this problem by studying a phase transition between two different quantum phases which have a universal topological phase. We define a Hamiltonian as interpolation of the toric code model with Z2 topological order and the color code model with Z2×Z2 topological order on a hexagonal lattice. We show such a model is exactly mapped to many copies of 1D quantum Ising model in transverse field by rewriting the Hamiltonian in a new complete basis. Consequently, we show that the universal topological phase of the color code model and the toric code model reflects in the 1D nature of the phase transition. We also consider the expectation value of Wilson loops by a perturbative calculation and show that behavior of the Wilson loop captures the nontopological nature of the quantum phase transition. The result on the point of phase transition also shows that the color code model is strongly robust against the toric code model.
NASA Technical Reports Server (NTRS)
Checlair, Jade; McKay, Christopher P.; Imanaka, Hiroshi
2016-01-01
Extensive studies characterizing Titan present an opportunity to study the atmospheric properties of Titan-like exoplanets. Using an existing model of Titan's atmospheric haze, we computed geometric albedo spectra and effective transit height spectra for six values of the haze production rate (zero haze to twice present) over a wide range of wavelengths (0.2-2 microns). In the geometric albedo spectra, the slope in the UV-visible changes from blue to red when varying the haze production rate values from zero to twice the current Titan value. This spectral feature is the most effective way to characterize the haze production rates. Methane absorption bands in the visible-NIR compete with the absorbing haze, being more prominent for smaller haze production rates. The effective transit heights probe a region of the atmosphere where the haze and gas are optically thin and that is thus not effectively probed by the geometric albedo. The effective transit height decreases smoothly with increasing wavelength, from 376 km to 123 km at 0.2 and 2 microns, respectively. When decreasing the haze production rate, the methane absorption bands become more prominent, and the effective transit height decreases with a steeper slope with increasing wavelength. The slope of the geometric albedo in the UV-visible increases smoothly with increasing haze production rate, while the slope of the effective transit height spectra is not sensitive to the haze production rate other than showing a sharp rise when the haze production rate increases from zero. We conclude that geometric albedo spectra provide the most sensitive indicator of the haze production rate and the background Rayleigh gas. Our results suggest that important and complementary information can be obtained from the geometric albedo and motivates improvements in the technology for direct imaging of nearby exoplanets.
NASA Astrophysics Data System (ADS)
Checlair, Jade; McKay, Christopher P.; Imanaka, Hiroshi
2016-09-01
Extensive studies characterizing Titan present an opportunity to study the atmospheric properties of Titan-like exoplanets. Using an existing model of Titan's atmospheric haze, we computed geometric albedo spectra and effective transit height spectra for six values of the haze production rate (zero haze to twice present) over a wide range of wavelengths (0.2-2 μm). In the geometric albedo spectra, the slope in the UV-visible changes from blue to red when varying the haze production rate values from zero to twice the current Titan value. This spectral feature is the most effective way to characterize the haze production rates. Methane absorption bands in the visible-NIR compete with the absorbing haze, being more prominent for smaller haze production rates. The effective transit heights probe a region of the atmosphere where the haze and gas are optically thin and that is thus not effectively probed by the geometric albedo. The effective transit height decreases smoothly with increasing wavelength, from 376 km to 123 km at 0.2 and 2 μm, respectively. When decreasing the haze production rate, the methane absorption bands become more prominent, and the effective transit height decreases with a steeper slope with increasing wavelength. The slope of the geometric albedo in the UV-visible increases smoothly with increasing haze production rate, while the slope of the effective transit height spectra is not sensitive to the haze production rate other than showing a sharp rise when the haze production rate increases from zero. We conclude that geometric albedo spectra provide the most sensitive indicator of the haze production rate and the background Rayleigh gas. Our results suggest that important and complementary information can be obtained from the geometric albedo and motivates improvements in the technology for direct imaging of nearby exoplanets.
STM studies of topological phase transition in (Bi,In)2Se3
NASA Astrophysics Data System (ADS)
Zhang, Wenhan; Wang, Xueyun; Cheong, Sang-Wook; Wu, Weida; Weida Wu Team; Sang-Wook Cheong Collaboration
Topological insulators (TI) are a class of materials with insulating bulk and metallic surface state, which is the result of band inversion induced by strong spin-orbit coupling (SOC). The transition from topological phase to non-topological phase is of great significance. In theory, topological phase transition is realized by tuning SOC strength. It is characterized by the process of gap closing and reopening. Experimentally it was observed in two systems: TlBi(S1-xSex)2 and (Bi1-xInx)2 Se3 where the transition is realized by varying isovalent elements doping concentration. However, none of the previous studies addressed the impact of disorder, which is inevitable in doped systems. Here, we present a systematic scanning tunneling microscopy/spectroscopy study on (Bi1-xInx)2 Se3 single crystals with different In concentrations across the transition. Our results reveal an electronic inhomogeneity due to the random distribution of In defects which locally suppress the topological surface states. Our study provides a new angle of understanding the topological transition in the presence of strong disorders. This work is supported by NSF DMR-1506618.
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.
Efficient Geometric Probabilities of Multi-Transiting Exoplanetary Systems from CORBITS
NASA Astrophysics Data System (ADS)
Brakensiek, Joshua; Ragozzine, Darin
2016-04-01
NASA’s Kepler Space Telescope has successfully discovered thousands of exoplanet candidates using the transit method, including hundreds of stars with multiple transiting planets. In order to estimate the frequency of these valuable systems, it is essential to account for the unique geometric probabilities of detecting multiple transiting extrasolar planets around the same parent star. In order to improve on previous studies that used numerical methods, we have constructed an efficient, semi-analytical algorithm called the Computed Occurrence of Revolving Bodies for the Investigation of Transiting Systems (CORBITS), which, given a collection of conjectured exoplanets orbiting a star, computes the probability that any particular group of exoplanets can be observed to transit. The algorithm applies theorems of elementary differential geometry to compute the areas bounded by circular curves on the surface of a sphere. The implemented algorithm is more accurate and orders of magnitude faster than previous algorithms, based on comparisons with Monte Carlo simulations. We use CORBITS to show that the present solar system would only show a maximum of three transiting planets, but that this varies over time due to dynamical evolution. We also used CORBITS to geometrically debias the period ratio and mutual Hill sphere distributions of Kepler's multi-transiting planet candidates, which results in shifting these distributions toward slightly larger values. In an Appendix, we present additional semi-analytical methods for determining the frequency of exoplanet mutual events, i.e., the geometric probability that two planets will transit each other (planet–planet occultation, relevant to transiting circumbinary planets) and the probability that this transit occurs simultaneously as they transit their star. The CORBITS algorithms and several worked examples are publicly available.
Efficient Geometric Probabilities of Multi-Transiting Exoplanetary Systems from CORBITS
NASA Astrophysics Data System (ADS)
Brakensiek, Joshua; Ragozzine, Darin
2016-04-01
NASA’s Kepler Space Telescope has successfully discovered thousands of exoplanet candidates using the transit method, including hundreds of stars with multiple transiting planets. In order to estimate the frequency of these valuable systems, it is essential to account for the unique geometric probabilities of detecting multiple transiting extrasolar planets around the same parent star. In order to improve on previous studies that used numerical methods, we have constructed an efficient, semi-analytical algorithm called the Computed Occurrence of Revolving Bodies for the Investigation of Transiting Systems (CORBITS), which, given a collection of conjectured exoplanets orbiting a star, computes the probability that any particular group of exoplanets can be observed to transit. The algorithm applies theorems of elementary differential geometry to compute the areas bounded by circular curves on the surface of a sphere. The implemented algorithm is more accurate and orders of magnitude faster than previous algorithms, based on comparisons with Monte Carlo simulations. We use CORBITS to show that the present solar system would only show a maximum of three transiting planets, but that this varies over time due to dynamical evolution. We also used CORBITS to geometrically debias the period ratio and mutual Hill sphere distributions of Kepler's multi-transiting planet candidates, which results in shifting these distributions toward slightly larger values. In an Appendix, we present additional semi-analytical methods for determining the frequency of exoplanet mutual events, i.e., the geometric probability that two planets will transit each other (planet-planet occultation, relevant to transiting circumbinary planets) and the probability that this transit occurs simultaneously as they transit their star. The CORBITS algorithms and several worked examples are publicly available.
NASA Astrophysics Data System (ADS)
Stehno, M. P.; Orlyanchik, V.; Nugroho, C. D.; Ghaemi, P.; Brahlek, M.; Koirala, N.; Oh, S.; Van Harlingen, D. J.
2016-01-01
Topological insulators (TIs) hold great promise for topological quantum computation in solid-state systems. Recently, several groups reported experimental data suggesting that signatures of Majorana modes have been observed in topological insulator Josephson junctions (TIJJs). A prerequisite for the exploration of Majorana physics is to obtain a good understanding of the properties of low-energy Andreev bound states (ABSs) in a material with a topologically nontrivial band structure. Here, we present experimental data and a theoretical analysis demonstrating that the band-structure inversion close to the surface of a TI has observable consequences for supercurrent transport in TIJJs prepared on surface-doped Bi2Se3 thin films. Electrostatic carrier depletion of the film surface leads to an abrupt drop in the critical current of such devices. The effect can be understood as a relocation of low-energy ABSs from a region deeper in the bulk of the material to the more strongly disordered surface, which is driven by the topology of the effective band structure in the presence of surface dopants.
Kinetic transitions in diffusion-reaction space. II. Geometrical effects
NASA Astrophysics Data System (ADS)
Kozak, John J.
1999-02-01
We extend the stochastic master equation approach described earlier [J. J. Kozak and R. Davidson, J. Chem. Phys. 101, 6101 (1994)] to examine the influence on reaction efficiency of multipolar correlations between a fixed target molecule and a diffusing coreactant, the latter constrained to move on the surface of a host medium (e.g., a colloidal catalyst or molecular organizate) modeled as a Cartesian shell [Euler characteristic, χ=2]. Our most comprehensive results are for processes involving ion pairs, and we find that there exists a transition between two qualitatively different types of behavior in diffusion-reaction space, viz., a regime where the coreactant's motion is totally correlated with respect to the target ion, and a regime where the coreactant's motion is effectively uncorrelated. This behavior emerges both in the situation where correlations between the ion pair are strictly confined to the surface of the host medium or where correlations can be propagated through the host medium. The effects of system size are also examined and comparisons with diffusion-reaction processes taking place on surfaces characterized by Euler characteristic χ=0 are made. In all cases studied, the most dramatic effects on the reaction efficiency are uncovered in the regime where the Onsager (thermalization) length is comparable to the mean displacement of the coreactant, a conclusion consistent with results reported in earlier work.
Interacting weak topological insulators and their transition to Dirac semimetal phases
NASA Astrophysics Data System (ADS)
Sangiovanni, Giorgio; Hanke, Werner; Li, Gang; Trauzettel, Bjoern
Topological insulators in the presence of strong Coulomb interaction constitute novel phases of matter. Transitions between these phases can be driven by single-particle or many-body effects. On the basis of ab-initio calculations, we identify a concrete material, i.e. Ca2PtO4, that turns out to be a hole-doped weak topological insulator. Interestingly, the Pt- d orbitals in this material are relevant for the band inversion that gives rise to the topological phase. Therefore, Coulomb interaction should be of importance in Ca2PtO4. To study the influence of interactions on the weak topological insulating phase, we look at a toy model corresponding to a layer-stacked 3D version of the Bernevig-Hughes-Zhang model with local interactions. For small to intermediate interaction strength, we discover novel interaction-driven topological phase transitions between the weak topological insulator and two Dirac semimetal phases. The latter correspond to gapless topological phases. For strong interactions, the system eventually becomes a Mott insulator. DFG Grant No. Ha 1537/23-1 within the Forschergruppe FOR 1162, SPP Grant Ha 1537/24-2, SFB 1170 ``ToCoTronics'', SPP 1666, the Helmholtz Foundation (VITI), the ``Elitenetzwerk Bayern'' (ENB graduate school on ``Topological insulators'').
Morse, Peter K; Corwin, Eric I
2016-01-28
A jammed packing of frictionless spheres at zero temperature is perfectly specified by the network of contact forces from which mechanical properties can be derived. However, we can alternatively consider a packing as a geometric structure, characterized by a Voronoi tessellation which encodes the local environment around each particle. We find that this local environment characterizes systems both above and below jamming and changes markedly at the transition. A variety of order parameters derived from this tessellation carry signatures of the jamming transition, complete with scaling exponents. Furthermore, we define a real space geometric correlation function which also displays a signature of jamming. Taken together, these results demonstrate the validity and usefulness of a purely geometric approach to jamming. PMID:26611105
Wang, Yusu
2013-03-25
Shape analysis plays an important role in many applications. In particular, in molecular biology, analyzing molecular shapes is essential to the fundamental problem of understanding how molecules interact. This project aims at developing efficient and effective algorithms to characterize and analyze molecular structures using geometric and topological methods. Two main components of this project are (1) developing novel molecular shape descriptors; and (2) identifying and representing meaningful features based on those descriptors. The project also produces accompanying (visualization) software. Results from this project (09/2006-10/2009) include the following publications. We have also set up web-servers for the software developed in this period, so that our new methods are accessible to a broader scientific community. The web sites are given below as well. In this final technical report, we first list publications and software resulted from this project. We then briefly explain the research conducted and main accomplishments during the period of this project.
Topological phase transition in a ladder of the dimerized Kitaev superconductor chains
NASA Astrophysics Data System (ADS)
Zhou, Bo-Zhen; Zhou, Bin
2016-10-01
We investigate the topological properties of a ladder model of the dimerized Kitaev superconductor chains. The topological class of the system is determined by the relative phase θ between the inter- and intra-chain superconducting pairing. One topological class is the class BDI characterized by the ℤ index, and the other is the class D characterized by the ℤ2 index. For the two different topological classes, the topological phase diagrams of the system are presented by calculating two different topological numbers, i.e., the ℤ index winding number W and the ℤ2 index Majorana number ℳ, respectively. In the case of θ =0, the topological class belongs to the class BDI, multiple topological phase transitions accompanying the variation of the number of Majorana zero modes are observed. In the case of θ =π/2 it belongs to the class D. Our results show that for the given value of dimerization, the topologically nontrivial and trivial phases alternate with the variation of chemical potential. Project supported by the National Natural Science Foundation of China (Grant No. 11274102), the Program for New Century Excellent Talents in University of Ministry of Education of China (Grant No. NCET-11-0960), and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20134208110001).
First-order topological phase transition of the Haldane-Hubbard model
NASA Astrophysics Data System (ADS)
Imriška, Jakub; Wang, Lei; Troyer, Matthias
2016-07-01
We study the interplay of topological band structure and conventional magnetic long-range order in spinful Haldane model with on-site repulsive interaction. Using the dynamical cluster approximation with clusters of up to 24 sites we find evidence of a first-order phase transition from a Chern insulator at weak coupling to a topologically trivial antiferromagnetic insulator at strong coupling. These results call into question a previously found intermediate state with coexisting topological character and antiferromagnetic long-range order. Experimentally measurable signatures of the first-order transition include hysteretic behavior of the double occupancy, single-particle excitation gap, and nearest neighbor spin-spin correlations. This first-order transition is contrasted with a continuous phase transition from the conventional band insulator to the antiferromagnetic insulator in the ionic Hubbard model on the honeycomb lattice.
NASA Astrophysics Data System (ADS)
You, Yi-Zhuang; Bi, Zhen; Mao, Dan; Xu, Cenke
2016-03-01
We propose a series of simple two-dimensional (2D) lattice interacting fermion models that we demonstrate at low energy describe bosonic symmetry-protected topological (SPT) states and quantum phase transitions between them. This is because due to interaction, the fermions are gapped both at the boundary of the SPT states and at the bulk quantum phase transition, thus these models at low energy can be described completely by bosonic degrees of freedom. We show that the bulk of these models is described by a Sp (N ) principal chiral model with a topological Θ term, whose boundary is described by a Sp (N ) principal chiral model with a Wess-Zumino-Witten term at level 1. The quantum phase transition between SPT states in the bulk is tuned by a particular interaction term, which corresponds to tuning Θ in the field theory, and the phase transition occurs at Θ =π . The simplest version of these models with N =1 is equivalent to the familiar O(4) nonlinear sigma model (NLSM) with a topological term, whose boundary is a (1 +1 )D conformal field theory with central charge c =1 . After breaking the O(4) symmetry to its subgroups, this model can be viewed as bosonic SPT states with U(1), or Z2 symmetries, etc. All of these fermion models, including the bulk quantum phase transitions, can be simulated with the determinant quantum Monte Carlo method without the sign problem. Recent numerical results strongly suggest that the quantum disordered phase of the O(4) NLSM with precisely Θ =π is a stable (2 +1 )D conformal field theory with gapless bosonic modes.
Signatures of topological phase transitions in Josephson current-phase discontinuities
NASA Astrophysics Data System (ADS)
Marra, Pasquale; Citro, Roberta; Braggio, Alessandro
2016-06-01
Topological superconductors differ from topologically trivial ones due to the presence of topologically protected zero-energy modes. To date, experimental evidence of topological superconductivity in nanostructures has been mainly obtained by measuring the zero-bias conductance peak via tunneling spectroscopy. Here, we propose an alternative and complementary experimental recipe to detect topological phase transitions in these systems. We show in fact that, for a finite-sized system with broken time-reversal symmetry, discontinuities in the Josephson current-phase relation correspond to the presence of zero-energy modes and to a change in the fermion parity of the ground state. Such discontinuities can be experimentally revealed by a characteristic temperature dependence of the current, and can be related to a finite anomalous current at zero phase in systems with broken phase-inversion symmetry.
NASA Astrophysics Data System (ADS)
Anderson, Brandon M.; Wu, Chien-Te; Boyack, Rufus; Levin, K.
2015-10-01
We investigate the effects of topological order on the transition temperature, Tc, and response functions in spin-orbit-coupled fermionic superfluids with a transverse Zeeman field in three dimensions. Our calculations include fluctuation effects beyond mean-field theory and are compatible with f -sum rules. In the topological phase we find that Tc can be as large as 10 % of the Fermi temperature, which should be experimentally accessible in cold-gas experiments. At higher temperatures, above Tc, the spin and density response functions provide signatures of topological phases via the recombination or amplification of frequency-dependent peaks.
NASA Astrophysics Data System (ADS)
Griffin, Sinead
2012-02-01
Jumping from the expanse of galactic scales to land in the laboratory might seem a gargantuan task. Common to both, however, is the the concept of symmetry breaking and in particular the formation of topological defects. Here I discuss the formation of topological defects in multiferroic YMnO3 whose ferroelectric behavior enables the direct imaging of these defects. I also show how this material can be used to study the Kibble-Zurek model of topological defect formation in the early universe and give quantitative insights on the number of domains formed during the spontaneous symmetry breaking phase transition.
Quantum Phase Transition between a Topological and a Trivial Semimetal from Holography.
Landsteiner, Karl; Liu, Yan; Sun, Ya-Wen
2016-02-26
We present a holographic model of a topological Weyl semimetal. A key ingredient is a time-reversal breaking parameter and a mass deformation. Upon varying the ratio of mass to time-reversal breaking parameter the model undergoes a quantum phase transition from a topologically nontrivial semimetal to a trivial one. The topological nontrivial semimetal is characterized by the presence of an anomalous Hall effect. The results can be interpreted in terms of the holographic renormalization group (RG) flow leading to restoration of time reversal at the end point of the RG flow in the trivial phase. PMID:26967408
NASA Astrophysics Data System (ADS)
Fessel, Adrian; Oettmeier, Christina; Bernitt, Erik; Gauthier, Nils C.; Döbereiner, Hans-Günther
2012-08-01
We study the formation of transportation networks of the true slime mold Physarum polycephalum after fragmentation by shear. Small fragments, called microplasmodia, fuse to form macroplasmodia in a percolation transition. At this topological phase transition, one single giant component forms, connecting most of the previously isolated microplasmodia. Employing the configuration model of graph theory for small link degree, we have found analytically an exact solution for the phase transition. It is generally applicable to percolation as seen, e.g., in vascular networks.
Hyperbolic Plasmons and Topological Transitions Over Uniaxial Metasurfaces
NASA Astrophysics Data System (ADS)
Gomez-Diaz, J. Sebastian; Tymchenko, Mykhailo; AlÃ¹, Andrea
2015-06-01
We explore the unusual electromagnetic response of ultrathin anisotropic σ -near-zero uniaxial metasurfaces, demonstrating extreme topological transitions—from closed elliptical to open hyperbolic—for surface plasmon propagation, associated with a dramatic tailoring of the local density of states. The proposed metasurfaces may be implemented using nanostructured graphene monolayers and open unprecedented venues for extreme light confinement and unusual propagation and guidance, combined with large tunability via electric bias.
Geometrically thin, hot accretion disks - Topology of the thermal equilibrium curves
NASA Technical Reports Server (NTRS)
Kusunose, Masaaki; Mineshige, Shin
1992-01-01
All the possible thermal equilibrium states of geometrically thin alpha-disks around stellar-mass black holes are presented. A (vertically) one-zone disk model is employed and it is assumed that a main energy source is viscous heating of protons and that cooling is due to bremsstrahlung and Compton scattering. There exist various branches of the thermal equilibrium solution, depending on whether disks are effectively optically thick or thin, radiation pressure-dominated or gas pressure-dominated, composed of one-temperature plasmas or of two-temperature plasmas, and with high concentration of e(+)e(-) pairs or without pairs. The thermal equilibrium curves at high temperatures (greater than or approximately equal to 10 exp 8 K) are substantially modified by the presence of e(+)e(-) pairs. The thermal stability of these branches are examined.
On suppression of topological transitions in quantum gravity
Barvinsky, A.O.
2012-09-01
We discuss the effect of dynamical suppression for a special class of topological configurations in cosmology, which occur in Euclidean quantum gravity (EQG) when the latter is viewed as the derivative of the physical theory in the Lorentzian signature spacetime. At the topological level EQG inherits from the Lorentzian theory the arrow of time and incorporates special junction conditions on quantum fields whose quantum fluctuations make the contribution of such topologies vanishing. This effect is more general than the recently suggested conformal mechanism of suppression of vacuum no-boundary instantons in the microcanonical statistical sum of quantum cosmology driven by a conformal field theory (CFT). In contrast to conformal properties of the CFT driven cosmology, this effect is based only on short-distance behavior of local boson fields and Pauli principle for fermions. Application of this effect in the CFT cosmology treated as initial conditions for inflationary Universe suggests the thermal nature of the primordial power spectrum of the CMB anisotropy. This can be responsible for a thermal contribution to the red tilt of this spectrum, additional to its conventional vacuum component.
Quantum topological transition in hyperbolic metamaterials based on high Tc superconductors.
Smolyaninov, Igor I
2014-07-30
Hyperbolic metamaterials are known to exhibit a transition in the topology of the photon iso-frequency surface from a closed ellipsoid to an open hyperboloid, resulting in a considerable increase of the photonic density of states. This topological transition may also be described as a change of metric signature of the effective optical space. Here we demonstrate that high Tc superconductors exhibit hyperbolic metamaterial behavior in the far infrared and THz frequency ranges. In the THz range the hyperbolic behavior occurs only in the normal state, while no propagating photon modes exist in the superconducting state. Thus, a quantum topological transition may be observed for THz photons at zero temperature as a function of the external magnetic field, in which the effective Minkowski spacetime arises in the mixed state of the superconductor at some critical value of the external magnetic field. Nucleation of effective Minkowski spacetime occurs via the formation of quantized Abrikosov vortices. PMID:25001512
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
Strong correlation effects on topological quantum phase transitions in three dimensions
NASA Astrophysics Data System (ADS)
Amaricci, A.; Budich, J. C.; Capone, M.; Trauzettel, B.; Sangiovanni, G.
2016-06-01
We investigate the role of short-ranged electron-electron interactions in a paradigmatic model of three-dimensional topological insulators, using dynamical mean-field theory and focusing on nonmagnetically ordered solutions. The noninteracting band structure is controlled by a mass term M , whose value discriminates between three different insulating phases, a trivial band insulator and two distinct topologically nontrivial phases. We characterize the evolution of the transitions between the different phases as a function of the local Coulomb repulsion U and find a remarkable dependence of the U -M phase diagram on the value of the local Hund's exchange coupling J . However, regardless of the value of J , following the evolution of the topological transition line between a trivial band insulator and a topological insulator, we find a critical value of U separating a continuous transition from a first-order one. When the Hund's coupling is significant, a Mott insulator is stabilized at large U . In proximity of the Mott transition we observe the emergence of an anomalous "Mott-like" strong topological insulator state.
Geometric entanglement and quantum phase transitions in two-dimensional quantum lattice models
NASA Astrophysics Data System (ADS)
Shi, Qian-Qian; Wang, Hong-Lei; Li, Sheng-Hao; Cho, Sam Young; Batchelor, Murray T.; Zhou, Huan-Qiang
2016-06-01
Geometric entanglement (GE), as a measure of multipartite entanglement, has been investigated as a universal tool to detect phase transitions in quantum many-body lattice models. In this paper we outline a systematic method to compute GE for two-dimensional (2D) quantum many-body lattice models based on the translational invariant structure of infinite projected entangled pair state (iPEPS) representations. By employing this method, the q -state quantum Potts model on the square lattice with q ∈{2 ,3 ,4 ,5 } is investigated as a prototypical example. Further, we have explored three 2D Heisenberg models: the antiferromagnetic spin-1/2 X X X and anisotropic X Y X models in an external magnetic field, and the antiferromagnetic spin-1 X X Z model. We find that continuous GE does not guarantee a continuous phase transition across a phase transition point. We observe and thus classify three different types of continuous GE across a phase transition point: (i) GE is continuous with maximum value at the transition point and the phase transition is continuous, (ii) GE is continuous with maximum value at the transition point but the phase transition is discontinuous, and (iii) GE is continuous with nonmaximum value at the transition point and the phase transition is continuous. For the models under consideration, we find that the second and the third types are related to a point of dual symmetry and a fully polarized phase, respectively.
Quantum phase transitions out of a Z2×Z2 topological phase
NASA Astrophysics Data System (ADS)
Jahromi, Saeed S.; Masoudi, S. Farhad; Kargarian, Mehdi; Schmidt, Kai Phillip
2013-12-01
We investigate the low-energy spectral properties and robustness of the topological phase of color code, which is a quantum spin model for the aim of fault-tolerant quantum computation, in the presence of a uniform magnetic field or Ising interactions, using high-order series expansion and exact diagonalization. In a uniform magnetic field, we find first-order phase transitions in all field directions. In contrast, our results for the Ising interactions unveil that for strong enough Ising couplings, the Z2×Z2 topological phase of color code breaks down to symmetry broken phases by first- or second-order phase transitions.
Disorder-driven topological phase transition in B i2S e3 films
NASA Astrophysics Data System (ADS)
Brahlek, Matthew; Koirala, Nikesh; Salehi, Maryam; Moon, Jisoo; Zhang, Wenhan; Li, Haoxiang; Zhou, Xiaoqing; Han, Myung-Geun; Wu, Liang; Emge, Thomas; Lee, Hang-Dong; Xu, Can; Rhee, Seuk Joo; Gustafsson, Torgny; Armitage, N. Peter; Zhu, Yimei; Dessau, Daniel S.; Wu, Weida; Oh, Seongshik
2016-10-01
Topological insulators (TI) are a phase of matter that host unusual metallic surface states. Unlike the states that exist on the surface of conventional materials, these so-called topological surfaces states (TSS) are protected against disorder-related localization effects by time reversal symmetry through strong spin-orbit coupling. By combining transport measurements, angle-resolved photoemission spectroscopy, and scanning tunneling microscopy, we show that there exists a critical level of disorder beyond which the TI B i2S e3 loses its ability to protect the metallic TSS and transitions to a fully insulating state. The absence of the metallic surface channels dictates that there is a change in the material's topological character, implying that disorder can lead to a topological phase transition even without breaking the time reversal symmetry. This observation challenges the conventional notion of topologically protected surface states and should prompt new studies as to the fundamental nature of topological phase of matter in the presence of disorder.
Topological states and phase transitions in Sb2Te3-GeTe multilayers.
Nguyen, Thuy-Anh; Backes, Dirk; Singh, Angadjit; Mansell, Rhodri; Barnes, Crispin; Ritchie, David A; Mussler, Gregor; Lanius, Martin; Grützmacher, Detlev; Narayan, Vijay
2016-01-01
Topological insulators (TIs) are bulk insulators with exotic 'topologically protected' surface conducting modes. It has recently been pointed out that when stacked together, interactions between surface modes can induce diverse phases including the TI, Dirac semimetal, and Weyl semimetal. However, currently a full experimental understanding of the conditions under which topological modes interact is lacking. Here, working with multilayers of the TI Sb2Te3 and the band insulator GeTe, we provide experimental evidence of multiple topological modes in a single Sb2Te3-GeTe-Sb2Te3 structure. Furthermore, we show that reducing the thickness of the GeTe layer induces a phase transition from a Dirac-like phase to a gapped phase. By comparing different multilayer structures we demonstrate that this transition occurs due to the hybridisation of states associated with different TI films. Our results demonstrate that the Sb2Te3-GeTe system offers strong potential towards manipulating topological states as well as towards controlledly inducing various topological phases. PMID:27291288
Topological states and phase transitions in Sb2Te3-GeTe multilayers
NASA Astrophysics Data System (ADS)
Nguyen, Thuy-Anh; Backes, Dirk; Singh, Angadjit; Mansell, Rhodri; Barnes, Crispin; Ritchie, David A.; Mussler, Gregor; Lanius, Martin; Grützmacher, Detlev; Narayan, Vijay
2016-06-01
Topological insulators (TIs) are bulk insulators with exotic ‘topologically protected’ surface conducting modes. It has recently been pointed out that when stacked together, interactions between surface modes can induce diverse phases including the TI, Dirac semimetal, and Weyl semimetal. However, currently a full experimental understanding of the conditions under which topological modes interact is lacking. Here, working with multilayers of the TI Sb2Te3 and the band insulator GeTe, we provide experimental evidence of multiple topological modes in a single Sb2Te3-GeTe-Sb2Te3 structure. Furthermore, we show that reducing the thickness of the GeTe layer induces a phase transition from a Dirac-like phase to a gapped phase. By comparing different multilayer structures we demonstrate that this transition occurs due to the hybridisation of states associated with different TI films. Our results demonstrate that the Sb2Te3-GeTe system offers strong potential towards manipulating topological states as well as towards controlledly inducing various topological phases.
Topological states and phase transitions in Sb2Te3-GeTe multilayers
Nguyen, Thuy-Anh; Backes, Dirk; Singh, Angadjit; Mansell, Rhodri; Barnes, Crispin; Ritchie, David A.; Mussler, Gregor; Lanius, Martin; Grützmacher, Detlev; Narayan, Vijay
2016-01-01
Topological insulators (TIs) are bulk insulators with exotic ‘topologically protected’ surface conducting modes. It has recently been pointed out that when stacked together, interactions between surface modes can induce diverse phases including the TI, Dirac semimetal, and Weyl semimetal. However, currently a full experimental understanding of the conditions under which topological modes interact is lacking. Here, working with multilayers of the TI Sb2Te3 and the band insulator GeTe, we provide experimental evidence of multiple topological modes in a single Sb2Te3-GeTe-Sb2Te3 structure. Furthermore, we show that reducing the thickness of the GeTe layer induces a phase transition from a Dirac-like phase to a gapped phase. By comparing different multilayer structures we demonstrate that this transition occurs due to the hybridisation of states associated with different TI films. Our results demonstrate that the Sb2Te3-GeTe system offers strong potential towards manipulating topological states as well as towards controlledly inducing various topological phases. PMID:27291288
Bona fide interaction-driven topological phase transition in correlated SPT states
NASA Astrophysics Data System (ADS)
Meng, Zi Yang; He, Yuan-Yao; Wu, Han-Qing; You, Yi-Zhuang; Xu, Cenke; Lu, Zhong-Yi
It is expected the interplay between non-trivial band topology and strong electron correlation will lead to very rich physics. Thus a controlled study of the competition between topology and correlation is of great interest. Here, employing large-scale quantum Monte Carlo simulations, we provide a concrete example of the Kane-Mele-Hubbard model on an AA stacking bilayer honeycomb lattice with inter-layer antiferromagnetic interaction. Our simulation identified several different phases: a quantum spin-Hall insulator (QSH), a xy-plane antiferromagnetic Mott insulator (xy-AFM) and an inter-layer dimer-singlet insulator (dimer-singlet). Most importantly, a bona fide topological phase transition between the QSH and the dimer-singlet insulators, purely driven by the inter-layer antiferromagnetic interaction is found. At the transition, the spin and charge gap of the system close while the single-particle excitations remain gapped, which means that this transition has no mean field analogue and it can be viewed as a transition between bosonic SPT states. At one special point, this transition is described by a (2+1)d O(4) nonlinear sigma model with exact SO(4) symmetry, and a topological term at theta=p. Relevance of this work towards more general interacting SPT states is discussed.
Dynamical Quantum Phase Transitions: Role of Topological Nodes in Wave Function Overlaps.
Huang, Zhoushen; Balatsky, Alexander V
2016-08-19
A sudden quantum quench of a Bloch band from one topological phase toward another has been shown to exhibit an intimate connection with the notion of a dynamical quantum phase transition (DQPT), where the returning probability of the quenched state to the initial state-i.e., the Loschmidt echo-vanishes at critical times {t^{*}}. Analytical results to date are limited to two-band models, leaving the exact relation between topology and DQPT unclear. In this Letter, we show that, for a general multiband system, a robust DQPT relies on the existence of nodes (i.e., zeros) in the wave function overlap between the initial band and the postquench energy eigenstates. These nodes are topologically protected if the two participating wave functions have distinctive topological indices. We demonstrate these ideas in detail for both one and two spatial dimensions using a three-band generalized Hofstadter model. We also discuss possible experimental observations. PMID:27588874
Dynamical Quantum Phase Transitions: Role of Topological Nodes in Wave Function Overlaps
NASA Astrophysics Data System (ADS)
Huang, Zhoushen; Balatsky, Alexander V.
2016-08-01
A sudden quantum quench of a Bloch band from one topological phase toward another has been shown to exhibit an intimate connection with the notion of a dynamical quantum phase transition (DQPT), where the returning probability of the quenched state to the initial state—i.e., the Loschmidt echo—vanishes at critical times {t*}. Analytical results to date are limited to two-band models, leaving the exact relation between topology and DQPT unclear. In this Letter, we show that, for a general multiband system, a robust DQPT relies on the existence of nodes (i.e., zeros) in the wave function overlap between the initial band and the postquench energy eigenstates. These nodes are topologically protected if the two participating wave functions have distinctive topological indices. We demonstrate these ideas in detail for both one and two spatial dimensions using a three-band generalized Hofstadter model. We also discuss possible experimental observations.
Transition from nonresonant to resonant random lasers by the geometrical confinement of disorder.
Ghofraniha, N; Viola, I; Zacheo, A; Arima, V; Gigli, G; Conti, C
2013-12-01
We report on a transition in random lasers that is induced by the geometrical confinement of the emitting material. Different dye doped paper devices with controlled geometry are fabricated by soft lithography and show two distinguished behaviors in the stimulated emission: in the absence of boundary constraints, the energy threshold decreases for larger laser volumes showing the typical trend of diffusive nonresonant random lasers, while when the same material is lithographed into channels, the walls act as cavity and the resonant behavior typical of standard lasers is observed. The experimental results are consistent with the general theories of random and standard lasers and a clear phase diagram of the transition is reported.
Quantum anomalous Hall effect and tunable topological states in 3d transition metals doped silicene.
Zhang, Xiao-Long; Liu, Lan-Feng; Liu, Wu-Ming
2013-01-01
Silicene is an intriguing 2D topological material which is closely analogous to graphene but with stronger spin orbit coupling effect and natural compatibility with current silicon-based electronics industry. Here we demonstrate that silicene decorated with certain 3d transition metals (Vanadium) can sustain a stable quantum anomalous Hall effect using both analytical model and first-principles Wannier interpolation. We also predict the quantum valley Hall effect and electrically tunable topological states could be realized in certain transition metal doped silicene where the energy band inversion occurs. Our findings provide new scheme for the realization of quantum anomalous Hall effect and platform for electrically controllable topological states which are highly desirable for future nanoelectronics and spintronics application. PMID:24105063
Strain-induced topological phase transition in phosphorene and in phosphorene nanoribbons
NASA Astrophysics Data System (ADS)
Taghizadeh Sisakht, E.; Fazileh, F.; Zare, M. H.; Zarenia, M.; Peeters, F. M.
2016-08-01
Using the tight-binding (TB) approximation with inclusion of the spin-orbit interaction, we predict a topological phase transition in the electronic band structure of phosphorene in the presence of axial strains. We derive a low-energy TB Hamiltonian that includes the spin-orbit interaction for bulk phosphorene. Applying a compressive biaxial in-plane strain and perpendicular tensile strain in ranges where the structure is still stable leads to a topological phase transition. We also examine the influence of strain on zigzag phosphorene nanoribbons (zPNRs) and the formation of the corresponding protected edge states when the system is in the topological phase. For zPNRs up to a width of 100 nm the energy gap is at least three orders of magnitude larger than the thermal energy at room temperature.
Topological Transitions in Mitochondrial Membranes controlled by Apoptotic Proteins
NASA Astrophysics Data System (ADS)
Hwee Lai, Ghee; Sanders, Lori K.; Mishra, Abhijit; Schmidt, Nathan W.; Wong, Gerard C. L.; Ivashyna, Olena; Schlesinger, Paul H.
2010-03-01
The Bcl-2 family comprises pro-apoptotic proteins, capable of permeabilizing the mitochondrial membrane, and anti-apoptotic members interacting in an antagonistic fashion to regulate programmed cell death (apoptosis). They offer potential therapeutic targets to re-engage cellular suicide in tumor cells but the extensive network of implicated protein-protein interactions has impeded full understanding of the decision pathway. We show, using synchrotron x-ray diffraction, that pro-apoptotic proteins interact with mitochondrial-like model membranes to generate saddle-splay (negative Gaussian) curvature topologically required for pore formation, while anti-apoptotic proteins can deactivate curvature generation by molecules drastically different from Bcl-2 family members and offer evidence for membrane-curvature mediated interactions general enough to affect very disparate systems.
Gurzhiy, Vladislav V.
2015-09-15
for investigation of topologies of structural units. • The method of orientation matrices was applied to distinguish geometrical isomers. • The flexibility of structural complexes specifies the undulation of layered structural units.
NASA Astrophysics Data System (ADS)
Nogueira, Flavio S.; Sudbø, Asle; Eremin, Ilya
2015-12-01
We demonstrate that the Higgs mechanism in three-dimensional topological superconductors exhibits unique features with experimentally observable consequences. The Higgs model we discuss has two superconducting components and an axionlike magnetoelectric term with the phase difference of the superconducting order parameters playing the role of the axion field. Due to this additional term, quantum electromagnetic and phase fluctuations lead to a robust topologically nontrivial state that holds also in the presence of interactions. In this sense, we show that the renormalization flow of the topologically nontrivial phase cannot be continuously deformed into a topologically nontrivial one. One consequence of our analysis of quantum critical fluctuations is the possibility of having a first-order phase transition in the bulk and a second-order phase transition on the surface. We also explore another consequence of the axionic Higgs electrodynamics, namely, the anomalous Hall effect. In the low-frequency London regime an anomalous Hall effect is induced in the presence of an applied electric field parallel to the surface. This anomalous Hall current is induced by a Lorentz-like force arising from the axion term, and it involves the relative superfluid velocity of the superconducting components. The anomalous Hall current has a negative sign, a situation reminiscent of but quite distinct in physical origin from the anomalous Hall effect observed in high-Tc superconductors. In contrast to the latter, the anomalous Hall effect in topological superconductors is nondissipative and occurs in the absence of vortices.
Electric control of topological phase transitions in Dirac semimetal thin films.
Pan, Hui; Wu, Meimei; Liu, Ying; Yang, Shengyuan A
2015-09-30
Dirac semimetals host three-dimensional (3D) Dirac fermion states in the bulk of crystalline solids, which can be viewed as 3D analogs of graphene. Owing to their relativistic spectrum and unique topological character, these materials hold great promise for fundamental-physics exploration and practical applications. Particularly, they are expected to be ideal parent compounds for engineering various other topological states of matter. In this report, we investigate the possibility to induce and control the topological quantum spin Hall phase in a Dirac semimetal thin film by using a vertical electric field. We show that through the interplay between the quantum confinement effect and the field-induced coupling between sub-bands, the sub-band gap can be tuned and inverted. During this process, the system undergoes a topological phase transition between a trivial band insulator and a quantum spin Hall insulator. Consequently, one can switch the topological edge channels on and off by purely electrical means, making the system a promising platform for constructing topological field effect transistors.
Electric control of topological phase transitions in Dirac semimetal thin films
Pan, Hui; Wu, Meimei; Liu, Ying; Yang, Shengyuan A.
2015-01-01
Dirac semimetals host three-dimensional (3D) Dirac fermion states in the bulk of crystalline solids, which can be viewed as 3D analogs of graphene. Owing to their relativistic spectrum and unique topological character, these materials hold great promise for fundamental-physics exploration and practical applications. Particularly, they are expected to be ideal parent compounds for engineering various other topological states of matter. In this report, we investigate the possibility to induce and control the topological quantum spin Hall phase in a Dirac semimetal thin film by using a vertical electric field. We show that through the interplay between the quantum confinement effect and the field-induced coupling between sub-bands, the sub-band gap can be tuned and inverted. During this process, the system undergoes a topological phase transition between a trivial band insulator and a quantum spin Hall insulator. Consequently, one can switch the topological edge channels on and off by purely electrical means, making the system a promising platform for constructing topological field effect transistors. PMID:26420343
Self-induced topological transitions and edge states supported by nonlinear staggered potentials
NASA Astrophysics Data System (ADS)
Hadad, Yakir; Khanikaev, Alexander B.; Alò, Andrea
2016-04-01
The canonical Su-Schrieffer-Heeger (SSH) array is one of the basic geometries that have spurred significant interest in topological band-gap modes. Here, we show that the judicious inclusion of third-order Kerr nonlinearities in SSH arrays opens rich physics in topological insulators, including the possibility of supporting self-induced topological transitions, as a function of the applied intensity. We highlight the emergence of a class of topological solutions in nonlinear SSH arrays localized at the array edges and with unusual properties. As opposed to their linear counterparts, these nonlinear states decay to a plateau of nonzero amplitude inside the array, highlighting the local nature of topologically nontrivial band gaps in nonlinear systems. We study the conditions under which these states can be excited and their temporal dynamics as a function of the applied excitation, paving the way to interesting directions in the physics of topological edge states with robust propagation properties based on nonlinear interactions in suitably designed periodic arrays.
Topological phase transition in hexagonal boron-nitride bilayers modulated by gate voltage
NASA Astrophysics Data System (ADS)
Jin, Guojun; Zhai, Xuechao
2013-03-01
We study the gate-voltage modulated electronic properties of hexagonal boron-nitride bilayers with two different stacking structures in the presence of intrinsic and Rashba spin-orbit interactions. Our analytical results show that there are striking cooperation effects arising from the spin-orbit interactions and the interlayer bias voltage. For realizing topological phase transition, in contrast to a gated graphene bilayer for increasing its energy gap, the energy gap of a boron-nitride bilayer is significantly reduced by an applied gate voltage. For the AA stacking-bilayer which has the inversion symmetry, a strong topological phase is found, and there is an interesting reentrant behavior from a normal phase to a topological phase and then to a normal phase again, characterized by the topological index. Therefore, the gate voltage modulated AA-boron nitride bilayer can be taken as a newcomer of the topological insulator family. For the AB stacking-bilayer which is lack of the inversion symmetry, it is always topologically trivial, but exhibits an unusual quantum Hall phase with four degenerate low-energy states localized at a single edge. It is suggested that these theoretical findings could be verified experimentally in the transport properties of boron-nitride bylayers. This research was supported by the NSFC (Nos. 60876065, 11074108), PAPD, and NBRPC (Nos. 2009CB929504, 2011CB922102).
Adiabatic continuity, wave-function overlap, and topological phase transitions
NASA Astrophysics Data System (ADS)
Gu, Jiahua; Sun, Kai
2016-09-01
In this paper, we study the relation between wave-function overlap and adiabatic continuity in gapped quantum systems. We show that for two band insulators, a scalar function can be defined in the momentum space, which characterizes the wave-function overlap between Bloch states in the two insulators. If this overlap is nonzero for all momentum points in the Brillouin zone, these two insulators are adiabatically connected, i.e., we can deform one insulator into the other smoothly without closing the band gap. In addition, we further prove that this adiabatic path preserves all the symmetries of the insulators. The existence of such an adiabatic path implies that two insulators with nonzero wave-function overlap belong to the same topological phase. This relation, between adiabatic continuity and wave-function overlap, can be further generalized to correlated systems. The generalized relation cannot be applied to study generic many-body systems in the thermodynamic limit, because of the orthogonality catastrophe. However, for certain interacting systems (e.g., quantum Hall systems), the quantum wave-function overlap can be utilized to distinguish different quantum states. Experimental implications are also discussed.
Spin-glass transition in geometrically frustrated antiferromagnets with weak disorder
NASA Astrophysics Data System (ADS)
Andreanov, A.; Chalker, J. T.; Saunders, T. E.; Sherrington, D.
2010-01-01
We study the effect in geometrically frustrated antiferromagnets of weak, random variations in the strength of exchange interactions. Without disorder the simplest classical models for these systems have macroscopically degenerate ground states, and this degeneracy may prevent ordering at any temperature. Weak exchange randomness favors a small subset of these ground states and induces a spin-glass transition at an ordering temperature determined by the amplitude of modulations in interaction strength. We use the replica approach to formulate a theory for this transition, showing that it falls into the same universality class as conventional spin-glass transitions. In addition, we show that a model with a low concentration of defect bonds can be mapped onto a system of randomly located pseudospins that have dipolar effective interactions. We also present detailed results from Monte Carlo simulations of the classical Heisenberg antiferromagnet on the pyrochlore lattice with weak randomness in nearest-neighbor exchange.
Topological transitions in unidirectional flow of nematic liquid crystal
NASA Astrophysics Data System (ADS)
Cummings, Linda; Anderson, Thomas; Mema, Ensela; Kondic, Lou
2015-11-01
Recent experiments by Sengupta et al. (Phys. Rev. Lett. 2013) revealed interesting transitions that can occur in flow of nematic liquid crystal under carefully controlled conditions within a long microfluidic channel of rectangular cross-section, with homeotropic anchoring at the walls. At low flow rates the director field of the nematic adopts a configuration that is dominated by the surface anchoring, being nearly parallel to the channel height direction over most of the cross-section; but at high flow rates there is a transition to a flow-dominated state, where the director configuration at the channel centerline is aligned with the flow (perpendicular to the channel height direction). We analyze simple channel-flow solutions to the Leslie-Ericksen model for nematics. We demonstrate that two solutions exist, at all flow rates, but that there is a transition between the elastic free energies of these solutions: the anchoring-dominated solution has the lowest energy at low flow rates, and the flow-dominated solution has lowest energy at high flow rates. NSF DMS 1211713.
Stripe melting and a transition between weak and strong symmetry protected topological phases
NASA Astrophysics Data System (ADS)
You, Yizhi; You, Yi-Zhuang
2016-05-01
For a gapped disordered many-body system with both internal and translation symmetry, one can define the corresponding weak and strong symmetry protected topological (SPT) phases. A strong SPT phase is protected by the internal symmetry G only while a weak SPT phase, fabricated by alignment of a strong SPT state in a lower dimension, requires additional discrete translation symmetry protection. In this paper, we construct a phase transition between weak and strong SPT phase in a strongly interacting boson system. The starting point of our construction is the superconducting Dirac fermions with pair density wave (PDW) order in 2 d . We first demonstrate that the nodal line of the PDW contains a 1 d boson SPT phase. We further show that melting the PDW stripe and condensing the nodal line provoke the transition from weak to strong SPT phase in 2 d . The phase transition theory contains an O(4) nonlinear-σ model (NL σ M ) with topological Θ term emerging from the proliferation of domain walls bound to an SPT chain. A similar scheme also applies to weak-strong SPT transition in other dimensions and predicts possible phase transition from 2 d to 3 d topological order.
Topological phase transitions with non-Abelian gauge potentials on square lattices
NASA Astrophysics Data System (ADS)
Chen, Yao-Hua; Li, Jian; Ting, C. S.
2013-11-01
We investigate the topological phase transition on interacting square lattices via the non-Abelian potential by employing the real-space cellular dynamical mean-field theory combining with the continuous-time Monte Carlo method. For a weak on-site Hubbard interaction, a topological band insulating state with a pair of gapless edge states is induced by a next-nearest-neighbor hopping. A phase transition from the metallic phase to the Mott insulating phase is observed when the interaction is increased. These two phases can be distinguished by detecting whether a bulk gap in the K-dependent spectral function exists. The whole phase diagrams as functions of the interaction, next-nearest-neighbor hopping energy, and temperature are presented. The experimental setup to observe these new interesting phase transitions is also discussed.
Electronic topological transition in zinc under pressure: An x-ray absorption spectroscopy study
NASA Astrophysics Data System (ADS)
Aquilanti, G.; Trapananti, A.; Minicucci, M.; Liscio, F.; Twaróg, A.; Principi, E.; Pascarelli, S.
2007-10-01
Zinc metal has been studied at high pressure using x-ray absorption spectroscopy. In order to investigate the role of the different degrees of hydrostaticity on the occurrence of structural anomalies following the electronic topological transition, two pressure transmitting media have been used. Results show that the electronic topological transition, if it exists, does not induce an anomaly in the local environment of compressed Zn as a function of hydrostatic pressure and any anomaly must be related to a loss of hydrostaticity of the pressure transmitting medium. The near-edge structures of the spectra, sensitive to variations in the electronic density of states above the Fermi level, do not show any evidence of electronic transition whatever pressure transmitting medium is used.
Topological phase transition and quantum spin Hall edge states of antimony few layers
Kim, Sung Hwan; Jin, Kyung-Hwan; Park, Joonbum; Kim, Jun Sung; Jhi, Seung-Hoon; Yeom, Han Woong
2016-01-01
While two-dimensional (2D) topological insulators (TI’s) initiated the field of topological materials, only very few materials were discovered to date and the direct access to their quantum spin Hall edge states has been challenging due to material issues. Here, we introduce a new 2D TI material, Sb few layer films. Electronic structures of ultrathin Sb islands grown on Bi2Te2Se are investigated by scanning tunneling microscopy. The maps of local density of states clearly identify robust edge electronic states over the thickness of three bilayers in clear contrast to thinner islands. This indicates that topological edge states emerge through a 2D topological phase transition predicted between three and four bilayer films in recent theory. The non-trivial phase transition and edge states are confirmed for epitaxial films by extensive density-functional-theory calculations. This work provides an important material platform to exploit microscopic aspects of the quantum spin Hall phase and its quantum phase transition. PMID:27624972
Topological phase transition and quantum spin Hall edge states of antimony few layers
NASA Astrophysics Data System (ADS)
Kim, Sung Hwan; Jin, Kyung-Hwan; Park, Joonbum; Kim, Jun Sung; Jhi, Seung-Hoon; Yeom, Han Woong
2016-09-01
While two-dimensional (2D) topological insulators (TI’s) initiated the field of topological materials, only very few materials were discovered to date and the direct access to their quantum spin Hall edge states has been challenging due to material issues. Here, we introduce a new 2D TI material, Sb few layer films. Electronic structures of ultrathin Sb islands grown on Bi2Te2Se are investigated by scanning tunneling microscopy. The maps of local density of states clearly identify robust edge electronic states over the thickness of three bilayers in clear contrast to thinner islands. This indicates that topological edge states emerge through a 2D topological phase transition predicted between three and four bilayer films in recent theory. The non-trivial phase transition and edge states are confirmed for epitaxial films by extensive density-functional-theory calculations. This work provides an important material platform to exploit microscopic aspects of the quantum spin Hall phase and its quantum phase transition.
Topological phase transition and quantum spin Hall edge states of antimony few layers.
Kim, Sung Hwan; Jin, Kyung-Hwan; Park, Joonbum; Kim, Jun Sung; Jhi, Seung-Hoon; Yeom, Han Woong
2016-01-01
While two-dimensional (2D) topological insulators (TI's) initiated the field of topological materials, only very few materials were discovered to date and the direct access to their quantum spin Hall edge states has been challenging due to material issues. Here, we introduce a new 2D TI material, Sb few layer films. Electronic structures of ultrathin Sb islands grown on Bi2Te2Se are investigated by scanning tunneling microscopy. The maps of local density of states clearly identify robust edge electronic states over the thickness of three bilayers in clear contrast to thinner islands. This indicates that topological edge states emerge through a 2D topological phase transition predicted between three and four bilayer films in recent theory. The non-trivial phase transition and edge states are confirmed for epitaxial films by extensive density-functional-theory calculations. This work provides an important material platform to exploit microscopic aspects of the quantum spin Hall phase and its quantum phase transition. PMID:27624972
Terahertz detection of magnetic field-driven topological phase transition in HgTe-based transistors
Kadykov, A. M.; Teppe, F. Consejo, C.; Ruffenach, S.; Marcinkiewicz, M.; Desrat, W.; Dyakonova, N.; Knap, W.; Viti, L.; Vitiello, M. S.; Krishtopenko, S. S.; Morozov, S. V.; Gavrilenko, V. I.; Mikhailov, N. N.; Dvoretsky, S. A.
2015-10-12
We report on terahertz photoconductivity under magnetic field up to 16 T of field effect transistor based on HgTe quantum well (QW) with an inverted band structure. We observe pronounced cyclotron resonance and Shubnikov-de Haas-like oscillations, indicating a high mobility electron gas in the transistor channel. We discover that nonlinearity of the transistor channel allows for observation of characteristic features in photoconductivity at critical magnetic field corresponding to the phase transition between topological quantum spin Hall and trivial quantum Hall states in HgTe QW. Our results pave the way towards terahertz topological field effect transistors.
NASA Astrophysics Data System (ADS)
Fransson, J.
2015-09-01
Inelastic scattering off magnetic impurities in a spin-chiral two-dimensional electron gas, e.g., the Rashba system, is shown to generate topological changes in the spin texture of the electron waves emanating from the scattering center. While elastic scattering gives rise to a purely in-plane spin texture for an in-plane magnetic scattering potential, out-of-plane components emerge upon activation of inelastic scattering processes. This property leads to a possibility to make controlled transitions between trivial and nontrivial topologies of the spin texture.
Phase transition of charged Black Holes in Brans-Dicke theory through geometrical thermodynamics
NASA Astrophysics Data System (ADS)
Hendi, S. H.; Panahiyan, S.; Panah, B. Eslam; Armanfard, Z.
2016-07-01
In this paper, we take into account black hole solutions of Brans-Dicke-Maxwell theory and investigate their stability and phase transition points. We apply the concept of geometry in thermodynamics to obtain phase transition points and compare its results with those, calculated in the canonical ensemble through heat capacity. We show that these black holes enjoy second order phase transitions. We also show that there is a lower bound for the horizon radius of physical charged black holes in Brans-Dicke theory, which originates from restrictions of positivity of temperature. In addition, we find that employing a specific thermodynamical metric in the context of geometrical thermodynamics yields divergencies for the thermodynamical Ricci scalar in places of the phase transitions. It will be pointed out that due to the characteristic behavior of the thermodynamical Ricci scalar around its divergence points, one is able to distinguish the physical limitation point from the phase transitions. In addition, the free energy of these black holes will be obtained and its behavior will be investigated. It will be shown that the behavior of the free energy in the place where the heat capacity diverges demonstrates second order phase transition characteristics.
Fessel, Adrian; Oettmeier, Christina; Bernitt, Erik; Gauthier, Nils C; Döbereiner, Hans-Günther
2012-08-17
We study the formation of transportation networks of the true slime mold Physarum polycephalum after fragmentation by shear. Small fragments, called microplasmodia, fuse to form macroplasmodia in a percolation transition. At this topological phase transition, one single giant component forms, connecting most of the previously isolated microplasmodia. Employing the configuration model of graph theory for small link degree, we have found analytically an exact solution for the phase transition. It is generally applicable to percolation as seen, e.g., in vascular networks. PMID:23006405
Trugenberger, Carlo A
2015-12-01
Recently I proposed a simple dynamical network model for discrete space-time that self-organizes as a graph with Hausdorff dimension d(H)=4. The model has a geometric quantum phase transition with disorder parameter (d(H)-d(s)), where d(s) is the spectral dimension of the dynamical graph. Self-organization in this network model is based on a competition between a ferromagnetic Ising model for vertices and an antiferromagnetic Ising model for edges. In this paper I solve a toy version of this model defined on a bipartite graph in the mean-field approximation. I show that the geometric phase transition corresponds exactly to the antiferromagnetic transition for edges, the dimensional disorder parameter of the former being mapped to the staggered magnetization order parameter of the latter. The model has a critical point with long-range correlations between edges, where a continuum random geometry can be defined, exactly as in Kazakov's famed 2D random lattice Ising model but now in any number of dimensions. PMID:26764755
Critical space-time networks and geometric phase transitions from frustrated edge antiferromagnetism
NASA Astrophysics Data System (ADS)
Trugenberger, Carlo A.
2015-12-01
Recently I proposed a simple dynamical network model for discrete space-time that self-organizes as a graph with Hausdorff dimension dH=4 . The model has a geometric quantum phase transition with disorder parameter (dH-ds) , where ds is the spectral dimension of the dynamical graph. Self-organization in this network model is based on a competition between a ferromagnetic Ising model for vertices and an antiferromagnetic Ising model for edges. In this paper I solve a toy version of this model defined on a bipartite graph in the mean-field approximation. I show that the geometric phase transition corresponds exactly to the antiferromagnetic transition for edges, the dimensional disorder parameter of the former being mapped to the staggered magnetization order parameter of the latter. The model has a critical point with long-range correlations between edges, where a continuum random geometry can be defined, exactly as in Kazakov's famed 2D random lattice Ising model but now in any number of dimensions.
Zhou, Tong; Zhang, Jiayong; Zhao, Bao; Zhang, Huisheng; Yang, Zhongqin
2015-08-12
Electronic and topological behaviors of Sb(111) monolayers decorated with H and certain magnetic atoms are investigated by using ab initio methods. The drastic exchange field induced by the magnetic atoms, together with strong spin-orbit coupling (SOC) of Sb atoms, generates one new category of valley polarized topological insulators, called quantum spin-quantum anomalous Hall (QSQAH) insulators in the monolayer, with a band gap up to 53 meV. The strong SOC is closely related to Sb px and py orbitals, instead of pz orbitals in usual two-dimensional (2D) materials. Topological transitions from quantum anomalous Hall states to QSQAH states and then to time-reversal-symmetry-broken quantum spin Hall states are achieved by tuning the SOC strength. The behind mechanism is revealed. Our work is helpful for future valleytronic and spintronic applications in 2D materials.
Topological transition in Bi1-xSbx studied as a function of Sb doping
NASA Astrophysics Data System (ADS)
Nakamura, Fumitaka; Kousa, Yuka; Taskin, Alexey A.; Takeichi, Yasuo; Nishide, Akinori; Kakizaki, Akito; D'Angelo, Marie; Lefevre, Patrick; Bertran, Francois; Taleb-Ibrahimi, Amina; Komori, Fumio; Kimura, Shin-Ichi; Kondo, Hiroshi; Ando, Yoichi; Matsuda, Iwao
2011-12-01
Spin- and angle-resolved photoemission spectroscopy measurements were performed on Bi1-xSbx samples at x=0.04, 0.07, and 0.21 to study the change of the surface band structure from nontopological to topological. Energy shift of the T and Ls bulk bands with Sb concentration is quantitatively evaluated. An edge state becomes topologically nontrivial at x=0.04. An additional trivial edge state appears at the L band gap that forms at x>0.04 and apparently hybridize with the nontrivial edge state. A scenario for the topological transition mechanism is presented. Related issues of self-energy and temperature dependence of the surface state are also considered.
NASA Astrophysics Data System (ADS)
Wang, Rui; Qiao, Qian; Wang, Bin; Ding, Xiu-Huan; Zhang, Yi-Fu
2016-09-01
The quantum spin Hall (QSH) effect and the quantum anomalous Hall (QAH) effect in Lieb lattice are investigated in the presence of both Rashba spin-orbit coupling (SOC) and uniform exchange field. The Lieb lattice has a simple cubic symmetry, which is characterized by the single Dirac-cone per Brillouin zone and the middle flat band in the band structure. The intrinsic SOC is essentially needed to open the full energy gap in the bulk. The QSH effect could survive even in the presence of the exchange field. In terms of the first Chern number and the spin Chern number, we study the topological nature and the topological phase transition from the time-reversal symmetry broken QSH effect to the QAH effect. For Lieb lattice ribbons, the energy spectrum and the wave-function distributions are obtained numerically, where the helical edge states and the chiral edge states reveal the non-trivial topological QSH and QAH properties, respectively.
Topological phase transition in the Scheidegger model of river networks
NASA Astrophysics Data System (ADS)
Oppenheim, Jacob N.; Magnasco, Marcelo O.
2012-08-01
Transport networks are found at the heart of myriad natural systems, yet are poorly understood, except for the case of river networks. The Scheidegger model, in which rivers are convergent random walks, has been studied only in the case of flat topography, ignoring the variety of curved geometries found in nature. Embedding this model on a cone, we find a convergent and a divergent phase, corresponding to few, long basins and many, short basins, respectively, separated by a singularity, indicating a phase transition. Quantifying basin shape using Hacks law l˜ah gives distinct values for h, providing a method of testing our hypotheses. The generality of our model suggests implications for vascular morphology, in particular, differing number and shapes of arterial and venous trees.
NASA Astrophysics Data System (ADS)
Kharitonov, Maxim; Juergens, Stefan; Trauzettel, Björn
2016-07-01
We consider a class of quantum Hall topological insulators: topologically nontrivial states with zero Chern number at finite magnetic field, in which the counterpropagating edge states are protected by a symmetry (spatial or spin) other than time-reversal. HgTe-type heterostructures and graphene are among the relevant systems. We study the effect of electron interactions on the topological properties of the system. We particularly focus on the vicinity of the topological phase transition, marked by the crossing of two Landau levels, where the system is a strongly interacting quantum Hall ferromagnet. We analyze the edge properties using the formalism of the nonlinear σ -model. We establish the symmetry requirement for the topological protection in this interacting system: effective continuous U(1) symmetry with respect to uniaxial isospin rotations must be preserved. If U(1) symmetry is preserved, the topologically nontrivial phase persists; its edge is a helical Luttinger liquid with highly tunable effective interactions. We obtain explicit analytical expressions for the parameters of the Luttinger liquid in the quantum-Hall-ferromagnet regime. However, U(1) symmetry may be broken, either spontaneously or by U(1)-asymmetric interactions. In either case, interaction-induced transitions occur to the respective topologically trivial phases with gapped edge charge excitations.
Aspects of Floquet bands and topological phase transitions in a continuously driven superlattice
NASA Astrophysics Data System (ADS)
Zhou, Longwen; Wang, Hailong; Ho, Derek Y. H.; Gong, Jiangbin
2014-09-01
The recent creation of novel topological states of matter via periodic driving fields has attracted much attention. To contribute to the growing knowledge on this subject, we study the well-known Harper-Aubry-André model modified by a continuous time-periodic modulation and report on its topological properties along with several other interesting features. The Floquet bands are found to have non-zero Chern numbers which are generally different from those in the original static model. Topological phase transitions (discontinuous change of Chern numbers) take place as we tune the amplitude or period of the driving field. We demonstrate that the non-trivial Floquet band topology manifests via the quantized transport of Wannier states in the lattice space. For certain parameter choices, very flat yet topologically non-trivial Floquet bands emerge, a feature potentially useful for simulating the physics of strongly correlated systems. In some cases with an even number of Floquet bands, the spectrum features linearly dispersing Dirac cones which hold potential for the simulation of high energy physics or Klein tunnelling. Taking open boundary conditions, we observe anomalous counter-propagating chiral edge modes and degenerate zero modes. We end by discussing how these theoretical predictions may be verified experimentally.
Mean-field dynamic criticality and geometric transition in the Gaussian core model
NASA Astrophysics Data System (ADS)
Coslovich, Daniele; Ikeda, Atsushi; Miyazaki, Kunimasa
2016-04-01
We use molecular dynamics simulations to investigate dynamic heterogeneities and the potential energy landscape of the Gaussian core model (GCM). Despite the nearly Gaussian statistics of particles' displacements, the GCM exhibits giant dynamic heterogeneities close to the dynamic transition temperature. The divergence of the four-point susceptibility is quantitatively well described by the inhomogeneous version of the mode-coupling theory. Furthermore, the potential energy landscape of the GCM is characterized by large energy barriers, as expected from the lack of activated, hopping dynamics, and display features compatible with a geometric transition. These observations demonstrate that all major features of mean-field dynamic criticality can be observed in a physically sound, three-dimensional model.
Mean-field dynamic criticality and geometric transition in the Gaussian core model.
Coslovich, Daniele; Ikeda, Atsushi; Miyazaki, Kunimasa
2016-04-01
We use molecular dynamics simulations to investigate dynamic heterogeneities and the potential energy landscape of the Gaussian core model (GCM). Despite the nearly Gaussian statistics of particles' displacements, the GCM exhibits giant dynamic heterogeneities close to the dynamic transition temperature. The divergence of the four-point susceptibility is quantitatively well described by the inhomogeneous version of the mode-coupling theory. Furthermore, the potential energy landscape of the GCM is characterized by large energy barriers, as expected from the lack of activated, hopping dynamics, and display features compatible with a geometric transition. These observations demonstrate that all major features of mean-field dynamic criticality can be observed in a physically sound, three-dimensional model. PMID:27176347
Disorder-induced structural transitions in topological insulating Ge-Sb-Te compounds
Kim, Jeongwoo; Jhi, Seung-Hoon
2015-05-21
The mechanism for the fast switching between amorphous, metastable, and crystalline structures in chalcogenide phase-change materials has been a long-standing puzzle. Based on first-principles calculations, we study the atomic and electronic properties of metastable Ge{sub 2}Sb{sub 2}Te{sub 5} and investigate the atomic disorder to understand the transition between crystalline hexagonal and cubic structures. In addition, we study the topological insulating property embedded in these compounds and its evolution upon structural changes and atomic disorder. We also discuss the role of the surface-like states arising from the topological insulating property in the metal-insulator transition observed in the hexagonal structure.
Nie, Yaozhuang; Rahman, Mavlanjan; Wang, Daowei; Wang, Can; Guo, Guanghua
2015-01-01
We present first-principles calculations of electronic structures of a class of two-dimensional (2D) honeycomb structures of group-V binary compounds. Our results show these new 2D materials are stable semiconductors with direct or indirect band gaps. The band gap can be tuned by applying lattice strain. During their stretchable regime, they all exhibit metal-indirect gap semiconductor-direct gap semiconductor-topological insulator (TI) transitions with increasing strain from negative (compressive) to positive (tensile) values. The topological phase transition results from the band inversion at the Γ point which is due to the evolution of bonding and anti-bonding states under lattice strain. PMID:26656257
Valley polarized quantum Hall effect and topological insulator phase transitions in silicene.
Tahir, M; Schwingenschlögl, U
2013-01-01
The electronic properties of silicene are distinct from both the conventional two dimensional electron gas and the famous graphene due to strong spin orbit interaction and the buckled structure. Silicene has the potential to overcome limitations encountered for graphene, in particular the zero band gap and weak spin orbit interaction. We demonstrate a valley polarized quantum Hall effect and topological insulator phase transitions. We use the Kubo formalism to discuss the Hall conductivity and address the longitudinal conductivity for elastic impurity scattering in the first Born approximation. We show that the combination of an electric field with intrinsic spin orbit interaction leads to quantum phase transitions at the charge neutrality point, providing a tool to experimentally tune the topological state. Silicene constitutes a model system for exploring the spin and valley physics not accessible in graphene due to the small spin orbit interaction.
Strain-tunable topological quantum phase transition in buckled honeycomb lattices
Yan, Jia-An Cruz, Mack A. Dela; Barraza-Lopez, Salvador; Yang, Li
2015-05-04
Low-buckled silicene is a prototypical quantum spin Hall insulator with the topological quantum phase transition controlled by an out-of-plane electric field. We show that this field-induced electronic transition can be further tuned by an in-plane biaxial strain ε, owing to the curvature-dependent spin-orbit coupling (SOC): There is a Z{sub 2} = 1 topological insulator phase for biaxial strain |ε| smaller than 0.07, and the band gap can be tuned from 0.7 meV for ε=+0.07 up to 3.0 meV for ε=−0.07. First-principles calculations also show that the critical field strength E{sub c} can be tuned by more than 113%, with the absolute values nearly 10 times stronger than the theoretical predictions based on a tight-binding model. The buckling structure of the honeycomb lattice thus enhances the tunability of both the quantum phase transition and the SOC-induced band gap, which are crucial for the design of topological field-effect transistors based on two-dimensional materials.
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
Kim, Jinsu; Lee, Kyujoon; Takabatake, Toshiro; Kim, Hanchul; Kim, Miyoung; Jung, Myung-Hwa
2015-05-14
There are many interests to achieve long-range magnetic order in topological insulators of Bi2Se3 or Bi2Te3 by doping magnetic transition metals such as Fe and Mn. The transition metals act as not only magnetic dopants but also electric dopants because they are usually divalent. However, if the doping elements are rare-earth metals such as Gd, which are trivalent, only magnetic moments can be introduced. We fabricated single crystals of Bi2-xGdxTe3 (0 ≤ × ≤ 0.2), in which we observed magnetic phase change from paramagnetic (PM) to antiferromagnetic (AFM) phase by increasing x. This PM-to-AFM phase transition agrees with the density functional theory calculations showing a weak and short-ranged Gd-Gd AFM coupling via the intervening Te ions. The critical point corresponding to the magnetic phase transition is x = 0.09, where large linear magnetoresistance and highly anisotropic Shubnikov-de Haas oscillations are observed. These results are discussed with two-dimensional properties of topological surface state electrons.
Universal fidelity near quantum and topological phase transitions in finite one-dimensional systems
NASA Astrophysics Data System (ADS)
König, E. J.; Levchenko, A.; Sedlmayr, N.
2016-06-01
We study the quantum fidelity (ground-state overlap) near quantum phase transitions of the Ising universality class in one-dimensional (1D) systems of finite-size L . Prominent examples occur in magnetic systems (e.g., spin-Peierls, the anisotropic X Y model) and in 1D topological insulators of any topologically nontrivial Altland-Zirnbauer-Kitaev universality class. The rescaled fidelity susceptibility is a function of the only dimensionless parameter L M , where 2 M is the gap in the fermionic spectrum. We present analytic expressions for the fidelity susceptibility for periodic and open boundaries conditions with zero, one, or two edge states. The latter are shown to have a crucial impact and alter the susceptibility both quantitatively and qualitatively. We support our analytical solutions with numerical data.
Pressure induced Ag2Te polymorphs in conjunction with topological non trivial to metal transition
NASA Astrophysics Data System (ADS)
Zhu, J.; Oganov, A. R.; Feng, W. X.; Yao, Y. G.; Zhang, S. J.; Yu, X. H.; Zhu, J. L.; Yu, R. C.; Jin, C. Q.; Dai, X.; Fang, Z.; Zhao, Y. S.
2016-08-01
Silver telluride (Ag2Te) is well known as superionic conductor and topological insulator with polymorphs. Pressure induced three phase transitions in Ag2Te have been reported in previous. Here, we experimentally identified high pressure phase above 13 GPa of Ag2Te by using high pressure synchrotron x ray diffraction method in combination with evolutionary crystal structure prediction, showing it crystallizes into a monoclinic structure of space group C2/m with lattice parameters a = 6.081Å, b = 5.744Å, c = 6.797 Å, β = 105.53°. The electronic properties measurements of Ag2Te reveal that the topologically non-trivial semiconducting phase I and semimetallic phase II previously predicated by theory transformed into bulk metals for high pressure phases in consistent with the first principles calculations.
Topological Quantum Phase Transitions in a Majorana Chain with Spatial Modulation
NASA Astrophysics Data System (ADS)
Ohta, Takumi; Totsuka, Keisuke
2016-07-01
We numerically study the quantum phase transitions and the stability of Majorana zero modes in a generalized Kitaev model in one dimension when the chemical potential is periodically modulating in space. By using the exact diagonalization method for open boundary condition, we investigate the ground-state phases in terms of the non-local properties such as the entanglement spectrum (ES) and the string correlation functions. When we vary the phase of the modulation, the number of the Majorana zero modes changes, which manifests itself in the degeneracy of the lowest level of the ES. Next, we study the quantum phase transitions driven by the change in the amplitude of the modulation. In particular, for certain values of the wave number and the phase of the modulation, we observe a quantum phase transition from one topological phase into another where the string correlation function oscillates in space. We also show a case where the degeneracy of the ES does not change even for large enough amplitude of the modulation. Finally, we characterize the phases of the system with periodic boundary condition by the topological invariant, which reflects the number of the zero-energy excitations.
Structural properties of Sb2S3 under pressure: Evidence of an electronic topological transition
Efthimiopoulos, Ilias; Buchan, Cienna; Wang, Yuejian
2016-04-06
High-pressure Raman spectroscopy and x-ray diffraction of Sb2S3 up to 53 GPa reveals two phase transitions at 5 GPa and 15 GPa. The first transition is evidenced by noticeable compressibility changes in distinct Raman-active modes, in the lattice parameter axial ratios, the unit cell volume, as well as in specific interatomic bond lengths and bond angles. By taking into account relevant results from the literature, we assign these effects to a second-order isostructural transition arising from an electronic topological transition in Sb2S3 near 5 GPa. Close comparison between Sb2S3 and Sb2S3 up to 10 GPa reveals a slightly diverse structuralmore » behavior for these two compounds after the isostructural transition pressure. This structural diversity appears to account for the different pressure-induced electronic behavior of Sb2S3 and Sb2S3 up to 10 GPa, i.e. the absence of an insulator-metal transition in Sb2S3 up to that pressure. Lastly, the second high-pressure modification appearing above 15 GPa appears to trigger a structural disorder at ~20 GPa; full decompression from 53 GPa leads to the recovery of an amorphous state.« less
Structural properties of Sb2S3 under pressure: evidence of an electronic topological transition
Efthimiopoulos, Ilias; Buchan, Cienna; Wang, Yuejian
2016-01-01
High-pressure Raman spectroscopy and x-ray diffraction of Sb2S3 up to 53 GPa reveals two phase transitions at 5 GPa and 15 GPa. The first transition is evidenced by noticeable compressibility changes in distinct Raman-active modes, in the lattice parameter axial ratios, the unit cell volume, as well as in specific interatomic bond lengths and bond angles. By taking into account relevant results from the literature, we assign these effects to a second-order isostructural transition arising from an electronic topological transition in Sb2S3 near 5 GPa. Close comparison between Sb2S3 and Sb2Se3 up to 10 GPa reveals a slightly diverse structural behavior for these two compounds after the isostructural transition pressure. This structural diversity appears to account for the different pressure-induced electronic behavior of Sb2S3 and Sb2Se3 up to 10 GPa, i.e. the absence of an insulator-metal transition in Sb2S3 up to that pressure. Finally, the second high-pressure modification appearing above 15 GPa appears to trigger a structural disorder at ~20 GPa; full decompression from 53 GPa leads to the recovery of an amorphous state. PMID:27048930
Wang, Jing; Zhou, Quan; Lian, Biao; Zhang, Shou -Cheng
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 will 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.
Topological phase transition and quantum spin Hall state in TlBiS{sub 2}
Singh, Bahadur Prasad, R.; Lin, Hsin; Bansil, A.
2014-07-21
We have investigated the bulk and surface electronic structures and band topology of TlBiS{sub 2} as a function of strain and electric field using ab-initio calculations. In its pristine form, TlBiS{sub 2} is a normal insulator, which does not support any non-trivial surface states. We show however that a compressive strain along the (111) direction induces a single band inversion with Z{sub 2} = (1;000), resulting in a Dirac cone surface state with a large in-plane spin polarization. Our analysis shows that a critical point lies between the normal and topological phases where the dispersion of the 3D bulk Dirac cone at the Γ-point becomes nearly linear. The band gap in thin films of TlBiS{sub 2} can be tuned through an out-of-the-plane electric field to realize a topological phase transition from a trivial insulator to a quantum spin Hall state. An effective k·p model Hamiltonian is presented to simulate our first-principles results on TlBiS{sub 2}.
Wang, Jing; Zhou, Quan; Lian, Biao; Zhang, Shou -Cheng
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 e2 /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
Topological Yu-Shiba-Rusinov chain in monolayer transition-metal dichalcogenide superconductors
NASA Astrophysics Data System (ADS)
Zhang, Junhua; Aji, Vivek
2016-08-01
Monolayers of transition-metal dichalcogenides (TMDs) are two-dimensional materials whose low-energy sector consists of two inequivalent valleys. The valence bands have a large spin splitting due to lack of inversion symmetry and strong spin-orbit coupling. Furthermore the spin is polarized up in one valley and down in the other (in directions perpendicular to the two-dimensional crystal). We focus on lightly hole-doped systems where the Fermi surface consists of two disconnected circles with opposite spins. For both proximity induced and intrinsic local attractive interaction induced superconductivity, a fully gapped intervalley pairing state is favored in this system, which is an equal superposition of the singlet and the m =0 triplet for the lack of centrosymmetry. We show that a ferromagnetically ordered magnetic-adatom chain placed on a monolayer TMD superconductor provides a platform to realize a one-dimensional topological superconducting state characterized by the presence of Majorana zero modes at its ends. We obtain the topological phase diagram and show that the topological superconducting phase is affected not only by the adatom spacing and the direction of the magnetic moment, but also by the orientation of the chain relative to the crystal.
NASA Astrophysics Data System (ADS)
Bensaci, Jalil; Chen, Zhao Yang; Mack, M. Catherine; Guillaud, Martial; Stamatas, Georgios N.
2015-09-01
Reflectance confocal microscopy is successfully used in infant skin research. Infant skin structure, function, and composition are undergoing a maturation process. We aimed to uncover how the epidermal architecture and cellular topology change with time. Images were collected from three age groups of healthy infants between one and four years of age and adults. Cell centers were manually identified on the images at the stratum granulosum (SG) and stratum spinosum (SS) levels. Voronoi diagrams were used to calculate geometrical and topological parameters. Infant cell density is higher than that of adults and decreases with age. Projected cell area, cell perimeter, and average distance to the nearest neighbors increase with age but do so distinctly between the two layers. Structural entropy is different between the two strata, but remains constant with time. For all ages and layers, the distribution of the number of nearest neighbors is typical of a cooperator network architecture. The topological analysis provides evidence of the maturation process in infant skin. The differences between infant and adult are more pronounced in the SG than SS, while cell cooperation is evident in all cases of healthy skin examined.
Internal phase transition induced by external forces in Finsler geometric model for membranes
NASA Astrophysics Data System (ADS)
Koibuchi, Hiroshi; Shobukhov, Andrey
2016-10-01
In this paper, we numerically study an anisotropic shape transformation of membranes under external forces for two-dimensional triangulated surfaces on the basis of Finsler geometry. The Finsler metric is defined by using a vector field, which is the tangential component of a three-dimensional unit vector σ corresponding to the tilt or some external macromolecules on the surface of disk topology. The sigma model Hamiltonian is assumed for the tangential component of σ with the interaction coefficient λ. For large (small) λ, the surface becomes oblong (collapsed) at relatively small bending rigidity. For the intermediate λ, the surface becomes planar. Conversely, fixing the surface with the boundary of area A or with the two-point boundaries of distance L, we find that the variable σ changes from random to aligned state with increasing of A or L for the intermediate region of λ. This implies that an internal phase transition for σ is triggered not only by the thermal fluctuations, but also by external mechanical forces. We also find that the frame (string) tension shows the expected scaling behavior with respect to A/N (L/N) at the intermediate region of A (L) where the σ configuration changes between the disordered and ordered phases. Moreover, we find that the string tension γ at sufficiently large λ is considerably smaller than that at small λ. This phenomenon resembles the so-called soft-elasticity in the liquid crystal elastomer, which is deformed by small external tensile forces.
Strain-induced topological transition in SrRu2O6 and CaOs2O6
NASA Astrophysics Data System (ADS)
Ochi, Masayuki; Arita, Ryotaro; Trivedi, Nandini; Okamoto, Satoshi
2016-05-01
The topological property of SrRu2O6 and isostructural CaOs2O6 under various strain conditions is investigated using density functional theory. Based on an analysis of parity eigenvalues, we anticipate that a three-dimensional strong topological insulating state should be realized when band inversion is induced at the A point in the hexagonal Brillouin zone. For SrRu2O6 , such a transition requires rather unrealistic tuning, where only the c axis is reduced while other structural parameters are unchanged. However, given the larger spin-orbit coupling and smaller lattice constants in CaOs2O6 , the desired topological transition does occur under uniform compressive strain. Our study paves a way to realize a topological insulating state in a complex oxide, which has not been experimentally demonstrated so far.
Strain-induced topological transition in SrRu2O6 and CaOs2O6
Ochi, Masayuki; Arita, Ryotaro; Trivedi, Nandini; Okamoto, Satoshi
2016-05-24
The topological property of SrRu$_2$O$_6$ and isostructural CaOs$_2$O$_6$ under various strain conditions is investigated using density functional theory. Based on an analysis of parity eigenvalues, we anticipate that a three-dimensional strong topological insulating state should be realized when band inversion is induced at the A point in the hexagonal Brillouin zone. For SrRu$_2$O$_6$, such a transition requires rather unrealistic tuning, where only the $c$ axis is reduced while other structural parameters are unchanged. However, given the larger spin-orbit coupling and smaller lattice constants in CaOs$_2$O$_6$, the desired topological transition does occur under uniform compressive strain. Our study paves a waymore » to realize a topological insulating state in a complex oxide, which has not been experimentally demonstrated so far.« less
Correlation-Driven Topological Fermi Surface Transition in FeSe.
Leonov, I; Skornyakov, S L; Anisimov, V I; Vollhardt, D
2015-09-01
The electronic structure and phase stability of paramagnetic FeSe is computed by using a combination of ab initio methods for calculating band structure and dynamical mean-field theory. Our results reveal a topological change (Lifshitz transition) of the Fermi surface upon a moderate expansion of the lattice. The Lifshitz transition is accompanied with a sharp increase of the local moments and results in an entire reconstruction of magnetic correlations from the in-plane magnetic wave vector, (π,π) to (π,0). We attribute this behavior to a correlation-induced shift of the van Hove singularity originating from the d(xy) and d(xz)/d(yz) bands at the M point across the Fermi level. We propose that superconductivity is strongly influenced, or even induced, by a van Hove singularity.
Correlation-Driven Topological Fermi Surface Transition in FeSe.
Leonov, I; Skornyakov, S L; Anisimov, V I; Vollhardt, D
2015-09-01
The electronic structure and phase stability of paramagnetic FeSe is computed by using a combination of ab initio methods for calculating band structure and dynamical mean-field theory. Our results reveal a topological change (Lifshitz transition) of the Fermi surface upon a moderate expansion of the lattice. The Lifshitz transition is accompanied with a sharp increase of the local moments and results in an entire reconstruction of magnetic correlations from the in-plane magnetic wave vector, (π,π) to (π,0). We attribute this behavior to a correlation-induced shift of the van Hove singularity originating from the d(xy) and d(xz)/d(yz) bands at the M point across the Fermi level. We propose that superconductivity is strongly influenced, or even induced, by a van Hove singularity. PMID:26382687
Electronic Topological Transition in Ag2Te at High-pressure
Zhang, Yuhang; Li, Yan; Ma, Yanmei; Li, Yuwei; Li, Guanghui; Shao, Xuecheng; Wang, Hui; Cui, Tian; Wang, Xin; Zhu, Pinwen
2015-01-01
Recently, Ag2Te was experimentally confirmed to be a 3D topological insulator (TI) at ambient pressure. However, the high-pressure behaviors and properties of Ag2Te were rarely reported. Here, a pressure-induced electronic topological transition (ETT) is firstly found in Ag2Te at 1.8 GPa. Before ETT, the positive pressure coefficient of bulk band-gap, which is firstly found in TIs family, is found by both first-principle calculations and in situ high-pressure resistivity measurements. The electrical resistivity obtained at room temperature shows a maximum at 1.8 GPa, which is nearly 3.3 times to that at ambient pressure. This result indicates that the best bulk insulating character and topological nature in Ag2Te can be obtained at this pressure. Furthermore, the high-pressure structural behavior of Ag2Te has been investigated by in situ high-pressure synchrotron powder X-ray diffraction technique up to 33.0 GPa. The accurate pressure-induced phase transition sequence is firstly determined as P21/c → Cmca → Pnma. It is worth noting that the reported isostructural P21/c phase is not existed, and the reported structure of Cmca phase is corrected by CALYPSO methodology. The second high-pressure structure, a long puzzle to previous reports, is determined as Pnma phase. A pressure-induced metallization in Ag2Te is confirmed by the results of temperature-dependent resistivity measurements. PMID:26419707
Quantum Oscillation Signatures of Pressure-induced Topological Phase Transition in BiTeI
Park, Joonbum; Jin, Kyung-Hwan; Jo, Y. J.; Choi, E. S.; Kang, W.; Kampert, E.; Rhyee, J.-S.; Jhi, Seung-Hoon; Kim, Jun Sung
2015-01-01
We report the pressure-induced topological quantum phase transition of BiTeI single crystals using Shubnikov-de Haas oscillations of bulk Fermi surfaces. The sizes of the inner and the outer FSs of the Rashba-split bands exhibit opposite pressure dependence up to P = 3.35 GPa, indicating pressure-tunable Rashba effect. Above a critical pressure P ~ 2 GPa, the Shubnikov-de Haas frequency for the inner Fermi surface increases unusually with pressure, and the Shubnikov-de Haas oscillations for the outer Fermi surface shows an abrupt phase shift. In comparison with band structure calculations, we find that these unusual behaviors originate from the Fermi surface shape change due to pressure-induced band inversion. These results clearly demonstrate that the topological quantum phase transition is intimately tied to the shape of bulk Fermi surfaces enclosing the time-reversal invariant momenta with band inversion. PMID:26522628
Electronic correlations and topological Fermi surface transition in the iron-based chalcogenides
NASA Astrophysics Data System (ADS)
Skornyakov, S.; Leonov, I.; Anisimov, V. I.; Vollhardt, D.
We present results of a theoretical investigation of the electronic structure and phase stability of paramagnetic FeSe obtained within a combination of abinitio methods for calculating band structure and dynamical mean-field theory. Our results reveal an entire reconstruction of the Fermi surface topology upon a moderate expansion of the lattice (Lifshitz transition), with a change of magnetic correlations from the in-plane magnetic wave vector (π , π) to (π , 0) . We attribute this behavior to a correlation-induced shift of the Van Hove singularity originating from the xy and xz / yz bands at the M-point across the Fermi level. Our results predict a structural transition of FeSe upon a ca. 10 % expansion of the lattice volume as well as a topological change of the Fermi surface of FeSe upon partial substitution Se by Te, which is accompanied with a sharp increase of the local moments. We expect that these changes are responsible for the experimentally observed increase of Tc in FeSe upon doping with Te. The microscopic origin for superconductivity in this system is then due to a Van Hove singularity close to the Fermi level. This identification may open a new route to increase Tc even further.
Pressure-induced electronic topological transition in Sb2S3
NASA Astrophysics Data System (ADS)
Sorb, Y. A.; Rajaji, V.; Malavi, P. S.; Subbarao, U.; Halappa, P.; Peter, S. C.; Karmakar, S.; Narayana, C.
2016-01-01
We report the high-pressure vibrational properties and a pressure-induced electronic topological transition in the wide bandgap semiconductor Sb2S3 (E g = 1.7-1.8 eV) using Raman spectroscopy, resistivity and x-ray diffraction (XRD) studies. In this report, high-pressure Raman spectroscopy and resistivity studies of Sb2S3 have been carried out to 22 GPa and 11 GPa, respectively. We observed the softening of phonon modes A\\text{g}2 , A\\text{g}3 and B 2g and a sharp anomaly in their line widths at 4 GPa. The resistivity studies corroborate this anomaly around similar pressures. The changes in resistivity as well as Raman line widths can be ascribed to the strong phonon-phonon coupling, indicating clear evidence of isostructural electronic topological transition in Sb2S3. The previously reported pressure dependence of a/c ratio plot obtained also showed a minimum at ~5 GPa consistent with our high-pressure Raman and resistivity results.
Slow quenches in a quantum Ising chain: Dynamical phase transitions and topology
NASA Astrophysics Data System (ADS)
Sharma, Shraddha; Divakaran, Uma; Polkovnikov, Anatoli; Dutta, Amit
2016-04-01
We study the slow quenching dynamics (characterized by an inverse rate τ-1) of a one-dimensional transverse Ising chain with nearest neighbor ferromagentic interactions across the quantum critical point (QCP) and analyze the Loschmidt overlap measured using the subsequent temporal evolution of the final wave function (reached at the end of the quenching) with the final time-independent Hamiltonian. Studying the Fisher zeros of the corresponding generalized "partition function," we probe nonanalyticities manifested in the rate function of the return probability known as dynamical phase transitions (DPTs). In contrast to the sudden quenching case, we show that DPTs survive in the subsequent temporal evolution following the quenching across two critical points of the model for a sufficiently slow rate; furthermore, an interesting "lobe" structure of Fisher zeros emerge. We have also made a connection to topological aspects studying the dynamical topological order parameter [νD(t ) ] as a function of time (t ) measured from the instant when the quenching is complete. Remarkably, the time evolution of νD(t ) exhibits drastically different behavior following quenches across a single QCP and two QCPs. In the former case, νD(t ) increases stepwise by unity at every DPT (i.e., Δ νD=1 ). In the latter case, on the other hand, νD(t ) essentially oscillates between 0 and 1 (i.e., successive DPTs occur with Δ νD=1 and Δ νD=-1 , respectively), except for instants where it shows a sudden jump by a factor of unity when two successive DPTs carry a topological charge of the same sign.
NASA Astrophysics Data System (ADS)
Mondragon-Shem, Ian; Song, Juntao; Hughes, Taylor L.; Prodan, Emil
2014-03-01
We study the disorder-induced topological phase transition of a one-dimensional model belonging to class AIII of the Altland-Zirnbauer classification of fermions. To characterize the topological state, we derive a covariant real-space representation of the integer invariant. Using this invariant, we show that the system remains topological even after all the single particle states of the system become localized and the energy spectrum becomes gapless. For a critical disorder strength which we compute analytically, there emerges a delocalized state at zero energy where the topological invariant changes value and the nontrivial ground state transforms into a trivial one. This type of topological phase transition is fundamentally different from the levitation and annihilation paradigm that is found in higher-dimensional systems e.g. the quantum Hall state. In order to understand this type of phase transition, we map the system to a spin-1/2 model which provides an insightful real-space picture of the underlying physics near the critical point. EP and JTS were supported by U.S. NSF grants DMS 1066045, DMR-1056168, NSFC grant 11204065 and RFDPHEC grant. A2013205168. TLH and IM-S were supported by ONR Grant No. N0014-12-1-0935.
NASA Astrophysics Data System (ADS)
Chou, Po-Hao; Zhai, Liang-Jun; Chung, Chung-Hou; Lee, Ting-Kuo; Mou, Chung-Yu
The energy gap in Dirac materials controls the topology and critical behaviors of the quantum phase transition associated with the critical point when the gap vanishes. However, it is often difficult to access the critical point as it requires tunablity of electronic structures. Here by exploiting the many-body screening interaction of localized spins and conduction electrons in a Kondo lattice, we demonstrate that the electronic band structures in a Kondo lattice are tunable in temperature. When spin-orbit interactions are included, we find that below the Kondo temperature, the Kondo lattice is a strong topological insulator at low temperature and undergoes a topological transition to a weak topological insulator at a higher temperature TD. At TD, Dirac points emerge and the Kondo lattice becomes a Dirac semimetal. Our results indicate that the topological phase transition though a Dirac semi-metallic phase at finite temperatures also manifests profound physics and results in critical-like behavior both in magnetic and transport properties near TD. We acknowledge support from NCTS and Ministry of Science and Technology (MoST), Taiwan.
Li, Wei
2016-06-01
This paper considers a unified geometric projection approach for: 1) decomposing a general system of cooperative agents coupled via Laplacian matrices or stochastic matrices and 2) deriving a centroid-subsystem and many shape-subsystems, where each shape-subsystem has the distinct properties (e.g., preservation of formation and stability of the original system, sufficiently simple structures and explicit formation evolution of agents, and decoupling from the centroid-subsystem) which will facilitate subsequent analyses. Particularly, this paper provides an additional merit of the approach: considering adjustments of coupling topologies of agents which frequently occur in system design (e.g., to add or remove an edge, to move an edge to a new place, and to change the weight of an edge), the corresponding new shape-subsystems can be derived by a few simple computations merely from the old shape-subsystems and without referring to the original system, which will provide further convenience for analysis and flexibility of choice. Finally, such fast recalculations of new subsystems under topology adjustments are provided with examples. PMID:26955056
NASA Astrophysics Data System (ADS)
Campione, Salvatore; Luk, Ting S.; Liu, Sheng; Sinclair, Michael B.
2015-09-01
We employ both the effective medium approximation (EMA) and Bloch theory to compare the dispersion properties of semiconductor hyperbolic metamaterials (SHMs) at mid-infrared frequencies and metallic hyperbolic metamaterials (MHMs) at visible frequencies. This analysis reveals the conditions under which the EMA can be safely applied for both MHMs and SHMs. We find that the combination of precise nanoscale layering and the longer infrared operating wavelengths puts the SHMs well within the effective medium limit and, in contrast to MHMs, allows the attainment of very high photon momentum states. In addition, SHMs allow for new phenomena such as ultrafast creation of the hyperbolic manifold through optical pumping. In particular, we examine the possibility of achieving ultrafast topological transitions through optical pumping which can photo-dope appropriately designed quantum wells on the femtosecond time scale.
Campione, Salvatore; Liu, Sheng; Luk, Ting S.; Sinclair, Michael B.
2015-08-05
We employ both the effective medium approximation (EMA) and Bloch theory to compare the dispersion properties of semiconductor hyperbolic metamaterials (SHMs) at mid-infrared frequencies and metallic hyperbolic metamaterials (MHMs) at visible frequencies. This analysis reveals the conditions under which the EMA can be safely applied for both MHMs and SHMs. We find that the combination of precise nanoscale layering and the longer infrared operating wavelengths puts the SHMs well within the effective medium limit and, in contrast to MHMs, allows for the attainment of very high photon momentum states. Additionally, SHMs allow for new phenomena such as ultrafast creation of the hyperbolic manifold through optical pumping. Furthermore, we examine the possibility of achieving ultrafast topological transitions through optical pumping which can photo-dope appropriately designed quantum wells on the femtosecond time scale.
Local electronic structures and 2D topological phase transition of ultrathin Sb films
NASA Astrophysics Data System (ADS)
Kim, Sunghwan; Jin, Kyung-Hwan; Park, Joonbum; Kim, Jun Sung; Jhi, Seung-Hoon; Yeom, Han Woong
We investigate local electronic structures of ultrathin Sb islands and their edges grown on Bi2Te2Se by scanning tunneling microscopy/spectroscopy (STM/STS) and density functional theory (DFT) calculations. The Sb islands of various thickness are grown with atomically well ordered edge structure over the 3 bilayers (BL). On the surfaces and edges of these islands, we clearly resolve edge-localized electronic states by STS measurements, which depend on the thickness. The DFT calculations identify that the strongly localized edge states of 4 and 5 BL films correspond to a quantum spin Hall (QSH) states while the edge states of 3 BL are trivial. Our experimental and theoretical results confirm the 2D topological phase transition of the ultrathin Sb films from trivial to QSH phase. Center for Artificial Low Dimensional Electronic Systems, Institute for Basic Science and Department of Physics, Pohang University of Science and Technology, Korea.
Exotic topological states near a quantum metal-insulator transition in pyrochlore iridates
NASA Astrophysics Data System (ADS)
Tian, Zhaoming
Pyrochlore iridates have attracted great interest as prime candidates that may host topologically nontrivial states, spin ice ordering and quantum spin liquid states, in particular through the interplay between different degrees of freedom, such as local moments and mobile electrons. Based on our extensive study using our high quality single crystals, we will discuss such examples, i.e. chiral spin liquid in a quadratic band touching state, Weyl semimetallic state and chiral domain wall transport nearby a quantum insulator-semimetal transition in pyrochlore iridates. This work is based on the collaboration with Nakatsuji Satoru, Kohama Yoshimitsu, Tomita Takahiro, Kindo Koichi, Jun J. Ishikawa, Balents Leon, Ishizuka Hiroaki, Timothy H. Hsieh. ZM. Tian was supported by JSPS Postdoctoral Fellowship (No.P1402).
Campione, Salvatore; Liu, Sheng; Luk, Ting S.; Sinclair, Michael B.
2015-08-05
We employ both the effective medium approximation (EMA) and Bloch theory to compare the dispersion properties of semiconductor hyperbolic metamaterials (SHMs) at mid-infrared frequencies and metallic hyperbolic metamaterials (MHMs) at visible frequencies. This analysis reveals the conditions under which the EMA can be safely applied for both MHMs and SHMs. We find that the combination of precise nanoscale layering and the longer infrared operating wavelengths puts the SHMs well within the effective medium limit and, in contrast to MHMs, allows for the attainment of very high photon momentum states. Additionally, SHMs allow for new phenomena such as ultrafast creation ofmore » the hyperbolic manifold through optical pumping. Furthermore, we examine the possibility of achieving ultrafast topological transitions through optical pumping which can photo-dope appropriately designed quantum wells on the femtosecond time scale.« less
NASA Astrophysics Data System (ADS)
Kim, Heon-Jung; Kim, Ki-Seok; Wang, J.-F.; Kulbachinskii, V. A.; Ogawa, K.; Sasaki, M.; Ohnishi, A.; Kitaura, M.; Wu, Y.-Y.; Li, L.; Yamamoto, I.; Azuma, J.; Kamada, M.; Dobrosavljević, V.
2013-03-01
We propose a phase diagram for FexBi2Te3 (0≤x≤0.1) single crystals, which belong to a class of magnetically bulk-doped topological insulators. The evolution of magnetic correlations from ferromagnetic to antiferromagnetic gives rise to topological phase transitions, where the paramagnetic topological insulator of Bi2Te3 turns into a band insulator with ferromagnetic-cluster glassy behavior around x˜0.025, and it further evolves to a topological insulator with valence-bond glassy behavior, which spans over the region from x˜0.03 up to x˜0.1. This phase diagram is verified by measuring magnetization, magnetotransport, and angle-resolved photoemission spectra with theoretical discussions.
Schoop, Leslie M.; Xie, Lilia S.; Chen, Ru; Gibson, Quinn D.; Lapidus, Saul H.; Kimchi, Itamar; Hirschberger, Max; Haldolaarachchige, Neel; Ali, Mazhar N.; Belvin, Carina A.; Liang, Tian; Neaton, Jeffrey B.; Ong, N P; Vishwanath, Ashvin; Cava, R. J.
2015-06-23
Three-dimensionalDirac semimetals (DSMs) arematerials that have masslessDirac electrons and exhibit exotic physical properties. It has been suggested that structurally distorting a DSM can create a topological insulator but this has not yet been experimentally verified. Furthermore, Majorana fermions have been theoretically proposed to exist inmaterials that exhibit both superconductivity and topological surface states. Herewe showthat the cubic Laves phase Au2Pb has a bulk Dirac cone that is predicted to gap on cooling through a structural phase transition at 100 K. The low temperature phase can be assigned a Z(2) = -1 topological index, and this phase becomes superconducting below 1.2 K. These characteristics make Au2Pb a unique platform for studying the transition between bulk Dirac electrons and topological surface states as well as studying the interaction of superconductivity with topological surface states, combining many different properties of emergent materials-superconductivity, bulk Dirac electrons, and a topologically nontrivial Z(2) invariant.
Pacaud, F.; Micoulaut, M.
2015-08-14
The thermodynamic, dynamic, structural, and rigidity properties of densified liquid germania (GeO{sub 2}) have been investigated using classical molecular dynamics simulation. We construct from a thermodynamic framework an analytical equation of state for the liquid allowing the possible detection of thermodynamic precursors (extrema of the derivatives of the free energy), which usually indicate the possibility of a liquid-liquid transition. It is found that for the present germania system, such precursors and the possible underlying liquid-liquid transition are hidden by the slowing down of the dynamics with decreasing temperature. In this respect, germania behaves quite differently when compared to parent tetrahedral systems such as silica or water. We then detect a diffusivity anomaly (a maximum of diffusion with changing density/volume) that is strongly correlated with changes in coordinated species, and the softening of bond-bending (BB) topological constraints that decrease the liquid rigidity and enhance transport. The diffusivity anomaly is finally substantiated from a Rosenfeld-type scaling law linked to the pair correlation entropy, and to structural relaxation.
Zero-field and time-reserval-symmetry-broken topological phase transitions in graphene
NASA Astrophysics Data System (ADS)
Guassi, Marcos R.; Diniz, Ginetom S.; Sandler, Nancy; Qu, Fanyao
2015-08-01
We propose a quantum electronic device based on a strained graphene nanoribbon. Mechanical strain, internal exchange field, and spin-orbit couplings (SOCs) have been exploited as principle parameters to tune physical properties of the device. We predict a remarkable zero-field topological quantum phase transition between the time-reversal-symmetry-broken quantum spin Hall (QSH) and quantum anomalous Hall states, which was previously thought to take place only in the presence of finite magnetic field. We illustrate as intrinsic SOC is tuned, how two different helicity edge states located in the opposite edges of the nanoribbon exchange their locations. Our results indicate that the pseudomagnetic field induced by the strain could be coupled to the spin degrees of freedom through the SOC responsible for the stability of a QSH state. The controllability of this zero-field phase transition with strength and direction of the strain is also demonstrated. Our prediction offers a tempting prospect of strain, electric, and magnetic manipulation of the QSH effect.
Distortion Pathways of Transition Metal Coordination Polyhedra Induced by Chelating Topology.
Alvarez, Santiago
2015-12-23
A continuous shape measures analysis of the coordination polyhedra of a host of transition metal complexes with bi- and multidentate ligands discloses the distortion pathway associated with each particular topology of the chelate rings formed. The basic parameter that controls the degree of distortion is the metal-donor atom bond distance that induces nonideal bond angles due to the rigidity of the ligands. Thus, the degree of distortion within each family of complexes depends on the atomic size, on which the high- or low-spin state has a large effect. Special attention is therefore paid to several spin-crossover systems and to the enhanced distortions that go along with the transition from low- to high-spin state affected by temperature, light, or pressure. Several families of complexes show deviations from the expected distortion pathways in the high-spin state that can be associated to the onset of intermolecular interactions such as secondary coordination of counterions or solvent molecules. Also, significant displacement of counterions in an extended solid may result from the changes in metal-ligand bond distances when ligands are involved in intermolecular hydrogen bonding. PMID:26575868
NASA Astrophysics Data System (ADS)
Caporaso, Nicola; Cirafici, Michele; Griguolo, Luca; Pasquetti, Sara; Seminara, Domenico; Szabo, Richard J.
2006-01-01
We continue our study of the large N phase transition in q-deformed Yang-Mills theory on the sphere and its role in connecting topological strings to black hole entropy. We study in detail the chiral theory defined in terms of uncoupled single U(N) representations at large N and write down the resulting partition function by means of the topological vertex. The emergent toric geometry has three Kähler parameters, one of which corresponds to the expected fibration over Bbb P1. By taking a suitable double-scaling limit we recover the chiral Gross-Taylor string expansion. To analyse the phase transition we construct a matrix model which describes the chiral gauge theory. It has three distinct phases, one of which should be described by the closed topological string expansion. We verify this expectation by explicit comparison between the matrix model and the chiral topological string free energies. We also show that the critical point in the pertinent phase of the matrix model corresponds to a divergence of the topological string perturbation series.
Wang, Hsiu-Wen; Bishop, David
2012-01-01
Relative humidity (PH2O, partial pressure of water)-dependent dehydration and accompanying phase transitions in NAT-topology zeolites (natrolite, scolecite, and mesolite) were studied under controlled temperature and known PH2O conditions by in situ diffuse-reflectance infrared Fourier transform spectroscopy and parallel X-ray powder diffraction. Dehydration was characterized by the disappearance of internal H2O vibrational modes. The loss of H2O molecules caused a sequence of structural transitions in which the host framework transformation path was coupled primarily via the thermal motion of guest Na?/Ca2? cations and H2O molecules. The observation of different interactions of H2O molecules and Na?/Ca2? cations with host aluminosilicate frameworks under highand low-PH2O conditions indicated the development of different local strain fields, arising from cation H2O interactions in NAT-type channels. These strain fields influence the Si O/Al O bond strength and tilting angles within and between tetrahedra as the dehydration temperature is approached. The newly observed infrared bands (at 2,139 cm-1 in natrolite, 2,276 cm-1 in scolecite, and 2,176 and 2,259 cm-1 in mesolite) result from strong cation H2O Al Si framework interactions in NAT-type channels, and these bands can be used to evaluate the energetic evolution of Na?/Ca2? cations before and after phase transitions, especially for scolecite and mesolite. The 2,176 and 2,259 cm-1 absorption bands in mesolite also appear to be related to Na?/Ca2? order disorder that occur when mesolite loses its Ow4 H2O molecules.
Topological phase transitions and chiral inelastic transport induced by the squeezing of light.
Peano, Vittorio; Houde, Martin; Brendel, Christian; Marquardt, Florian; Clerk, Aashish A
2016-03-02
There is enormous interest in engineering topological photonic systems. Despite intense activity, most works on topological photonic states (and more generally bosonic states) amount in the end to replicating a well-known fermionic single-particle Hamiltonian. Here we show how the squeezing of light can lead to the formation of qualitatively new kinds of topological states. Such states are characterized by non-trivial Chern numbers, and exhibit protected edge modes, which give rise to chiral elastic and inelastic photon transport. These topological bosonic states are not equivalent to their fermionic (topological superconductor) counterparts and, in addition, cannot be mapped by a local transformation onto topological states found in particle-conserving models. They thus represent a new type of topological system. We study this physics in detail in the case of a kagome lattice model, and discuss possible realizations using nonlinear photonic crystals or superconducting circuits.
Topological phase transitions and chiral inelastic transport induced by the squeezing of light
Peano, Vittorio; Houde, Martin; Brendel, Christian; Marquardt, Florian; Clerk, Aashish A.
2016-01-01
There is enormous interest in engineering topological photonic systems. Despite intense activity, most works on topological photonic states (and more generally bosonic states) amount in the end to replicating a well-known fermionic single-particle Hamiltonian. Here we show how the squeezing of light can lead to the formation of qualitatively new kinds of topological states. Such states are characterized by non-trivial Chern numbers, and exhibit protected edge modes, which give rise to chiral elastic and inelastic photon transport. These topological bosonic states are not equivalent to their fermionic (topological superconductor) counterparts and, in addition, cannot be mapped by a local transformation onto topological states found in particle-conserving models. They thus represent a new type of topological system. We study this physics in detail in the case of a kagome lattice model, and discuss possible realizations using nonlinear photonic crystals or superconducting circuits. PMID:26931620
NASA Astrophysics Data System (ADS)
Ramamurthy, Rajesh; Harding, Kevin; Du, Xiaoming; Lucas, Vincent; Liao, Yi; Paul, Ratnadeep; Jia, Tao
2015-05-01
Optical measurement techniques are often employed to digitally capture three dimensional shapes of components. The digital data density output from these probes range from a few discrete points to exceeding millions of points in the point cloud. The point cloud taken as a whole represents a discretized measurement of the actual 3D shape of the surface of the component inspected to the measurement resolution of the sensor. Embedded within the measurement are the various features of the part that make up its overall shape. Part designers are often interested in the feature information since those relate directly to part function and to the analytical models used to develop the part design. Furthermore, tolerances are added to these dimensional features, making their extraction a requirement for the manufacturing quality plan of the product. The task of "extracting" these design features from the point cloud is a post processing task. Due to measurement repeatability and cycle time requirements often automated feature extraction from measurement data is required. The presence of non-ideal features such as high frequency optical noise and surface roughness can significantly complicate this feature extraction process. This research describes a robust process for extracting linear and arc segments from general 2D point clouds, to a prescribed tolerance. The feature extraction process generates the topology, specifically the number of linear and arc segments, and the geometry equations of the linear and arc segments automatically from the input 2D point clouds. This general feature extraction methodology has been employed as an integral part of the automated post processing algorithms of 3D data of fine features.
NASA Astrophysics Data System (ADS)
Callan-Jones, Andrew
Topological defects play several roles in the physics of liquid crystalline matter. Their presence is felt over many length scales, necessitating modeling strategies ranging from continuum level finite element analysis of cholesteric elastomers to molecular dynamics simulation of liquid nematics. We have first studied the effect of a strain applied to a cholesteric elastomer, focusing on the transition from the twisted phase to the nematic phase, and extended work by others by including the Frank penalty for director distortions. This leads to metastability of the twisted state above the transition, prompting us to consider nucleation of topological defects as way to remove the twist walls. We explored the consequences of this idea and obtained analytical and numerical agreement, concluding that inhomogeneities in the strain field due to the coexisting phases are small, making the nucleation problem very similar to earlier studies on cholesteric liquids unwound by a magnetic field. Molecular dynamics simulations of a temperature quench of a fluid of rod-like molecules based on the Gay-Berne potential provide a way to study multiscale phenomena associated with defects, such as the structure of the core and the interaction between defect motion and the underlying orientational degrees of freedom. Locating and then studying defects in a fluid, as opposed to in a lattice simulation, however, are inherently challenging problems because of the mobility of the molecules. We have collaborated with researchers in scientific visualization to develop methods that overcome limitations of an earlier discrete finding method. In particular, new measures for describing nematic ordering are introduced, making observation of features such as the defect type and the nature of the core readily done. The dramatic improvement in spatial and temporal resolution of defect behavior afforded by the visualization opens up a number of possible routes to follow in studying static and dynamic
Kachalo, Sëma; Naveed, Hammad; Cao, Youfang; Zhao, Jieling; Liang, Jie
2015-01-01
Geometric and mechanical properties of individual cells and interactions among neighboring cells are the basis of formation of tissue patterns. Understanding the complex interplay of cells is essential for gaining insight into embryogenesis, tissue development, and other emerging behavior. Here we describe a cell model and an efficient geometric algorithm for studying the dynamic process of tissue formation in 2D (e.g. epithelial tissues). Our approach improves upon previous methods by incorporating properties of individual cells as well as detailed description of the dynamic growth process, with all topological changes accounted for. Cell size, shape, and division plane orientation are modeled realistically. In addition, cell birth, cell growth, cell shrinkage, cell death, cell division, cell collision, and cell rearrangements are now fully accounted for. Different models of cell-cell interactions, such as lateral inhibition during the process of growth, can be studied in detail. Cellular pattern formation for monolayered tissues from arbitrary initial conditions, including that of a single cell, can also be studied in detail. Computational efficiency is achieved through the employment of a special data structure that ensures access to neighboring cells in constant time, without additional space requirement. We have successfully generated tissues consisting of more than 20,000 cells starting from 2 cells within 1 hour. We show that our model can be used to study embryogenesis, tissue fusion, and cell apoptosis. We give detailed study of the classical developmental process of bristle formation on the epidermis of D. melanogaster and the fundamental problem of homeostatic size control in epithelial tissues. Simulation results reveal significant roles of solubility of secreted factors in both the bristle formation and the homeostatic control of tissue size. Our method can be used to study broad problems in monolayered tissue formation. Our software is publicly
Liu, Minhao; Wang, Wudi; Richardella, Anthony R.; Kandala, Abhinav; Li, Jian; Yazdani, Ali; Samarth, Nitin; Ong, N. Phuan
2016-01-01
A striking prediction in topological insulators is the appearance of the quantized Hall resistance when the surface states are magnetized. The surface Dirac states become gapped everywhere on the surface, but chiral edge states remain on the edges. In an applied current, the edge states produce a quantized Hall resistance that equals the Chern number C = ±1 (in natural units), even in zero magnetic field. This quantum anomalous Hall effect was observed by Chang et al. With reversal of the magnetic field, the system is trapped in a metastable state because of magnetic anisotropy. We investigate how the system escapes the metastable state at low temperatures (10 to 200 mK). When the dissipation (measured by the longitudinal resistance) is ultralow, we find that the system escapes by making a few very rapid transitions, as detected by large jumps in the Hall and longitudinal resistances. Using the field at which the initial jump occurs to estimate the escape rate, we find that raising the temperature strongly suppresses the rate. From a detailed map of the resistance versus gate voltage and temperature, we show that dissipation strongly affects the escape rate. We compare the observations with dissipative quantum tunneling predictions. In the ultralow dissipation regime, two temperature scales (T1 ~ 70 mK and T2 ~ 145 mK) exist, between which jumps can be observed. The jumps display a spatial correlation that extends over a large fraction of the sample. PMID:27482539
Dyachenko, P N; Molesky, S; Petrov, A Yu; Störmer, M; Krekeler, T; Lang, S; Ritter, M; Jacob, Z; Eich, M
2016-06-06
Control of thermal radiation at high temperatures is vital for waste heat recovery and for high-efficiency thermophotovoltaic (TPV) conversion. Previously, structural resonances utilizing gratings, thin film resonances, metasurfaces and photonic crystals were used to spectrally control thermal emission, often requiring lithographic structuring of the surface and causing significant angle dependence. In contrast, here, we demonstrate a refractory W-HfO2 metamaterial, which controls thermal emission through an engineered dielectric response function. The epsilon-near-zero frequency of a metamaterial and the connected optical topological transition (OTT) are adjusted to selectively enhance and suppress the thermal emission in the near-infrared spectrum, crucial for improved TPV efficiency. The near-omnidirectional and spectrally selective emitter is obtained as the emission changes due to material properties and not due to resonances or interference effects, marking a paradigm shift in thermal engineering approaches. We experimentally demonstrate the OTT in a thermally stable metamaterial at high temperatures of 1,000 °C.
NASA Astrophysics Data System (ADS)
Dyachenko, P. N.; Molesky, S.; Petrov, A. Yu; Störmer, M.; Krekeler, T.; Lang, S.; Ritter, M.; Jacob, Z.; Eich, M.
2016-06-01
Control of thermal radiation at high temperatures is vital for waste heat recovery and for high-efficiency thermophotovoltaic (TPV) conversion. Previously, structural resonances utilizing gratings, thin film resonances, metasurfaces and photonic crystals were used to spectrally control thermal emission, often requiring lithographic structuring of the surface and causing significant angle dependence. In contrast, here, we demonstrate a refractory W-HfO2 metamaterial, which controls thermal emission through an engineered dielectric response function. The epsilon-near-zero frequency of a metamaterial and the connected optical topological transition (OTT) are adjusted to selectively enhance and suppress the thermal emission in the near-infrared spectrum, crucial for improved TPV efficiency. The near-omnidirectional and spectrally selective emitter is obtained as the emission changes due to material properties and not due to resonances or interference effects, marking a paradigm shift in thermal engineering approaches. We experimentally demonstrate the OTT in a thermally stable metamaterial at high temperatures of 1,000 °C.
NASA Astrophysics Data System (ADS)
Lyanda-Geller, Yuli; Simion, George
2015-03-01
We investigate a ground state of the two-dimensional (2D) electron liquid in the presence of disorder for Landau level filling factors, for which the re-entrant integer quantum Hall effect is observed. Our particular interest is the range of filling factors, which in a clean 2D system is favorable to formation of the two-electron (2e) bubble crystal. For the smooth random potential due to charged impurities placed far away from the 2D gas, the ground state is a lightly distorted 2e bubble crystal. However, for positively or negatively charged residual impurities located approximately within about three magnetic lengths from the 2D electrons, the ground state contains charged 2e complexes formed either by positively charged impurity and 3e defect bubble, or negatively charged impurity and 2e defect bubble. In the vicinity of 1e and 3e defect bubbles, the 2e bubbles of the crystal change their shape from round to elongated forming hedgehog (for 1e defect) or vortex (for 3e defect) textures. The topological textures due to these complexes interact with vortex and hedgehog excitations, generated as temperature increases that are not bound by residual impurities. The temperature of insulator to metal transition calculated with both bound and unbound defects agrees with experiment. Research was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award DE-SC0010544.
Liu, Minhao; Wang, Wudi; Richardella, Anthony R; Kandala, Abhinav; Li, Jian; Yazdani, Ali; Samarth, Nitin; Ong, N Phuan
2016-07-01
A striking prediction in topological insulators is the appearance of the quantized Hall resistance when the surface states are magnetized. The surface Dirac states become gapped everywhere on the surface, but chiral edge states remain on the edges. In an applied current, the edge states produce a quantized Hall resistance that equals the Chern number C = ±1 (in natural units), even in zero magnetic field. This quantum anomalous Hall effect was observed by Chang et al. With reversal of the magnetic field, the system is trapped in a metastable state because of magnetic anisotropy. We investigate how the system escapes the metastable state at low temperatures (10 to 200 mK). When the dissipation (measured by the longitudinal resistance) is ultralow, we find that the system escapes by making a few very rapid transitions, as detected by large jumps in the Hall and longitudinal resistances. Using the field at which the initial jump occurs to estimate the escape rate, we find that raising the temperature strongly suppresses the rate. From a detailed map of the resistance versus gate voltage and temperature, we show that dissipation strongly affects the escape rate. We compare the observations with dissipative quantum tunneling predictions. In the ultralow dissipation regime, two temperature scales (T 1 ~ 70 mK and T 2 ~ 145 mK) exist, between which jumps can be observed. The jumps display a spatial correlation that extends over a large fraction of the sample. PMID:27482539
Dyachenko, P. N.; Molesky, S.; Petrov, A. Yu; Störmer, M.; Krekeler, T.; Lang, S.; Ritter, M.; Jacob, Z.; Eich, M.
2016-01-01
Control of thermal radiation at high temperatures is vital for waste heat recovery and for high-efficiency thermophotovoltaic (TPV) conversion. Previously, structural resonances utilizing gratings, thin film resonances, metasurfaces and photonic crystals were used to spectrally control thermal emission, often requiring lithographic structuring of the surface and causing significant angle dependence. In contrast, here, we demonstrate a refractory W-HfO2 metamaterial, which controls thermal emission through an engineered dielectric response function. The epsilon-near-zero frequency of a metamaterial and the connected optical topological transition (OTT) are adjusted to selectively enhance and suppress the thermal emission in the near-infrared spectrum, crucial for improved TPV efficiency. The near-omnidirectional and spectrally selective emitter is obtained as the emission changes due to material properties and not due to resonances or interference effects, marking a paradigm shift in thermal engineering approaches. We experimentally demonstrate the OTT in a thermally stable metamaterial at high temperatures of 1,000 °C. PMID:27263653
Dyachenko, P N; Molesky, S; Petrov, A Yu; Störmer, M; Krekeler, T; Lang, S; Ritter, M; Jacob, Z; Eich, M
2016-01-01
Control of thermal radiation at high temperatures is vital for waste heat recovery and for high-efficiency thermophotovoltaic (TPV) conversion. Previously, structural resonances utilizing gratings, thin film resonances, metasurfaces and photonic crystals were used to spectrally control thermal emission, often requiring lithographic structuring of the surface and causing significant angle dependence. In contrast, here, we demonstrate a refractory W-HfO2 metamaterial, which controls thermal emission through an engineered dielectric response function. The epsilon-near-zero frequency of a metamaterial and the connected optical topological transition (OTT) are adjusted to selectively enhance and suppress the thermal emission in the near-infrared spectrum, crucial for improved TPV efficiency. The near-omnidirectional and spectrally selective emitter is obtained as the emission changes due to material properties and not due to resonances or interference effects, marking a paradigm shift in thermal engineering approaches. We experimentally demonstrate the OTT in a thermally stable metamaterial at high temperatures of 1,000 °C. PMID:27263653
Xu, Lin; Wang, Hai-Xiao; Xu, Ya-Dong; Chen, Huan-Yang; Jiang, Jian-Hua
2016-08-01
A simple core-shell two-dimensional photonic crystal is studied where the triangular lattice symmetry and the C_{6} point group symmetry give rich physics in accidental touching points of photonic bands. We systematically evaluate different types of accidental nodal points at the Brillouin zone center for transverse-magnetic harmonic modes when the geometry and permittivity of the core-shell material are continuously tuned. The accidental nodal points can have different dispersions and topological properties (i.e., Berry phases). These accidental nodal points can be the critical states lying between a topological phase and a normal phase of the photonic crystal. They are thus very important for the study of topological photonic states. We show that, without breaking time-reversal symmetry, by tuning the geometry of the core-shell material, a phase transition into the photonic quantum spin Hall insulator can be achieved. Here the "spin" is defined as the orbital angular momentum of a photon. We study the topological phase transition as well as the properties of the edge and bulk states and their application potentials in optics. PMID:27505772
Magnetic transitions in the topological magnon insulator Cu(1,3-bdc)
NASA Astrophysics Data System (ADS)
Chisnell, R.; Helton, J. S.; Freedman, D. E.; Singh, D. K.; Demmel, F.; Stock, C.; Nocera, D. G.; Lee, Y. S.
2016-06-01
Topological magnon insulators are a new class of magnetic materials that possess topologically nontrivial magnon bands. As a result, magnons in these materials display properties analogous to those of electrons in topological insulators. Here we present magnetization, specific heat, and neutron scattering measurements of the ferromagnetic kagome magnet Cu(1,3-bdc). Our measurements provide a detailed description of the magnetic structure and interactions in this material and confirm that it is an ideal prototype for topological magnon physics in a system with a simple spin Hamiltonian.
NASA Astrophysics Data System (ADS)
Kim, Youngwook; Herlinger, Patrick; Moon, Pilkyung; Koshino, Mikito; Taniguchi, Takashi; Watanabe, Kenji; Smet, Jurgen H.
2016-08-01
Van Hove singularities (VHS's) in the density of states play an outstanding and diverse role for the electronic and thermodynamic properties of crystalline solids. At the critical point the Fermi surface connectivity changes and topological properties undergo a transition. Opportunities to systematically pass a VHS at the turn of a voltage knob and study its diverse impact are however rare. With the advent of van der Waals heterostructures, control over the atomic registry of neigbouring graphene layers offers an unprecedented tool to generate a low energy VHS easily accessible with conventional gating. Here we have addressed magnetotransport when the chemical potential crosses the twist angle induced VHS in twisted bilayer graphene. A topological phase transition is experimentally disclosed in the abrupt conversion of electrons to holes or vice versa, a loss of a non-zero Berry phase and distinct sequences of integer quantum Hall states above and below the singularity.
Zhou, Jing; Chen, Xi; Guo, L Jay
2016-04-20
Metal-dielectric multilayered metamaterials are proposed to work as wideband spectral-selective emitters/absorbers due to the topological change in isofrequency contour around the epsilon-near-zero point. By setting the transition at the border between the visible and IR ranges, the metal-dielectric multilayered metamaterials become good absorbers/emitters for visible light and good reflectors for IR light, which are desirable for efficient thermal-light interconversions.
Transition Induced by Fence Geometrics on Shuttle Orbiter at Mach 10
NASA Technical Reports Server (NTRS)
Everhart, Joel L.
2010-01-01
Fence-induced transition data simulating a raised gap filler have been acquired on the wing lower surface of a Shuttle Orbiter model in the Langley 31-Inch Mach 10 Tunnel to compare with the Shuttle Boundary Layer Transition Flight and HYTHIRM Experiments, and to provide additional correlation data for the Boundary Layer Transition Tool. In a qualitative assessment, the data exhibit the expected response to all parameter variations; however, it is unclear whether fully effective tripping at the fence was ever realized at any test condition with the present model hardware. A preliminary, qualitative comparison of the ground-based transition measurements with those obtained from the STS-128 HYTHIRM imagery at Mach 15 reveal similar transition-wake response characteristics in terms of the spreading and the path along the vehicle surface.
Wang, Hai Tao; Cho, Sam Young
2015-01-14
In order to investigate the quantum phase transition in the one-dimensional quantum compass model, we numerically calculate non-local string correlations, entanglement entropy and fidelity per lattice site by using the infinite matrix product state representation with the infinite time evolving block decimation method. In the whole range of the interaction parameters, we find that four distinct string orders characterize the four different Haldane phases and the topological quantum phase transition occurs between the Haldane phases. The critical exponents of the string order parameters β = 1/8 and the cental charges c = 1/2 at the critical points show that the topological phase transitions between the phases belong to an Ising type of universality classes. In addition to the string order parameters, the singularities of the second derivative of the ground state energies per site, the continuous and singular behaviors of the Von Neumann entropy and the pinch points of the fidelity per lattice site manifest that the phase transitions between the phases are of the second-order, in contrast to the first-order transition suggested in previous studies.
Zuhail, K P; Sathyanarayana, P; Seč, D; Čopar, S; Škarabot, M; Muševič, I; Dhara, S
2015-03-01
We observe that topological defects in nematic colloids are strongly influenced by the elasticity and onset of smectic layering across the nematic (N) to smectic-A (SmA) phase transition. When approaching the SmA phase from above, the nematic hyperbolic hedgehog defect that accompanies a spherical colloidal inclusion is transformed into a focal conic line in the SmA phase. This phase transformation has a strong influence on the pairwise colloidal interaction and is responsible for a structural transition of two-dimensional colloidal crystals. The pretransitional behavior of the point defect is supported by Landau-de Gennes Q-tensor modeling accounting for the increasing elastic anisotropy.
Synthetic Antimicrobial Oligomers Induce a Composition-Dependent Topological Transition in Membranes
Yang, L.; Gordon, V.D.; Mishra, A.; Som, A.; Purdy, K.R.; Davis, M.A.; Tew, G.N.; Wong, G.C.L.
2009-06-04
Antimicrobial peptides (AMPs) are cationic amphiphiles that comprise a key component of innate immunity. Synthetic analogues of AMPs, such as the family of phenylene ethynylene antimicrobial oligomers (AMOs), recently demonstrated broad-spectrum antimicrobial activity, but the underlying molecular mechanism is unknown. Homologues in this family can be inactive, specifically active against bacteria, or nonspecifically active against bacteria and eukaryotic cells. Using synchrotron small-angle X-ray scattering (SAXS), we show that observed antibacterial activity correlates with an AMO-induced topological transition of small unilamellar vesicles into an inverted hexagonal phase, in which hexagonal arrays of 3.4-nm water channels defined by lipid tubes are formed. Polarized and fluorescence microscopy show that AMO-treated giant unilamellar vesicles remain intact, instead of reconstructing into a bulk 3D phase, but are selectively permeable to encapsulated macromolecules that are smaller than 3.4 nm. Moreover, AMOs with different activity profiles require different minimum threshold concentrations of phosphoethanolamine (PE) lipids to reconstruct the membrane. Using ternary membrane vesicles composed of DOPG:DOPE:DOPC with a charge density fixed at typical bacterial values, we find that the inactive AMO cannot generate the inverted hexagonal phase even when DOPE completely replaces DOPC. The specifically active AMO requires a threshold ratio of DOPE:DOPC = 4:1, and the nonspecifically active AMO requires a drastically lower threshold ratio of DOPE:DOPC = 1.5:1. Since most gram-negative bacterial membranes have more PE lipids than do eukaryotic membranes, our results imply that there is a relationship between negative-curvature lipids such as PE and antimicrobial hydrophobicity that contributes to selective antimicrobial activity.
NASA Astrophysics Data System (ADS)
Chen, Long; Zhang, Cheng; Zhou, Jing; Guo, L. Jay
2015-09-01
An ideal hyperbolic metamaterial (HMM), which has a perfect hyperbolic dispersion curve, theoretically can support modes with indefinite wavenumbers, leading to large photon local density of states (LDOS) and many applications such as enhancing light-matter interactions, spontaneous emission and thermal radiation. Here in this presentation, HMMs based on ultrathin metal-dielectric multilayers have been studied by considering the nonlocal response of electrons in metal. Based on the hydrodynamic model of the nonlocal response, we investigate the effect of nonlocality on the performance (dispersion relation, ray refraction, LDOS and spontaneous emission) of HMMs when gradually approaching the ultrathin limit of the unit cell. We show that nonlocality will induce topological transitions of the iso-frequency surfaces and limit the wavenumber as well as LDOS for both type I and type II HMMs. Under nonlocal treatment, the iso-frequency surface of type II HMM transforms from a hyperbola to a bullet shape, while for type I HMM, the surface splits into two branches: a cylindrical-like branch at high k region and an elliptical branch at the low k region. In the high k region, the nonlocality set a cut-off k for the allowed wavenumbers in both type I and type II HMMs. This cut-off k which is defined by the electron Fermi velocity of the metal intrinsically limits the LDOS and light-matter interactions. These results indicate that in the aim of achieving high performance HMMs, merely thinning the constituent films according to the local theories is no longer valid.
NASA Astrophysics Data System (ADS)
You, Yizhi; Cho, Gil Young; Fradkin, Eduardo
We present a theory of isotropic-nematic quantum phase transition in the composite Fermi liquid arising in the half-filled Landau levels. We show that the quantum phase transition is triggered by the attractive quadrupolar interaction. By performing flux attachment, system turns into a composite Fermi liquid. The nematic order parameters act as the dynamical metric interplaying with the underlying topology, the Chern-Simons theory. Here both the fluctuations of the gauge field and the nematic order parameter can soften the Fermi surface and thus the fermions form a non-Fermi liquid. The effective field theory for the isotropic-nematic phase transition has z = 3 dynamical exponent due to the Landau damping due to the finite density of the fermions. We show that there is a Berry phase term of the nematic order parameter, which can be interpreted as the ``Hall viscosity'' of the dynamical metric. We also find the Wen-Zee-like term, which effectively dresses the nematic vortex with the electric charge. Both of the terms are originated from the time reversal breaking fluctuation of the Chern-Simons gauge fields. This indicates the fluctuations of the gauge fields modify the Hall viscosity and orbital spin of the compressible half-filled Landau level.
NASA Astrophysics Data System (ADS)
You, Yizhi; Cho, Gil Young; Fradkin, Eduardo
2016-05-01
We present a theory of the isotropic-nematic quantum phase transition in the composite Fermi liquid arising in half-filled Landau levels. We show that the quantum phase transition between the isotropic and the nematic phase is triggered by an attractive quadrupolar interaction between electrons, as in the case of conventional Fermi liquids. We derive the theory of the nematic state and of the phase transition. This theory is based on the flux attachment procedure, which maps an electron liquid in half-filled Landau levels into the composite Fermi liquid close to a nematic transition. We show that the local fluctuations of the nematic order parameters act as an effective dynamical metric interplaying with the underlying Chern-Simons gauge fields associated with the flux attachment. Both the fluctuations of the Chern-Simons gauge field and the nematic order parameter can destroy the composite fermion quasiparticles and drive the system into a non-Fermi liquid state. The effective-field theory for the isotropic-nematic phase transition is shown to have z =3 dynamical exponent due to the Landau damping of the dense Fermi system. We show that there is a Berry-phase-type term that governs the effective dynamics of the nematic order parameter fluctuations, which can be interpreted as a nonuniversal "Hall viscosity" of the dynamical metric. We also show that the effective-field theory of this compressible fluid has a Wen-Zee-type term. Both terms originate from the time-reversal breaking fluctuation of the Chern-Simons gauge fields. We present a perturbative (one-loop) computation of the Hall viscosity and also show that this term is also obtained by a Ward identity. We show that the topological excitation of the nematic fluid, the disclination, carries an electric charge. We show that a resonance observed in radio-frequency conductivity experiments can be interpreted as a Goldstone nematic mode gapped by lattice effects.
Bansal, Namrata; Cho, Myung Rae; Brahlek, Matthew; Koirala, Nikesh; Horibe, Yoichi; Chen, Jing; Wu, Weida; Park, Yun Daniel; Oh, Seongshik
2014-03-12
Mechanical exfoliation of bulk crystals has been widely used to obtain thin topological insulator (TI) flakes for device fabrication. However, such a process produces only microsized flakes that are highly irregular in shape and thickness. In this work, we developed a process to transfer the entire area of TI Bi2Se3 thin films grown epitaxially on Al2O3 and SiO2 to arbitrary substrates, maintaining their pristine morphology and crystallinity. Transport measurements show that these transferred films have lower carrier concentrations and comparable or higher mobilities than before the transfer. Furthermore, using this process we demonstrated a clear metal-insulator transition in an ultrathin Bi2Se3 film by gate-tuning its Fermi level into the hybridization gap formed at the Dirac point. The ability to transfer large area TI films to any substrate will facilitate fabrication of TI heterostructure devices, which will help explore exotic phenomena such as Majorana fermions and topological magnetoelectricity.
Kim, Young-Ki; Senyuk, Bohdan; Shin, Sung-Tae; Kohlmeier, Alexandra; Mehl, Georg H; Lavrentovich, Oleg D
2014-01-21
We perform optical, surface anchoring, and textural studies of an organo-siloxane "tetrapode" material in the broad temperature range of the nematic phase. The optical, structural, and topological features are compatible with the uniaxial nematic order rather than with the biaxial nematic order, in the entire nematic temperature range -25 °C < T < 46 °C studied. For homeotropic alignment, the material experiences surface anchoring transition, but the director can be realigned into an optically uniaxial texture by applying a sufficiently strong electric field. The topological features of textures in cylindrical capillaries, in spherical droplets and around colloidal inclusions are consistent with the uniaxial character of the long-range nematic order. In particular, we observe isolated surface point defects - boojums and bulk point defects - hedgehogs that can exist only in the uniaxial nematic liquid crystal. PMID:24651889
Lin, S.; Zhang, G.; Li, C.; Song, Z.
2016-01-01
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. PMID:27554930
NASA Astrophysics Data System (ADS)
Lin, S.; Zhang, G.; Li, C.; Song, Z.
2016-08-01
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.
Tuan, Nguyen Anh
2012-04-01
We present a density functional study on the geometric structure, electronic structure, and spin transition of a series of Fe{sup II} spin-crossover (SCO) molecules, i.e., [Fe(abpt){sub 2}(NCS){sub 2}] (1), [Fe(abpt){sub 2}(NCSe){sub 2}] (2), and [Fe(dpbo)(HIm){sub 2}] (3) with dpbo diethyl(E,E)-2,2'-[1,2-phenylbis(iminomethylidyne)]bis[3-oxobutanoate](2-), N',O{sup 3},O{sup 3}', and abpt = 4-amino-3,5-bis(pyridin-2-yl)-1,2,4-triazole in order to explore more about the way to control SCO behavior of transition metal complexes. Our calculated results show that the spin transition of these Fe{sup II} molecules is accompanied with charge transfer between the Fe atom and ligands. This causes change in the electrostatic energy ({Delta}U) as well as the total electronic energy of SCO molecules. Moreover, our calculated results demonstrate an important contribution of the interionic interactions to {Delta}U, and there is the relation between {Delta}U and the thermal hysteresis behavior of SCO molecules. These results should be helpful for developing new SCO molecules.
Magnetic field-induced transitions in geometrically frustrated Co3V2O8 single crystal
NASA Astrophysics Data System (ADS)
Szymczak, R.; Baran, M.; Diduszko, R.; Fink-Finowicki, J.; Gutowska, M.; Szewczyk, A.; Szymczak, H.
2006-03-01
Magnetization and specific heat of the S=3/2 antiferromagnet on a kagome staircase, Co3V2O8 , were investigated as a function of temperature and magnetic field. The low temperature magnetization data revealed unusual features related to the strongly frustrated spin lattice. Of particular interest were magnetic field induced phase transitions observed for various orientations of the magnetic field. Abrupt macroscopic magnetization jumps induced by a magnetic field directed along the c -axis have been observed below 6K . This effect was also observed for a high enough magnetic field applied in the a-c plane. It is suggested that the jump, observed for H∥c is due to a spin reorientation phase transition. It was shown that Co3V2O8 crystals are characterized by a strong magnetocrystalline anisotropy of an easy-plane type. This anisotropy is due to the presence of Co2+ ions in octahedral positions.
The dynamic and geometric phase transition in the cellular network of pancreatic islet
NASA Astrophysics Data System (ADS)
Wang, Xujing
2013-03-01
The pancreatic islet is a micro-organ that contains several thousands of endocrine cells, majority of which being the insulin releasing β - cells . - cellsareexcitablecells , andarecoupledtoeachother through gap junctional channels. Here, using percolation theory, we investigate the role of network structure in determining the dynamics of the β-cell network. We show that the β-cell synchronization depends on network connectivity. More specifically, as the site occupancy is reducing, initially the β-cell synchronization is barely affected, until it reaches around a critical value, where the synchronization exhibit a sudden rapid decline, followed by an slow exponential tail. This critical value coincides with the critical site open probability for percolation transition. The dependence over bond strength is similar, exhibiting critical-behavior like dependence around a certain value of bond strength. These results suggest that the β-cell network undergoes a dynamic phase transition when the network is percolated. We further apply the findings to study diabetes. During the development of diabetes, the β - cellnetworkconnectivitydecreases . Siteoccupancyreducesfromthe reducing β-cell mass, and the bond strength is increasingly impaired from β-cell stress and chronic hyperglycemia. We demonstrate that the network dynamics around the percolation transition explain the disease dynamics around onset, including a long time mystery in diabetes, the honeymoon phenomenon.
NASA Astrophysics Data System (ADS)
Ospina-Londoño, D. A.; Fulla, M. R.; Marín, J. H.
2013-03-01
In this work it is considered a versatile model to study two different ionization processes starting from a D20 homonuclear hydrogenic molecule confined in double concentric quantum donuts. Very narrow quantum donut circular cross sections are considered to separate the radial and angular variables in the D20 Hamiltonian by using the well-known adiabatic approximation D20 total energy as a function of the inter donor spacing and the outer donut center line radius is calculated. The salient features of an artificial D20 hydrogenic molecule such as the dissociation energy and the equilibrium length are strongly dependent on the quantum donut geometrical parameters. By increasing systematically the quantum donut outer center line radius, it is possible to understand a first ionization process: D20→D2++e-. A second ionization process D20→D-+D+ can be carried out by fixing the first donor position and gradually moving away the second one. The results obtained in this study are in good agreement with those previously obtained in the limiting cases of very large inter donor separation. The model proposed here is computationally economical and provides a realistic description of both ionization processes and the few-particle system confined in double concentric quantum donuts.
Electronic topological transition in AuX2 (X = In, Ga and Al) compounds at high pressures
NASA Astrophysics Data System (ADS)
Garg, Alka B.; Godwal, B. K.; Meenakshi, S.; Modak, P.; Rao, R. S.; Sikka, S. K.; Vijayakumar, V.; Lausi, A.; Bussetto, E.
2002-11-01
We present accurate x-ray diffraction data at high pressures for AuIn2,AuGa2 and AuAl2, obtained using a diamond anvil cell with the ELETTRA synchrotron source. The resulting P-V data obtained from the d-values were used to get the universal equation of state (UEOS), which is compared with theoretical estimates. Deviation from linearity is evident in the UEOS curves of AuIn2 and AuGa2, thus verifying that some of the observed anomalies in these systems below 5 GPa are due to electronic topological transitions.
Geometrically induced phase transitions in two-dimensional dumbbell-shaped domains
NASA Astrophysics Data System (ADS)
Morini, M.; Slastikov, V.
2015-08-01
We continue the analysis, started in [23], of a two-dimensional non-convex variational problem, motivated by studies on magnetic domain walls trapped by thin necks. The main focus is on the impact of extreme geometry on the structure of local minimizers representing the transition between two different constant phases. We address here the case of general non-symmetric dumbbell-shaped domains with a small constriction and general multi-well potentials. Our main results concern the existence and uniqueness of non-constant local minimizers, their full classification in the case of convex bulks, and the complete description of their asymptotic behavior, as the size of the constriction tends to zero.
NASA Astrophysics Data System (ADS)
Chung, Chung-Hou; Lee, Der-Hau; Chao, Sung-Po
2014-07-01
We study the quantum phases and phase transitions of the Kane-Mele Hubbard (KMH) model on a zigzag ribbon of honeycomb lattice at a finite size via the weak-coupling renormalization group (RG) approach. In the noninteracting limit, the Kane-Mele (KM) model is known to support topological edge states where electrons show helical property with orientations of the spin and momentum being locked. The effective interedge hopping terms are generated due to finite-size effect. In the presence of an on-site Coulomb (Hubbard) interaction and the interedge hoppings, special focus is put on the stability of the topological edge states (TI phase) in the KMH model against (i) the charge and spin gaped (II) phase, (ii) the charge gaped but spin gapless (IC) phase, and (iii) the spin gaped but charge gapless (CI) phase depending on the number (even/odd) of the zigzag ribbons, doping level (electron filling factor) and the ratio of the Coulomb interaction to the interedge tunneling. We discuss different phase diagrams for even and odd numbers of zigzag ribbons. We find the TI-CI, II-IC, and II-CI quantum phase transitions are of the Kosterlitz-Thouless (KT) type. By computing various correlation functions, we further analyze the nature and leading instabilities of these phases. The relevance of our results for graphene is discussed.
Tsujimura, Taro; Klein, Felix A.; Langenfeld, Katja; Glaser, Juliane; Huber, Wolfgang; Spitz, François
2015-01-01
Despite the well-documented role of remote enhancers in controlling developmental gene expression, the mechanisms that allocate enhancers to genes are poorly characterized. Here, we investigate the cis-regulatory organization of the locus containing the Tfap2c and Bmp7 genes in vivo, using a series of engineered chromosomal rearrangements. While these genes lie adjacent to one another, we demonstrate that they are independently regulated by distinct sets of enhancers, which in turn define non-overlapping regulatory domains. Chromosome conformation capture experiments reveal a corresponding partition of the locus in two distinct structural entities, demarcated by a discrete transition zone. The impact of engineered chromosomal rearrangements on the topology of the locus and the resultant gene expression changes indicate that this transition zone functionally organizes the structural partition of the locus, thereby defining enhancer-target gene allocation. This partition is, however, not absolute: we show that it allows competing interactions across it that may be non-productive for the competing gene, but modulate expression of the competed one. Altogether, these data highlight the prime role of the topological organization of the genome in long-distance regulation of gene expression. PMID:25569170
Fisher, Kaitlin M.; Haglund, Ellinor; Noel, Jeffrey K.; Hailey, Kendra L.; Onuchic, José N.; Jennings, Patricia A.
2015-01-01
Interleukin-33 (IL-33) is currently the focus of multiple investigations into targeting pernicious inflammatory disorders. This mediator of inflammation plays a prevalent role in chronic disorders such as asthma, rheumatoid arthritis, and progressive heart disease. In order to better understand the possible link between the folding free energy landscape and functional regions in IL-33, a combined experimental and theoretical approach was applied. IL-33 is a pseudo- symmetrical protein composed of three distinct structural elements that complicate the folding mechanism due to competition for nucleation on the dominant folding route. Trefoil 1 constitutes the majority of the binding interface with the receptor whereas Trefoils 2 and 3 provide the stable scaffold to anchor Trefoil 1. We identified that IL-33 folds with a three-state mechanism, leading to a rollover in the refolding arm of its chevron plots in strongly native conditions. In addition, there is a second slower refolding phase that exhibits the same rollover suggesting similar limitations in folding along parallel routes. Characterization of the intermediate state and the rate limiting steps required for folding suggests that the rollover is attributable to a moving transition state, shifting from a post- to pre-intermediate transition state as you move from strongly native conditions to the midpoint of the transition. On a structural level, we found that initially, all independent Trefoil units fold equally well until a QCA of 0.35 when Trefoil 1 will backtrack in order to allow Trefoils 2 and 3 to fold in the intermediate state, creating a stable scaffold for Trefoil 1 to fold onto during the final folding transition. The formation of this intermediate state and subsequent moving transition state is a result of balancing the difficulty in folding the functionally important Trefoil 1 onto the remainder of the protein. Taken together our results indicate that the functional element of the protein is
Huang, Chengxi; Zhou, Jian; Wu, Haiping; Deng, Kaiming; Jena, Puru; Kan, Erjun
2016-05-19
Two-dimensional (2D) topological insulators (TIs) that exhibit quantum spin Hall effects are a new class of materials with conducting edge and insulating bulk. The conducting edge bands are spin-polarized, free of back scattering, and protected by time-reversal symmetry with potential for high-efficiency applications in spintronics. On the basis of first-principles calculations, we show that under external pressure recently synthesized stanene and germanene buckled bilayers can automatically convert into a new dynamically stable phase with flat honeycomb meshes. In contrast with the active surfaces of buckled bilayer of stanene or germanene, the above new phase is chemically inert. Furthermore, we demonstrate that these flat bilayers are 2D TIs with sizable topologically nontrivial band gaps of ∼0.1 eV, which makes them viable for room-temperature applications. Our results suggest some new design principles for searching stable large-gap 2D TIs. PMID:27149183
Carrier-mediated magnetism in transition metal doped Bi₂Se₃ topological insulator.
Schmidt, Tome M; Miwa, R H; Fazzio, A
2013-11-01
The Dirac surface states of topological insulators are protected by time-reversal symmetry, suppressing backscattering. Magnetic impurities adsorbed on the surface of topological insulators are expected to degrade the coherence of these protected surface states, breaking time-reversal symmetry. Some results are in agreement with this prediction. There are others where no bandgap opening was observed. Here, based upon first principles calculations, we show that one mechanism that plays a key role in these controversial results is the intrinsic carrier concentration. The magnetic phase of Fe-, Co- and Ni-doped Bi2Se3 has been computed and compared to the same systems in the presence of n- or p-type doping. Our results show that the magnetic phase is dependent on both the carrier concentration and the magnetic impurity coverage, resulting in a phase diagram for the existence or not of the protected Dirac states.
NASA Astrophysics Data System (ADS)
Wang, Pei; Schmitt, Markus; Kehrein, Stefan
2016-02-01
We study the Hall conductance of a Chern insulator after a global quench of the Hamiltonian. The Hall conductance in the long time limit is obtained by applying the linear response theory to the diagonal ensemble. It is expressed as the integral of the Berry curvature weighted by the occupation number over the Brillouin zone. We identify a topologically driven nonequilibrium phase transition, which is indicated by the nonanalyticity of the Hall conductance as a function of the energy gap mf in the post-quench Hamiltonian Ĥf. The topological invariant for the quenched state is the winding number of the Green's function W , which equals the Chern number for the ground state of Ĥf. In the limit mf→0 , the derivative of the Hall conductance with respect to mf is proportional to ln| mf| , with the constant of proportionality being the ratio of the change of W at mf=0 to the energy gap in the initial state. This nonanalytic behavior is universal in two-band Chern insulators such as the Dirac model, the Haldane model, or the Kitaev honeycomb model in the fermionic basis.
NASA Astrophysics Data System (ADS)
Dietl, Tomasz
The magnitude of ferromagnetic coupling driven by inter-band (Bloembergen-Rowland - BR) and intra-band (Ruderman-Kittel-Kasuya-Yoshida - RKKY) spin polarization is evaluated within kp theory for topological semimetals Hg1-xMnxTe and Hg1-xMnxSe as well as for 3D Dirac semimetal (Cd1-xMnx)3As2. In these systems Mn2+ ions do not introduce any carriers. Since, however, both conduction and valence bands are built from anion p-type wave functions, hybridization of Mn d levels with neighboring anion p states leads to spin-dependent p - d coupling of both electrons and holes to localized Mn spins, resulting in sizable inter-band spin polarization and, thus in large BR interactions. We demonstrate that this ferromagnetic coupling, together with antiferromagnetic superexchange, elucidate a specific dependence of spin-glass freezing temperature on x, determined experimentally for these systems. Furthermore, by employing a multi-orbital tight-binding method, we find that superexchange becomes ferromagnetic when Mn is replaced by Cr or V. Since Cr should act as an isoelectronic impurity in HgTe, this opens a road for realization of ferromagnetic topological insulators based on (Hg,Cr)Te.
NASA Astrophysics Data System (ADS)
Enderlein, Carsten; Fontes, Magda; Baggio-Saitovich, Elisa; Continentino, Mucio A.
2016-01-01
The semimetal-to-semiconductor transition in fcc-Yb under modest pressure can be considered a picture book example of a metal-insulator transition of the Lifshitz type. We have performed transport measurements at low temperatures in the closest vicinity of the transition and related DFT calculations of the Fermi surface. Our resistivity measurements show a linear temperature dependence with an unusually low dρ / dT at low temperatures approaching the MIT. The calculations suggest fcc-ytterbium being an ultra-multi valley system with 24 electron and 6 hole pockets in the Brillouin zone. Such Fermi surface topology naturally supports the appearance of strongly correlated phases. An estimation of the quasiparticle-enhanced effective mass shows that the scattering rate is by at least two orders of magnitude lower than in other materials which exhibit linear-in-T behavior at a quantum critical point. However, we cannot exclude an excessive effective mass enhancement, when the van Hove singularity touches the Fermi level.
Chasapis, T. C. E-mail: m-kanatzidis@northwestern.edu; Calta, N. P.; Kanatzidis, M. G. E-mail: m-kanatzidis@northwestern.edu; Koumoulis, D.; Leung, B.; Lo, S.-H.; Dravid, V. P.; Bouchard, L.-S.
2015-08-01
The requirement for large bulk resistivity in topological insulators has led to the design of complex ternary and quaternary phases with balanced donor and acceptor levels. A common feature of the optimized phases is that they lie close to the p- to n-transition. The tetradymite Bi{sub 2}Te{sub 3−x}Se{sub x} system exhibits minimum bulk conductance at the ordered composition Bi{sub 2}Te{sub 2}Se. By combining local and integral measurements of the density of states, we find that the point of minimum electrical conductivity at x = 1.0 where carriers change from hole-like to electron-like is characterized by conductivity of the mixed type. Our experimental findings, which are interpreted within the framework of a two-band model for the different carrier types, indicate that the mixed state originates from different types of native defects that strongly compensate at the crossover point.
Zhao, Bao; Zhang, Jiayong; Wang, Yicheng; Yang, Zhongqin
2014-12-28
The electronic states and topological behaviors of Pt(Ni, Pd)-decorated silicene are investigated by using an ab-initio method. All the three kinds of the adatoms prefer hollow sites of the silicene, guaranteeing the Dirac cones unbroken. The Pt(Ni, Pd)-decorated silicene systems all present quantum valley Hall (QVH) states with the gap opened exactly at the Fermi level. The gaps of the QVH states can be increased substantially by applying a positive electric field. Very fascinating phase transitions from QVH to quantum spin Hall (QSH) and then to QVH again are achieved in the Pt/Ni-decorated silicene when a negative electric field is applied. The QSH state in the Pd case with a negative electric field is, however, quenched because of relatively larger Rashba spin-orbit coupling (SOC) than the intrinsic SOC in the system. Our findings may be useful for the applications of silicene-based devices in valleytronics and spintronics.
NASA Astrophysics Data System (ADS)
Chatterjee, Shubhayu; Qi, Yang; Sachdev, Subir; Steinberg, Julia
2016-07-01
The Schwinger boson theory of the frustrated square lattice antiferromagnet yields a stable, gapped Z2 spin liquid ground state with time-reversal symmetry, incommensurate spin correlations, and long-range Ising-nematic order. We obtain an equivalent description of this state using fermionic spinons (the fermionic spinons can be considered to be bound states of the bosonic spinons and the visons). Upon doping, the Z2 spin liquid can lead to a fractionalized Fermi liquid (FL*) with small Fermi pockets of electronlike quasiparticles, while preserving the Z2 topological and Ising-nematic orders. We describe a Higgs transition out of this deconfined metallic state into a confining superconducting state which is almost always of the Fulde-Ferrell-Larkin-Ovchinnikov type, with spatial modulation of the superconducting order.
Cioslowski, J.; Hay, P.J.; Ritchie, J.P. )
1990-01-11
Advantages and shortcomings of three different definitions of the atomic charges, namely, the Mulliken, the generalized atomic polar tensors (GAPT), and the topological ones, are judged by applying them to the results of ab initio calculations on the TiF{sub 4}, Ni(CO){sub 4}, and FeH{sub 6}{sup 4{minus}} molecules. In agreement with previous reports, we find that the Mulliken charges vary widely with the choice of basis sets and therefore their utilization for the analysis of electronic structure of the transition-metal complexes is of little practical importance. On the other hand, both the GAPT and Bader's charges show a remarkable insensitivity to the quality of the basis sets.
NASA Astrophysics Data System (ADS)
Qu, Fanyao; Villegas-Lelovsky, L.; Diniz, G. S.
2016-05-01
We propose a physical model based on disordered (a hole punched inside a material) monolayer transition metal dichalcogenides (TMDs) to demonstrate a large-gap quantum valley Hall insulator. We find an emergence of bound states lying inside the bulk gap of the TMDs. They are strongly affected by spin-valley coupling, rest- and kinetic- mass terms and the hole size. In addition, in the whole range of the hole size, at least two in-gap bound states with opposite angular momentum, circulating around the edge of the hole, exist. Their topological insulator (TI) feature is analyzed by the Chern number, characterized by spacial distribution of their probabilities and confirmed by energy dispersion curves (Energy vs. angular momentum). It not only sheds light on overcoming low-temperature operating limitation of existing narrow-gap TIs, but also opens an opportunity to realize valley- and spin- qubits.
Zhao, Bao; Zhang, Jiayong; Wang, Yicheng; Yang, Zhongqin
2014-12-28
The electronic states and topological behaviors of Pt(Ni, Pd)-decorated silicene are investigated by using an ab-initio method. All the three kinds of the adatoms prefer hollow sites of the silicene, guaranteeing the Dirac cones unbroken. The Pt(Ni, Pd)-decorated silicene systems all present quantum valley Hall (QVH) states with the gap opened exactly at the Fermi level. The gaps of the QVH states can be increased substantially by applying a positive electric field. Very fascinating phase transitions from QVH to quantum spin Hall (QSH) and then to QVH again are achieved in the Pt/Ni-decorated silicene when a negative electric field is applied. The QSH state in the Pd case with a negative electric field is, however, quenched because of relatively larger Rashba spin-orbit coupling (SOC) than the intrinsic SOC in the system. Our findings may be useful for the applications of silicene-based devices in valleytronics and spintronics.
Barkeshli, Maissam; Wen, Xiao-Gang
2010-11-19
We find a series of possible continuous quantum phase transitions between fractional quantum Hall states at the same filling fraction in two-component quantum Hall systems. These can be driven by tuning the interlayer tunneling and/or interlayer repulsion. One side of the transition is the Halperin (p,p,p-3) Abelian two-component state, while the other side is the non-Abelian Z4 parafermion (Read-Rezayi) state. We predict that the transition is a continuous transition in the 3D Ising class. The critical point is described by a Z2 gauged Ginzburg-Landau theory. These results have implications for experiments on two-component systems at ν=2/3 and single-component systems at ν=8/3. PMID:21231341
NASA Astrophysics Data System (ADS)
Barkeshli, Maissam; Wen, Xiao-Gang
2010-11-01
We find a series of possible continuous quantum phase transitions between fractional quantum Hall states at the same filling fraction in two-component quantum Hall systems. These can be driven by tuning the interlayer tunneling and/or interlayer repulsion. One side of the transition is the Halperin (p,p,p-3) Abelian two-component state, while the other side is the non-Abelian Z4 parafermion (Read-Rezayi) state. We predict that the transition is a continuous transition in the 3D Ising class. The critical point is described by a Z2 gauged Ginzburg-Landau theory. These results have implications for experiments on two-component systems at ν=2/3 and single-component systems at ν=8/3.
Yu, Na; Klepov, Vladislav V.; Villa, Eric M.; Bosbach, Dirk; Suleimanov, Evgeny V.; Depmeier, Wulf; Albrecht-Schmitt, Thomas E.; Alekseev, Evgeny V.
2014-07-01
The hydrothermal reaction of uranyl nitrate with rubidium nitrate and arsenic (III) oxide results in the formation of polymorphic α- and β-Rb[UO{sub 2}(AsO{sub 3}OH)(AsO{sub 2}(OH){sub 2})]·H{sub 2}O (α-, β-RbUAs) and the anhydrous phase Rb[UO{sub 2}(AsO{sub 3}OH)(AsO{sub 2}(OH){sub 2})] (RbUAs). These phases were structurally, chemically and spectroscopically characterized. The structures of all three compounds are based upon topologically identical, but geometrically isomeric layers. The layers are linked with each other by means of the Rb cations and hydrogen bonding. Dehydration experiments demonstrate that water deintercalation from hydrous α- and β-RbUAs yields anhydrous RbUAs via topotactic reactions. - Graphical abstract: Three different layer geometries observed in the structures of Rb[UO{sub 2}(AsO{sub 3}OH)(AsO{sub 2}(OH){sub 2})] and α- and β- Rb[UO{sub 2}(AsO{sub 3}OH)(AsO{sub 2}(OH){sub 2})]·H{sub 2}O. Two different coordination environments of uranium polyhedra (types I and II) are shown schematically on the top of the figure. - Highlights: • Three new uranyl arsenates were synthesized from the hydrothermal reactions. • The phases consist of the topologically identical but geometrically different layers. • Topotactic transitions were observed in the processes of mono-hyrates dehydration.
Morphology transition in lipid vesicles due to in-plane order and topological defects
Hirst, Linda S.; Ossowski, Adam; Fraser, Matthew; Geng, Jun; Selinger, Jonathan V.; Selinger, Robin L. B.
2013-01-01
Complex morphologies in lipid membranes typically arise due to chemical heterogeneity, but in the tilted gel phase, complex shapes can form spontaneously even in a membrane containing only a single lipid component. We explore this phenomenon via experiments and coarse-grained simulations on giant unilamellar vesicles of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine. When cooled from the untilted Lα liquid-crystalline phase into the tilted gel phase, vesicles deform from smooth spheres to disordered, highly crumpled shapes. We propose that this shape evolution is driven by nucleation of complex membrane microstructure with topological defects in the tilt orientation that induce nonuniform membrane curvature. Coarse-grained simulations demonstrate this mechanism and show that kinetic competition between curvature change and defect motion can trap vesicles in deeply metastable, defect-rich structures. PMID:23401499
Abou-Jaoudé, Wassim; Chaves, Madalena; Gouzé, Jean-Luc
2014-12-01
A class of piecewise affine differential (PWA) models, initially proposed by Glass and Kauffman (in J Theor Biol 39:103-129, 1973), has been widely used for the modelling and the analysis of biological switch-like systems, such as genetic or neural networks. Its mathematical tractability facilitates the qualitative analysis of dynamical behaviors, in particular periodic phenomena which are of prime importance in biology. Notably, a discrete qualitative description of the dynamics, called the transition graph, can be directly associated to this class of PWA systems. Here we present a study of periodic behaviours (i.e. limit cycles) in a class of two-dimensional piecewise affine biological models. Using concavity and continuity properties of Poincaré maps, we derive structural principles linking the topology of the transition graph to the existence, number and stability of limit cycles. These results notably extend previous works on the investigation of structural principles to the case of unequal and regulated decay rates for the 2-dimensional case. Some numerical examples corresponding to minimal models of biological oscillators are treated to illustrate the use of these structural principles.
Finzi, Andrés; Xiang, Shi-Hua; Pacheco, Beatriz; Wang, Liping; Haight, Jessica; Kassa, Aemro; Danek, Brenda; Pancera, Marie; Kwong, Peter D.; Sodroski, Joseph
2010-01-01
SUMMARY The entry of human immunodeficiency virus (HIV-1) into cells is initiated by binding of the gp120 exterior envelope glycoprotein to the receptor, CD4. How does CD4 binding trigger conformational changes in gp120 that allow the gp41 transmembrane envelope glycoprotein to mediate viral-cell membrane fusion? The transition from the unliganded to the CD4-bound state is regulated by two potentially flexible topological layers (“Layers 1 and 2”) in the gp120 inner domain. Both layers apparently contribute to the non-covalent association of unliganded gp120 with gp41. After CD4 makes initial contact with the gp120 outer domain, Layer 1-Layer 2 interactions strengthen gp120-CD4 binding by reducing the off-rate. Layer 1-Layer 2 interactions also destabilize the activated state induced on HIV-1 by treatment with soluble CD4. Thus, despite lack of contact with CD4, the gp120 inner domain layers govern CD4 triggering by participating in conformational transitions within gp120 and regulating the interaction with gp41. PMID:20227370
Wang, Zi-Fu; Li, Ming-Hao; Chen, Wei-Wen; Hsu, Shang-Te Danny; Chang, Ta-Chau
2016-05-01
The folding topology of DNA G-quadruplexes (G4s) depends not only on their nucleotide sequences but also on environmental factors and/or ligand binding. Here, a G4 ligand, 3,6-bis(1-methyl-4-vinylpyridium iodide)-9-(1-(1-methyl-piperidinium iodide)-3,6,9-trioxaundecane) carbazole (BMVC-8C3O), can induce topological conversion of non-parallel to parallel forms in human telomeric DNA G4s. Nuclear magnetic resonance (NMR) spectroscopy with hydrogen-deuterium exchange (HDX) reveals the presence of persistent imino proton signals corresponding to the central G-quartet during topological conversion of Tel23 and Tel25 G4s from hybrid to parallel forms, implying that the transition pathway mainly involves local rearrangements. In contrast, rapid HDX was observed during the transition of 22-CTA G4 from an anti-parallel form to a parallel form, resulting in complete disappearance of all the imino proton signals, suggesting the involvement of substantial unfolding events associated with the topological transition. Site-specific imino proton NMR assignments of Tel23 G4 enable determination of the interconversion rates of individual guanine bases and detection of the presence of intermediate states. Since the rate of ligand binding is much higher than the rate of ligand-induced topological conversion, a three-state kinetic model was evoked to establish the associated energy diagram for the topological conversion of Tel23 G4 induced by BMVC-8C3O. PMID:26975658
Hydrodesulphurization of thiophene by transition metal sulphides. A molecular orbital topology study
NASA Astrophysics Data System (ADS)
Smit, T. S.; Johnson, K. H.
1993-09-01
Transition metal sulphides have the ability to catalyze the hydrodesulphurization (HDS) process of thiophene and related compounds in the presence of hydrogen. We present the results of scattered-wave calculations on model catalyst clusters and catalyst—thiophene complexes, which indicate that pπ bonding, between the sulphur atoms in the catalyst and the sulphur and carbon atoms in the thiophene ring, is responsible for binding the thiophene molecule to the catalyst in the initial stages of the HDS process.
NASA Astrophysics Data System (ADS)
Caporaso, Nicola; Cirafici, Michele; Griguolo, Luca; Pasquetti, Sara; Seminara, Domenico; Szabo, Richard J.
2006-01-01
We examine the problem of counting bound states of BPS black holes on local Calabi-Yau threefolds which are fibrations over a Riemann surface by computing the partition function of q-deformed Yang-Mills theory on the Riemann surface. We study in detail the genus zero case and obtain, at finite N, the instanton expansion of the gauge theory. It can be written exactly as the partition function for U(N) Chern-Simons gauge theory on a Lens space, summed over all non-trivial vacua, plus a tower of non-perturbative instanton contributions. The correspondence between two and three dimensional gauge theories is elucidated by an explicit mapping between two-dimensional Yang-Mills instantons and flat connections on the Lens space. In the large N limit we find a peculiar phase structure in the model. At weak string coupling the theory reduces exactly to the trivial flat connection sector with instanton contributions exponentially suppressed, and the topological string partition function on the resolved conifold is reproduced in this regime. At a certain critical point all non-trivial vacua contribute, instantons are enhanced and the theory appears to undergo a phase transition into a strong coupling regime. We rederive these results by performing a saddle-point approximation to the exact partition function. We obtain a q-deformed version of the Douglas-Kazakov equation for two-dimensional Yang-Mills theory on the sphere, whose one-cut solution below the transition point reproduces the resolved conifold geometry. Above the critical point we propose a two-cut solution that should reproduce the chiral-antichiral dynamics found for black holes on the Calabi-Yau threefold and the Gross-Taylor string in the undeformed limit. The transition from the strong coupling phase to the weak coupling phase appears to be of third order.
NASA Astrophysics Data System (ADS)
Khazaei, Mohammad; Ranjbar, Ahmad; Arai, Masao; Yunoki, Seiji
2016-09-01
The family of two-dimensional transition metal carbides, so called MXenes, has recently found new members with ordered double transition metals M2'M″C2 , where M' and M″ stand for transition metals. Here, using a set of first-principles calculations, we demonstrate that some of the newly added members, oxide M2'M″C2 (M'=Mo , W; M″=Ti , Zr, Hf) MXenes, are topological insulators. The nontrivial topological states of the predicted MXenes are revealed by the Z2 index, which is evaluated from the parities of the occupied bands below the Fermi energy at time reversal invariant momenta, and also by the presence of the edge states. The predicted M2'M″C2O2 MXenes show nontrivial gaps in the range of 0.041-0.285 eV within the generalized gradient approximation and 0.119-0.409 eV within the hybrid functional. The band gaps are induced by the spin-orbit coupling within the degenerate states with dx2-y2 and dx y characters of M' and M″, while the band inversion occurs at the Γ point among the degenerate dx2-y2/dx y orbitals and a nondegenerate d3 z2-r2 orbital, which is driven by the hybridization of the neighboring orbitals. The phonon dispersion calculations find that the predicted topological insulators are structurally stable. The predicted W-based MXenes with large band gaps might be suitable candidates for many topological applications at room temperature. In addition, we study the electronic structures of thicker ordered double transition metals M2'M2″C3O2 (M'=Mo , W; M″=Ti , Zr, Hf) and find that they are nontrivial topological semimetals. Among the predicted topological insulators and topological semimetals, Mo2TiC2 and Mo2Ti2C3 functionalized with a mixture of F, O, and OH have already been synthesized, and therefore some of the topological materials proposed here can be experimentally accessed.
NASA Astrophysics Data System (ADS)
Kimme, Lukas; Hyart, Timo
2016-01-01
We consider the effects of impurities on topological insulators and superconductors. We start by identifying the general conditions under which the eigenenergies of an arbitrary Hamiltonian H belonging to one of the Altland-Zirnbauer symmetry classes undergo a robust zero energy crossing as a function of an external parameter which can be, for example, the impurity strength. We define a generalized root of detH and use it to predict or rule out robust zero-energy crossings in all symmetry classes. We complement this result with an analysis based on almost degenerate perturbation theory, which allows a derivation of the asymptotic low-energy behavior of the ensemble averaged density of states ρ ˜Eα for all symmetry classes and makes it transparent that the exponent α does not depend on the choice of the random matrix ensemble. Finally, we show that a lattice of impurities can drive a topologically trivial system into a nontrivial phase, and in particular we demonstrate that impurity bands carrying extremely large Chern numbers can appear in different symmetry classes of two-dimensional topological insulators and superconductors. We use the generalized root of detH (k ) to reveal a spiderweblike momentum space structure of the energy gap closings that separate the topologically distinct phases in px+i py superconductors in the presence of an impurity lattice.
Geometric diffusion of quantum trajectories.
Yang, Fan; Liu, Ren-Bao
2015-07-16
A quantum object can acquire a geometric phase (such as Berry phases and Aharonov-Bohm phases) when evolving along a path in a parameter space with non-trivial gauge structures. Inherent to quantum evolutions of wavepackets, quantum diffusion occurs along quantum trajectories. Here we show that quantum diffusion can also be geometric as characterized by the imaginary part of a geometric phase. The geometric quantum diffusion results from interference between different instantaneous eigenstate pathways which have different geometric phases during the adiabatic evolution. As a specific example, we study the quantum trajectories of optically excited electron-hole pairs in time-reversal symmetric insulators, driven by an elliptically polarized terahertz field. The imaginary geometric phase manifests itself as elliptical polarization in the terahertz sideband generation. The geometric quantum diffusion adds a new dimension to geometric phases and may have applications in many fields of physics, e.g., transport in topological insulators and novel electro-optical effects.
Finite-Size and Composition-Driven Topological Phase Transition in (Bi1–xInx)2Se3Thin Films
NASA Astrophysics Data System (ADS)
Salehi, Maryam; Shapourian, Hassan; Koirala, Nikesh; Brahlek, Matthew J.; Moon, Jisoo; Oh, Seongshik
2016-09-01
In a topological insulator (TI), if its spin-orbit coupling (SOC) strength is gradually reduced, the TI eventually transforms into a trivial insulator beyond a critical point of SOC, at which point the bulk gap closes: this is the standard description of the topological phase transition (TPT). However, this description of TPT, driven solely by the SOC (or something equivalent) and followed by closing and reopening of the bulk band gap, is valid only for infinite-size samples, and little is known how TPT occurs for finite-size samples. Here, using both systematic transport measurements on interface-engineered(Bi$_{1-x}$In$_x$)$_2$Se$_3$ thin films and theoretical simulations (with animations in Supporting Information) we show that description of TPT in finite-size samples needs to be substantially modified from the conventional picture of TPT due to surface-state hybridization and bulk confinement effects. We also show that the finite-size TPT is composed of two separate transitions, topological-normal transition (TNT) and metal-insulator transition (MIT) by providing a detailed phase diagram in the two-dimensional phase space of sample size and SOC strength.
Finite-Size and Composition-Driven Topological Phase Transition in (Bi1-xInx)2Se3 Thin Films.
Salehi, Maryam; Shapourian, Hassan; Koirala, Nikesh; Brahlek, Matthew J; Moon, Jisoo; Oh, Seongshik
2016-09-14
In a topological insulator (TI), if its spin-orbit coupling (SOC) strength is gradually reduced, the TI eventually transforms into a trivial insulator beyond a critical point of SOC, at which point the bulk gap closes: this is the standard description of the topological phase transition (TPT). However, this description of TPT, driven solely by the SOC (or something equivalent) and followed by closing and reopening of the bulk band gap, is valid only for infinite-size samples, and little is known how TPT occurs for finite-size samples. Here, using both systematic transport measurements on interface-engineered (Bi1-xInx)2Se3 thin films and theoretical simulations (with animations in the Supporting Information), we show that description of TPT in finite-size samples needs to be substantially modified from the conventional picture of TPT due to surface-state hybridization and bulk confinement effects. We also show that the finite-size TPT is composed of two separate transitions, topological-normal transition (TNT) and metal-insulator transition (MIT), by providing a detailed phase diagram in the two-dimensional phase space of sample size and SOC strength.
Finite-Size and Composition-Driven Topological Phase Transition in (Bi1-xInx)2Se3 Thin Films.
Salehi, Maryam; Shapourian, Hassan; Koirala, Nikesh; Brahlek, Matthew J; Moon, Jisoo; Oh, Seongshik
2016-09-14
In a topological insulator (TI), if its spin-orbit coupling (SOC) strength is gradually reduced, the TI eventually transforms into a trivial insulator beyond a critical point of SOC, at which point the bulk gap closes: this is the standard description of the topological phase transition (TPT). However, this description of TPT, driven solely by the SOC (or something equivalent) and followed by closing and reopening of the bulk band gap, is valid only for infinite-size samples, and little is known how TPT occurs for finite-size samples. Here, using both systematic transport measurements on interface-engineered (Bi1-xInx)2Se3 thin films and theoretical simulations (with animations in the Supporting Information), we show that description of TPT in finite-size samples needs to be substantially modified from the conventional picture of TPT due to surface-state hybridization and bulk confinement effects. We also show that the finite-size TPT is composed of two separate transitions, topological-normal transition (TNT) and metal-insulator transition (MIT), by providing a detailed phase diagram in the two-dimensional phase space of sample size and SOC strength. PMID:27558142
Colloquium: Topological band theory
NASA Astrophysics Data System (ADS)
Bansil, A.; Lin, Hsin; Das, Tanmoy
2016-04-01
The first-principles band theory paradigm has been a key player not only in the process of discovering new classes of topologically interesting materials, but also for identifying salient characteristics of topological states, enabling direct and sharpened confrontation between theory and experiment. This review begins by discussing underpinnings of the topological band theory, which involve a layer of analysis and interpretation for assessing topological properties of band structures beyond the standard band theory construct. Methods for evaluating topological invariants are delineated, including crystals without inversion symmetry and interacting systems. The extent to which theoretically predicted properties and protections of topological states have been verified experimentally is discussed, including work on topological crystalline insulators, disorder and interaction driven topological insulators (TIs), topological superconductors, Weyl semimetal phases, and topological phase transitions. Successful strategies for new materials discovery process are outlined. A comprehensive survey of currently predicted 2D and 3D topological materials is provided. This includes binary, ternary, and quaternary compounds, transition metal and f -electron materials, Weyl and 3D Dirac semimetals, complex oxides, organometallics, skutterudites, and antiperovskites. Also included is the emerging area of 2D atomically thin films beyond graphene of various elements and their alloys, functional thin films, multilayer systems, and ultrathin films of 3D TIs, all of which hold exciting promise of wide-ranging applications. This Colloquium concludes by giving a perspective on research directions where further work will broadly benefit the topological materials field.
NASA Astrophysics Data System (ADS)
Wang, Na; Wang, JianFeng; Si, Chen; Gu, Bing-Lin; Duan, WenHui
2016-08-01
The introduction of magnetism in SnTe-class topological crystalline insulators is a challenging subject with great importance in the quantum device applications. Based on the first-principles calculations, we have studied the defect energetics and magnetic properties of 3 d transition-metal (TM)-doped SnTe. We find that the doped TM atoms prefer to stay in the neutral states and have comparatively high formation energies, suggesting that the uniform TMdoping in SnTe with a higher concentration will be difficult unless clustering. In the dilute doping regime, all the magnetic TMatoms are in the high-spin states, indicating that the spin splitting energy of 3 d TM is stronger than the crystal splitting energy of the SnTe ligand. Importantly, Mn-doped SnTe has relatively low defect formation energy, largest local magnetic moment, and no defect levels in the bulk gap, suggesting that Mn is a promising magnetic dopant to realize the magnetic order for the theoretically-proposed large-Chern-number quantum anomalous Hall effect (QAHE) in SnTe.
Dynamical Generation of Topological Magnetic Lattices for Ultracold Atoms.
Yu, Jinlong; Xu, Zhi-Fang; Lü, Rong; You, Li
2016-04-01
We propose a scheme to dynamically synthesize a space-periodic effective magnetic field for neutral atoms by time-periodic magnetic field pulses. When atomic spin adiabatically follows the direction of the effective magnetic field, an adiabatic scalar potential together with a geometric vector potential emerges for the atomic center-of-mass motion, due to the Berry phase effect. While atoms hop between honeycomb lattice sites formed by the minima of the adiabatic potential, complex Peierls phase factors in the hopping coefficients are induced by the vector potential, and these phase factors facilitate a topological Chern insulator. With further tuning of external parameters, both a topological phase transition and topological flat bands can be achieved, highlighting realistic prospects for studying strongly correlated phenomena in this system. Our Letter presents an alternative pathway towards creating and manipulating topological states of ultracold atoms by magnetic fields.
King, R Bruce
2003-12-29
The bismuth polyhedra in ternary transition metal-centered bismuth cluster halides may form discrete molecules or ions, infinite chains, and/or infinite layers. The chemical bonding in many of these diverse structures is related to that in deltahedral boranes exhibiting three-dimensional aromaticity by replacing the multicenter core bond in the boranes with two-center two-electron (2c-2e) bonds from the central transition metal to the nearest neighbor bismuth vertices. Examples of discrete molecules or ions include octahedral MBi(6)(micro-X)(12)(z)()(-) (X = Br, I; M = Rh, Ir, z = 3; M = Ru, z = 4) with exclusively 2c-2e bonds and pentagonal bipyramidal RhBi(7)Br(8) with a 5c-4e bond in the equatorial pentagonal plane indicative of Möbius aromaticity. The compound Ru(3)Bi(24)Br(20) contains a more complicated discrete bismuth cluster ion Ru(2)Bi(17)(micro-Br)(4)(5+), which can be dissected into a RuBi(5) closo octahedron and a RuBi(8) nido capped square antiprism bridged by a Ru(2)Bi(4)(micro-Br)(4) structural unit. In RuBi(4)X(2) (X = Br, I), the same Ru(2)Bi(4)(micro-Br)(4) structural unit bridges Bi(4) squares similar to those found in the known Zintl ion Bi(4)(2)(-) to give infinite chains of Ru(2)Bi(4) octahedra. The electron counts of the RuBi(5), RuBi(8), and Ru(2)Bi(4) polyhedra in these structures follow the Wade-Mingos rules. A different infinite chain structure is constructed from fused RhBi(7/2)Bi bicapped trigonal prisms in Rh(2)Bi(9)Br(3). This Rh(2)Bi(9)Br(3) structure can alternatively be derived from alternating Rh(2/2)Bi(4) octahedra and Rh(2/)(2)Bi(5) pentagonal bipyramids with electron counts obeying the Wade-Mingos rules. Related chemical bonding principles appear to apply to more complicated layer structures such as Pt(3)Bi(13)I(7) containing Kagomé nets of PtBi(8/2) cubes and Ni(4)Bi(12)X(3) containing linked chains of NiBi(6/3)Bi capped trigonal prisms.
Collectively induced many-vortices topology via rotatory Dicke quantum phase transition
NASA Astrophysics Data System (ADS)
Das, Priyam; Emre Tasgin, Mehmet; Müstecaplıoğlu, Özgür E.
2016-09-01
We examine the superradiance of a Bose-Einstein condensate pumped with a Laguerre-Gaussian laser of high winding number, e.g., {\\ell }=7. The laser beam transfers its orbital angular momentum (OAM) to the condensate at once due to the collectivity of the superradiance. An ℓ-fold rotational symmetric structure emerges with the rotatory superradiance. ℓ number of single-charge vortices appear at the arms of this structure. Even though the pump and the condensate profiles initially have cylindrical symmetry, we observe that it is broken to ℓ-fold rotational symmetry at the superradiance. Breaking of the cylindrical symmetry into the ℓ-fold symmetry and OAM transfer to the condensate become significant after the same critical pump strength. Reorganization of the condensate resembles the ordering in the experiment by Esslinger and colleagues (2010 Nature 264 1301). We numerically verify that the critical point for the onset of the reorganization, as well as the properties of the emitted pulse, conform to the characteristics of superradiant quantum phase transition.
Collectively induced many-vortices topology via rotatory Dicke quantum phase transition
NASA Astrophysics Data System (ADS)
Das, Priyam; Emre Tasgin, Mehmet; Müstecaplıoğlu, Özgür E.
2016-09-01
We examine the superradiance of a Bose–Einstein condensate pumped with a Laguerre–Gaussian laser of high winding number, e.g., {\\ell }=7. The laser beam transfers its orbital angular momentum (OAM) to the condensate at once due to the collectivity of the superradiance. An ℓ-fold rotational symmetric structure emerges with the rotatory superradiance. ℓ number of single-charge vortices appear at the arms of this structure. Even though the pump and the condensate profiles initially have cylindrical symmetry, we observe that it is broken to ℓ-fold rotational symmetry at the superradiance. Breaking of the cylindrical symmetry into the ℓ-fold symmetry and OAM transfer to the condensate become significant after the same critical pump strength. Reorganization of the condensate resembles the ordering in the experiment by Esslinger and colleagues (2010 Nature 264 1301). We numerically verify that the critical point for the onset of the reorganization, as well as the properties of the emitted pulse, conform to the characteristics of superradiant quantum phase transition.
NASA Astrophysics Data System (ADS)
Kim, Tae-Hyeon; Jeong, Kwangsik; Park, Byung Cheol; Choi, Hyejin; Park, Sang Han; Jung, Seonghoon; Park, Jaehun; Jeong, Kwang-Ho; Kim, Jeong Won; Kim, Jae Hoon; Cho, Mann-Ho
2015-12-01
In a three-dimensional topological insulator Bi2Se3, a stress control for band gap manipulation was predicted but no systematic investigation has been performed yet due to the requirement of large external stress. We report herein on the strain-dependent results for Bi2Se3 films of various thicknesses that are grown via a self-organized ordering process. Using small angle X-ray scattering and Raman spectroscopy, the changes of d-spacings in the crystal structure and phonon vibration shifts resulted from stress are clearly observed when the film thickness is below ten quintuple layers. From the UV photoemission/inverse photoemission spectroscopy (UPS/IPES) results and ab initio calculations, significant changes of the Fermi level and band gap were observed. The deformed band structure also exhibits a Van Hove singularity at specific energies in the UV absorption experiment and ab initio calculations. Our results, including the synthesis of a strained ultrathin topological insulator, suggest a new direction for electronic and spintronic applications for the future.In a three-dimensional topological insulator Bi2Se3, a stress control for band gap manipulation was predicted but no systematic investigation has been performed yet due to the requirement of large external stress. We report herein on the strain-dependent results for Bi2Se3 films of various thicknesses that are grown via a self-organized ordering process. Using small angle X-ray scattering and Raman spectroscopy, the changes of d-spacings in the crystal structure and phonon vibration shifts resulted from stress are clearly observed when the film thickness is below ten quintuple layers. From the UV photoemission/inverse photoemission spectroscopy (UPS/IPES) results and ab initio calculations, significant changes of the Fermi level and band gap were observed. The deformed band structure also exhibits a Van Hove singularity at specific energies in the UV absorption experiment and ab initio calculations. Our
NASA Astrophysics Data System (ADS)
Bouchiat, Marie-Anne; Bouchiat, Claude
2012-10-01
We have constructed the geometric phases emerging from the non-trivial topology of a space-dependent magnetic field B(r), interacting with the spin magnetic moment of a neutral particle. Our basic tool, adapted from a previous work on Berry’s phases, is the space-dependent unitary transformation {U}({\\mathbf {r}}), which leads to the identity, {U}({\\mathbf {r}})^{\\dag }\\, {\\mathbf {S}}\\,{\\bm \\cdot}\\, {\\mathbf {B}}({\\mathbf {r}}) \\, {U}({\\mathbf {r}}) = \\vert {\\mathbf {B}}({\\mathbf {r}}) \\vert \\, S_z, at each point r. In the ‘rotated’ Hamiltonian \\widehat{ H}, \\frac{ \\partial }{\\partial {\\mathbf {r}}} is replaced by the non-Abelian covariant derivative \\frac{ \\partial }{\\partial {\\mathbf {r}}}- \\frac{i}{\\hbar } {A}({\\mathbf {r}}) where {A}({\\mathbf {r}}) = i \\hbar \\, {U}^{\\dag }\\,{\\bm\\cdot}\\, \\frac{ \\partial }{\\partial {\\mathbf {r}}} {U} can be written as A1(r)Sx + A2(r)Sy + A3(r)Sz. The Abelian differentials Ak(r)·dr are given in terms of the Euler angles defining the orientation of B(r). The non-Abelian field {A}({\\mathbf {r}}) transforms as a Yang-Mills field; however, its vanishing ‘curvature’ reveals its purely geometric character. We have defined a perturbation scheme based upon the assumption that in \\widehat{ H} the longitudinal field A3(r) dominates the transverse field A1, 2(r) contributions, evaluated to second order. The geometry embedded in both the vector field A3(r) and the geometric magnetic field \\mathbf { B}_3 ({\\mathbf {r}}) = \\frac{ \\partial }{\\partial {\\mathbf {r}}}\\wedge {{\\mathbf {A}}}_3({\\mathbf {r}}) is described by their associated Aharonov-Bohm phase. As an illustration we study the physics of cold 171Yb atoms dressed by overlaying two circularly polarized stationary waves with orthogonal directions, which form a 2D square optical lattice. The frequency is tuned midway between the two hyperfine levels of the (6s6p)3P1 states to protect the optical B(r) field generated by the
Geometric Phase of Phase Space Trajectories:Mobius Strip and Nonlinear Oscillators
NASA Astrophysics Data System (ADS)
Balakrishnan, Radha; Satija, Indubala
2005-03-01
We present a gauge invariant formulation of associating a geometric phase with classical phase space trajectories. This geometric phase which depends upon the integrated torsion of the trajectory, bears a close analogy to the generalized Berry phase associated with the time evolution of the quantum wave functions. This topological quantity serves as an order parameter signalling phase transitions including novel geometrical transitions. One of the interesting aspects seen in Duffing and other nonlinear oscillators is the sudden jumps in the geometric phase which is accompanied by the divergence of the local torsion and the vanishing of the local curvature. Intriguingly, the analogous phenomenon was seen in a mobius strip when the ratio of the width to the length of the strip exceeds beyound a critical value.
Da Silva, David; Han, Liqi; Faivre, Robert; Costes, Evelyne
2014-01-01
Background and Aims The impact of a fruit tree's architecture on its performance is still under debate, especially with regard to the definition of varietal ideotypes and the selection of architectural traits in breeding programmes. This study aimed at providing proof that a modelling approach can contribute to this debate, by using in silico exploration of different combinations of traits and their consequences on light interception, here considered as one of the key parameters to optimize fruit tree production. Methods The variability of organ geometrical traits, previously described in a bi-parental population, was used to simulate 1- to 5-year-old apple trees (Malus × domestica). Branching sequences along trunks observed during the first year of growth of the same hybrid trees were used to initiate the simulations, and hidden semi-Markov chains previously parameterized were used in subsequent years. Tree total leaf area (TLA) and silhouette to total area ratio (STAR) values were estimated, and a sensitivity analysis was performed, based on a metamodelling approach and a generalized additive model (GAM), to analyse the relative impact of organ geometry and lateral shoot types on STAR. Key Results A larger increase over years in TLA mean and variance was generated by varying branching along trunks than by varying organ geometry, whereas the inverse was observed for STAR, where mean values stabilized from year 3 to year 5. The internode length and leaf area had the highest impact on STAR, whereas long sylleptic shoots had a more significant effect than proleptic shoots. Although the GAM did not account for interactions, the additive effects of the geometrical factors explained >90% of STAR variation, but much less in the case of branching factors. Conclusions This study demonstrates that the proposed modelling approach could contribute to screening architectural traits and their relative impact on tree performance, here viewed through light interception. Even
Triple Point Topological Metals
NASA Astrophysics Data System (ADS)
Zhu, Ziming; Winkler, Georg W.; Wu, QuanSheng; Li, Ju; Soluyanov, Alexey A.
2016-07-01
Topologically protected fermionic quasiparticles appear in metals, where band degeneracies occur at the Fermi level, dictated by the band structure topology. While in some metals these quasiparticles are direct analogues of elementary fermionic particles of the relativistic quantum field theory, other metals can have symmetries that give rise to quasiparticles, fundamentally different from those known in high-energy physics. Here, we report on a new type of topological quasiparticles—triple point fermions—realized in metals with symmorphic crystal structure, which host crossings of three bands in the vicinity of the Fermi level protected by point group symmetries. We find two topologically different types of triple point fermions, both distinct from any other topological quasiparticles reported to date. We provide examples of existing materials that host triple point fermions of both types and discuss a variety of physical phenomena associated with these quasiparticles, such as the occurrence of topological surface Fermi arcs, transport anomalies, and topological Lifshitz transitions.
Kim, Youngjae; Yun, Won Seok; Lee, J D
2016-01-01
Functionalized X-Bi bilayers (X = Ga, In, and Tl) with halogens bonded on their both sides have been recently claimed to be the giant topological insulators due to the strong band inversion strengths. Employing the first-principles electronic structure calculation, we find the topological band order transition from the order p - p - s of the X-Bi bilayers with halogens on their both sides to the new order p - s - p of the bilayers (especially for X = Ga and In) with halogen on one side and hydrogen on the other side, where the asymmetric hydrogen bonding simulates the substrate. We further find that the p - s bulk band gap of the bilayer bearing the new order p - s - p sensitively depends on the electric field, which enables a meaningful engineering of the quantum spin Hall edge state by controlling the external electric field. PMID:27623710
NASA Astrophysics Data System (ADS)
Kim, Youngjae; Yun, Won Seok; Lee, J. D.
2016-09-01
Functionalized X-Bi bilayers (X = Ga, In, and Tl) with halogens bonded on their both sides have been recently claimed to be the giant topological insulators due to the strong band inversion strengths. Employing the first-principles electronic structure calculation, we find the topological band order transition from the order p – p – s of the X-Bi bilayers with halogens on their both sides to the new order p – s – p of the bilayers (especially for X = Ga and In) with halogen on one side and hydrogen on the other side, where the asymmetric hydrogen bonding simulates the substrate. We further find that the p – s bulk band gap of the bilayer bearing the new order p – s – p sensitively depends on the electric field, which enables a meaningful engineering of the quantum spin Hall edge state by controlling the external electric field.
Kim, Youngjae; Yun, Won Seok; Lee, J. D.
2016-01-01
Functionalized X-Bi bilayers (X = Ga, In, and Tl) with halogens bonded on their both sides have been recently claimed to be the giant topological insulators due to the strong band inversion strengths. Employing the first-principles electronic structure calculation, we find the topological band order transition from the order p – p – s of the X-Bi bilayers with halogens on their both sides to the new order p – s – p of the bilayers (especially for X = Ga and In) with halogen on one side and hydrogen on the other side, where the asymmetric hydrogen bonding simulates the substrate. We further find that the p – s bulk band gap of the bilayer bearing the new order p – s – p sensitively depends on the electric field, which enables a meaningful engineering of the quantum spin Hall edge state by controlling the external electric field. PMID:27623710
NASA Astrophysics Data System (ADS)
Baker, David M. H.; Head, James W.; Neumann, Gregory A.; Smith, David E.; Zuber, Maria T.
2012-03-01
The morphologic transition from complex impact craters, to peak-ring basins, and to multi-ring basins has been well-documented for decades. Less clear has been the morphometric characteristics of these landforms due to their large size and the lack of global high-resolution topography data. We use data from the Lunar Orbiter Laser Altimeter (LOLA) instrument onboard the Lunar Reconnaissance Orbiter (LRO) spacecraft to derive the morphometric characteristics of impact basins on the Moon, assess the trends, and interpret the processes involved in the observed morphologic transitions. We first developed a new technique for measuring and calculating the geometric/morphometric properties of impact basins on the Moon. This new method meets a number of criteria that are important for consideration in any topographic analysis of crater landforms (e.g., multiple data points, complete range of azimuths, systematic, reproducible analysis techniques, avoiding effects of post-event processes, robustness with respect to the statistical techniques). The resulting data more completely capture the azimuthal variation in topography that is characteristic of large impact structures. These new calculations extend the well-defined geometric trends for simple and complex craters out to basin-sized structures. Several new geometric trends for peak-ring basins are observed. Basin depth: A factor of two reduction in the depth to diameter (d/Dr) ratio in the transition from complex craters to peak-ring basins may be characterized by a steeper trend than known previously. The d/Dr ratio for peak-ring basins decreases with rim-crest diameter, which may be due to a non-proportional change in excavation cavity growth or scaling, as may occur in the simple to complex transition, or increased magnitude of floor uplift associated with peak-ring formation. Wall height, width, and slope: Wall height and width increase with increasing rim-crest diameter, while wall slope decreases; decreasing ratios
NASA Astrophysics Data System (ADS)
Har-Shemesh, Omri; Quax, Rick; Hoekstra, Alfons G.; Sloot, Peter M. A.
2016-04-01
The Fisher–Rao metric from information geometry is related to phase transition phenomena in classical statistical mechanics. Several studies propose to extend the use of information geometry to study more general phase transitions in complex systems. However, it is unclear whether the Fisher–Rao metric does indeed detect these more general transitions, especially in the absence of a statistical model. In this paper we study the transitions between patterns in the Gray-Scott reaction–diffusion model using Fisher information. We describe the system by a probability density function that represents the size distribution of blobs in the patterns and compute its Fisher information with respect to changing the two rate parameters of the underlying model. We estimate the distribution non-parametrically so that we do not assume any statistical model. The resulting Fisher map can be interpreted as a phase-map of the different patterns. Lines with high Fisher information can be considered as boundaries between regions of parameter space where patterns with similar characteristics appear. These lines of high Fisher information can be interpreted as phase transitions between complex patterns.
Xu, Shuigang; Han, Yu; Chen, Xiaolong; Wu, Zefei; Wang, Lin; Han, Tianyi; Ye, Weiguang; Lu, Huanhuan; Long, Gen; Wu, Yingying; Lin, Jiangxiazi; Cai, Yuan; Ho, K M; He, Yuheng; Wang, Ning
2015-04-01
Two-dimensional (2D) atomic-layered heterostructures stacked by van der Waals interactions recently introduced new research fields, which revealed novel phenomena and provided promising applications for electronic, optical, and optoelectronic devices. In this study, we report the van der Waals epitaxial growth of high-quality atomically thin Bi2Se3 on single crystalline hexagonal boron nitride (h-BN) by chemical vapor deposition. Although the in-plane lattice mismatch between Bi2Se3 and h-BN is approximately 65%, our transmission electron microscopy analysis revealed that Bi2Se3 single crystals epitaxially grew on h-BN with two commensurate states; that is, the (1̅21̅0) plane of Bi2Se3 was preferably parallel to the (1̅100) or (1̅21̅0) plane of h-BN. In the case of the Bi2Se3 (2̅110) ∥ h-BN (11̅00) state, the Moiré pattern wavelength in the Bi2Se3/h-BN superlattice can reach 5.47 nm. These naturally formed thin crystals facilitated the direct assembly of h-BN/Bi2Se3/h-BN sandwiched heterostructures without introducing any impurity at the interfaces for electronic property characterization. Our quantum capacitance (QC) measurements showed a compelling phenomenon of thickness-dependent topological phase transition, which was attributed to the coupling effects of two surface states from Dirac Fermions at/or above six quintuple layers (QLs) to gapped Dirac Fermions below six QLs. Moreover, in ultrathin Bi2Se3 (e.g., 3 QLs), we observed the midgap states induced by intrinsic defects at cryogenic temperatures. Our results demonstrated that QC measurements based on h-BN/Bi2Se3/h-BN sandwiched structures provided rich information regarding the density of states of Bi2Se3, such as quantum well states and Landau quantization. Our approach in fabricating h-BN/Bi2Se3/h-BN sandwiched device structures through the combination of bottom-up growth and top-down dry transferring techniques can be extended to other two-dimensional layered heterostructures.
Monolayer Topological Insulators: Silicene, Germanene, and Stanene
NASA Astrophysics Data System (ADS)
Ezawa, Motohiko
2015-12-01
We report the recent progress on the theoretical aspects of monolayer topological insulators including silicene, germanene and stanene, which are monolayer honeycomb structures of silicon, germanium and tin, respectively. They show quantum spin Hall effects in nature due to the spin-orbit interaction. The band gap can be tuned by applying perpendicular electric field, which induces a topological phase transition. We also analyze the topological properties of generic honeycomb systems together with the classification of topological insulators. Phase diagrams of topological insulators and superconductors in honeycomb systems are explicitly determined. We also investigate topological electronics including a topological field-effect transistor, the topological Kirchhoff's law and the topological spin-valleytronics.
NASA Astrophysics Data System (ADS)
Laurita, N. J.; Arpino, K. A.; Koopayeh, S. M.; McQueen, T. M.; Armitage, N. P.
The search for an intrinsic single crystal topological superconductor is one of the most dynamic areas of modern condensed matter physics. One of the best candidates of such a material is Tl5Te3 (Tc = 2 . 3 K), which previous ARPES measurements have shown possesses a Dirac cone within its superconducting gap. However, the fundamental nature of superconductivity, i.e. the superconducting order parameter, in Tl5Te3 remains unknown. Additionally, it has been shown that Tl5Te3 undergoes a superconducting-insulator transition upon doping with Sn. With no band parity inversion expected in the fully Sn doped compound one expects a topological supercondutor - trivial insulator transition, the nature of which is also unknown. In this work we use highly sensitive microwave cavity perturbation measurements, a direct probe of the superfluid density, to study the low energy electrodynamics of superconductivity in Tl5Te3 and its corresponding superconductor-insulator transition upon Sn doping. Work at Johns Hopkins was supported by the Gordon and Betty Moore Foundation through Grant GBMF2628, the DOE-BES through DE-FG02-08ER46544, and the ARCS Foundation.
NASA Astrophysics Data System (ADS)
Sorokin, A. V.; Aparicio Alcalde, M.; Bastidas, V. M.; Engelhardt, G.; Angelakis, D. G.; Brandes, T.
2016-09-01
In this work we study a one-dimensional lattice of Lipkin-Meshkov-Glick models with alternating couplings between nearest-neighbors sites, which resembles the Su-Schrieffer-Heeger model. Typical properties of the underlying models are present in our semiclassical-topological hybrid system, allowing us to investigate an interplay between semiclassical bifurcations at mean-field level and topological phases. Our results show that bifurcations of the energy landscape lead to diverse ordered quantum phases. Furthermore, the study of the quantum fluctuations around the mean-field solution reveals the existence of nontrivial topological phases. These are characterized by the emergence of localized states at the edges of a chain with free open-boundary conditions.
NASA Astrophysics Data System (ADS)
Zhang, Shengli; Xie, Meiqiu; Cai, Bo; Zhang, Haijun; Ma, Yandong; Chen, Zhongfang; Zhu, Zhen; Hu, Ziyu; Zeng, Haibo
2016-06-01
A stibarsen [derived from Latin stibium (antimony) and arsenic] or allemontite, is a natural form of arsenic antimonide (SbAs) with the same layered structure as arsenic and antimony. Thus, exploring the two-dimensional SbAs nanosheets is of great importance to gain insights into the properties of group V-V compounds at the atomic scale. Here, we propose a class of two-dimensional V-V honeycomb binary compounds, SbAs monolayers, which can be tuned from semiconductor to topological insulator. By ab initio density functional theory, both α-SbAs and γ-SbAs display a significant direct band gap, while others are indirect semiconductors. Interestingly, in an atomically thin β-SbAs polymorph, spin-orbital coupling is significant, which reduces its band gap by 200 meV. Especially under biaxial tensile strain, the gap of β-SbAs can be closed and reopened with concomitant change of band shapes, which is reminiscent of band inversion known in many topological insulators. In addition, we find that the Z2 topological invariant is 1 for β-SbAs under the tensile strain of 12%, and the nontrivial topological feature of β-SbAs is also confirmed by the gapless edge states which cross linearly at the Γ point. These ultrathin group-V-V semiconductors with outstanding properties are highly favorable for applications in alternative optoelectronic and quantum spin Hall devices.
You, Jia-Bin; Chan, A.H.; Oh, C.H.; Vedral, Vlatko
2014-10-15
We examine the topological properties of a spin–singlet superconductor with Rashba and Dresselhaus (110) spin–orbit couplings. We demonstrate that there are several topological invariants in the Bogoliubov–de Gennes (BdG) Hamiltonian by symmetry analysis. In particular, the Pfaffian invariant P for the particle–hole symmetry can be used to demonstrate all the possible phase diagrams of the BdG Hamiltonian. We find that the edge spectrum is either Dirac cone or flat band which supports the emergence of the Majorana fermion in this system. For the Majorana flat bands, an edge index, namely the Pfaffian invariant P(k{sub y}) or the winding number W(k{sub y}), is needed to make them topologically stable. These edge indices can also be used in determining the location of the Majorana flat bands. - Highlights: • Majorana fermion can emerge in the spin–orbit coupled singlet superconductor. • Pfaffian invariant and 1D winding number can be used to identify the nontrivial topological phase where Majorana flat band exists. • All the possible phase diagrams in the spin–orbit coupled singlet superconductor are demonstrated. • Majorana flat band only exists in the y direction in our model. • Majorana flat band has a significant experimental signature in the tunneling conductance measurement.
Geometric assortative growth model for small-world networks.
Shang, Yilun
2014-01-01
It has been shown that both humanly constructed and natural networks are often characterized by small-world phenomenon and assortative mixing. In this paper, we propose a geometrically growing model for small-world networks. The model displays both tunable small-world phenomenon and tunable assortativity. We obtain analytical solutions of relevant topological properties such as order, size, degree distribution, degree correlation, clustering, transitivity, and diameter. It is also worth noting that the model can be viewed as a generalization for an iterative construction of Farey graphs. PMID:24578661
Geometric Assortative Growth Model for Small-World Networks
2014-01-01
It has been shown that both humanly constructed and natural networks are often characterized by small-world phenomenon and assortative mixing. In this paper, we propose a geometrically growing model for small-world networks. The model displays both tunable small-world phenomenon and tunable assortativity. We obtain analytical solutions of relevant topological properties such as order, size, degree distribution, degree correlation, clustering, transitivity, and diameter. It is also worth noting that the model can be viewed as a generalization for an iterative construction of Farey graphs. PMID:24578661
Geometric assortative growth model for small-world networks.
Shang, Yilun
2014-01-01
It has been shown that both humanly constructed and natural networks are often characterized by small-world phenomenon and assortative mixing. In this paper, we propose a geometrically growing model for small-world networks. The model displays both tunable small-world phenomenon and tunable assortativity. We obtain analytical solutions of relevant topological properties such as order, size, degree distribution, degree correlation, clustering, transitivity, and diameter. It is also worth noting that the model can be viewed as a generalization for an iterative construction of Farey graphs.
Werneburg, Ingmar; Wilson, Laura A B; Parr, William C H; Joyce, Walter G
2015-03-01
The unique ability of modern turtles to retract their head and neck into the shell through a side-necked (pleurodiran) or hidden-necked (cryptodiran) motion is thought to have evolved independently in crown turtles. The anatomical changes that led to the vertebral shapes of modern turtles, however, are still poorly understood. Here we present comprehensive geometric morphometric analyses that trace turtle vertebral evolution and reconstruct disparity across phylogeny. Disparity of vertebral shape was high at the dawn of turtle evolution and decreased after the modern groups evolved, reflecting a stabilization of morphotypes that correspond to the two retraction modes. Stem turtles, which had a very simple mode of retraction, the lateral head tuck, show increasing flexibility of the neck through evolution towards a pleurodiran-like morphotype. The latter was the precondition for evolving pleurodiran and cryptodiran vertebrae. There is no correlation between the construction of formed articulations in the cervical centra and neck mobility. An increasing mobility between vertebrae, associated with changes in vertebral shape, resulted in a more advanced ability to retract the neck. In this regard, we hypothesize that the lateral tucking retraction of stem turtles was not only the precondition for pleurodiran but also of cryptodiran retraction. For the former, a kink in the middle third of the neck needed to be acquired, whereas for the latter modification was necessary between the eighth cervical vertebra and first thoracic vertebra. Our paper highlights the utility of 3D shape data, analyzed in a phylogenetic framework, to examine the magnitude and mode of evolutionary modifications to vertebral morphology. By reconstructing and visualizing ancestral anatomical shapes, we provide insight into the anatomical features underlying neck retraction mode, which is a salient component of extant turtle classification.
NASA Astrophysics Data System (ADS)
Wang, Xujing
Living systems are characterized by complexity in structure and emergent dynamic orders. In many aspects the onset of a chronic disease resembles phase transition in a dynamic system: quantitative changes accumulate largely unnoticed until a critical threshold is reached, which causes abrupt qualitative changes of the system. In this study we investigate this idea in a real example, the insulin-producing pancreatic islet β-cells and the onset of type 1 diabetes. Within each islet, the β-cells are electrically coupled to each other, and function as a network with synchronized actions. Using percolation theory we show how normal islet function is intrinsically linked to network connectivity, and the critical point where the islet cellular network loses site percolation, is consistent with laboratory and clinical observations of the threshold β-cell loss that causes islet functional failure. Numerical simulations confirm that the islet cellular network needs to be percolated for β-cells to synchronize. Furthermore, the interplay between site percolation and bond strength predicts the existence of a transient phase of islet functional recovery after disease onset and introduction of treatment, potentially explaining a long time mystery in the clinical study of type 1 diabetes: the honeymoon phenomenon. Based on these results, we hypothesized that the onset of T1D may be the result of a phase transition of the islet β-cell network. We further discuss the potential applications in identifying disease-driving factors, and the critical parameters that are predictive of disease onset.
Garcia, L.; Carreras, B. A.; Llerena, I.; Calvo, I.
2009-10-15
For the resistive pressure-gradient-driven turbulence model, the transition from laminar regime to fully developed turbulence is not simple and goes through several phases. For low values of the plasma parameter {beta}, a single quasicoherent structure forms. As {beta} increases, several of these structures may emerge and in turn take the dominant role. Finally, at high {beta}, fully developed turbulence with a broad spectrum is established. A suitable characterization of this transition can be given in terms of topological properties of the flow. Here, we analyze these properties that provide an understanding of the turbulence-induced transport and give a measure of the breaking of the homogeneity of the turbulence. To this end, an approach is developed that allows discriminating between topological properties of plasma turbulence flows that are relevant to the transport dynamics and the ones that are not. This is done using computational homology tools and leads to a faster convergence of numerical results for a fixed level of resolution than previously presented in Phys. Rev. E 78, 066402 (2008)
Topological spectrum of classical configurations
Nettel, Francisco; Quevedo, Hernando
2007-11-14
For any classical field configuration or mechanical system with a finite number of degrees of freedom we introduce the concept of topological spectrum. It is based upon the assumption that for any classical configuration there exists a principle fiber bundle that contains all the physical and geometric information of the configuration. The topological spectrum follows from the investigation of the corresponding topological invariants. Examples are given which illustrate the procedure and the significance of the topological spectrum as a discretization relationship among the parameters that determine the physical meaning of classical configurations.
NASA Astrophysics Data System (ADS)
Zhang, Xiaowei; Xing, Peiqi; Geng, Xiujuan; Sun, Daofeng; Xiao, Zhenyu; Wang, Lei
2015-09-01
Eight new coordination polymers (CPs), namely, [Zn(1,2-mbix)(tbtpa)]n (1), [Co(1,2-mbix)(tbtpa)]n (2), [CdCl(1,2-mbix)(tbtpa)0.5]n (3), {[Cd(1,2-bix)(tbtpa)]·H2O}n (4), {[Cd0.5(1,2-bix)(tbtpa)0.5]·H2O}n (5), {[Co0.5(1,2-bix)(tbtpa)0.5]·2H2O}n (6), {[Co(1,2-bix)(tbtpa)]·H2O}n (7) and {[Co(1,2-bix)(tbtpa)]·Diox·2H2O}n (8), were synthesized under solvothermal conditions based on mix-ligand strategy (H2tbtpa=tetrabromoterephthalic acid and 1,2-mbix=1,2-bis((2-methyl-1H-imidazol-1-yl)methyl)benzene, 1,2-bix=1,2-bis(imidazol-1-ylmethyl)benzene). All of the CPs have been structurally characterized by single-crystal X-ray diffraction analyses and further characterized by elemental analyses, IR spectroscopy, powder X-ray diffraction (PXRD), and thermogravimetric analyses (TGA). X-ray diffraction analyses show that 1 and 2 are isotypics which have 2D highly undulated networks with (4,4)-sql topology with the existence of C-H ⋯Br interactions; for 3, it has a 2D planar network with (4,4)-sql topology with the occurrence of C-H ⋯Cl interactions other than C-H ⋯Br interactions; 4 shows a 3D 2-fold interpenetrated nets with rare 65·8-mok topology which has a self-catention property. As the same case as 1 and 2, 5 and 6 are also isostructural with planar layers with 44-sql topology which further assembled into 3D supramolecular structure through the interdigitated stacking fashion and the C-Br ⋯Cph interactions. As for 7, it has a 2D slightly undulated networks with (4,4)-sql topology which has one dimension channel. While 8 has a 2-fold interpenetrated networks with (3,4)-connect jeb topology with point symbol {63}{65·8}. And their structures can be tuned by conformations of bis(imidazol) ligands and solvent mixture. Besides, the TGA properties for all compounds and the luminescent properties for 1, 3, 4, 5 are discussed in detail.
Hybrid Topological Lie-Hamiltonian Learning in Evolving Energy Landscapes
NASA Astrophysics Data System (ADS)
Ivancevic, Vladimir G.; Reid, Darryn J.
2015-11-01
In this Chapter, a novel bidirectional algorithm for hybrid (discrete + continuous-time) Lie-Hamiltonian evolution in adaptive energy landscape-manifold is designed and its topological representation is proposed. The algorithm is developed within a geometrically and topologically extended framework of Hopfield's neural nets and Haken's synergetics (it is currently designed in Mathematica, although with small changes it could be implemented in Symbolic C++ or any other computer algebra system). The adaptive energy manifold is determined by the Hamiltonian multivariate cost function H, based on the user-defined vehicle-fleet configuration matrix W, which represents the pseudo-Riemannian metric tensor of the energy manifold. Search for the global minimum of H is performed using random signal differential Hebbian adaptation. This stochastic gradient evolution is driven (or, pulled-down) by `gravitational forces' defined by the 2nd Lie derivatives of H. Topological changes of the fleet matrix W are observed during the evolution and its topological invariant is established. The evolution stops when the W-topology breaks down into several connectivity-components, followed by topology-breaking instability sequence (i.e., a series of phase transitions).
On geometric interpretation of the berry phase
NASA Astrophysics Data System (ADS)
Katanaev, M. O.
2012-03-01
A geometric interpretation of the Berry phase and its Wilczek-Zee non-Abelian generalization are given in terms of connections on principal fiber bundles. It is demonstrated that a principal fiber bundle can be trivial in all cases, while the connection and its holonomy group are nontrivial. Therefore, the main role is played by geometric rather than topological effects.
An, Wei; Turner, C. H.
2009-04-30
The well-defined binding between transition-metals (TM) and the sidewall of carbon nanotubes (CNTs) plays a key role in the performance of CNT-based anoelectronics, as well as the stability of catalysts used in either heterogeneous catalysis or fuel-cell electrocatalysis. Spin-polarized density functional theory calculations demonstrate that either boron or nitrogen doping can increase the binding strength of TM atoms with singlewall carbon nanotubes (SWCNTs), and comparatively, boron doping is more effective. The binding nature can be identified as chemisorption, based on the magnitude of the binding energy and the formation of multiple bonds. The chemisorbed TM atoms can modify the electronic structure of the doped nanotubes in various ways, depending upon the TM and helicity of the CNT, rendering the TM/doped-SWCNT composite viable for a wide range of applications. A total of 11 technologically relevant TMs adsorbed on two distinct and stable doped-SWCNT models have been investigated in this study. The doping sites are arranged in either a locally concentrated or uniform fashion within semiconducting SWCNT(8,0) and metallic SWCNT(6,6). The results serve as a starting point for studying larger, more complex TM nanostructures anchored on the sidewall of boron- or nitrogen-doped CNTs.
Topological superconductivity, topological confinement, and the vortex quantum Hall effect
Diamantini, M. Cristina; Trugenberger, Carlo A.
2011-09-01
Topological matter is characterized by the presence of a topological BF term in its long-distance effective action. Topological defects due to the compactness of the U(1) gauge fields induce quantum phase transitions between topological insulators, topological superconductors, and topological confinement. In conventional superconductivity, because of spontaneous symmetry breaking, the photon acquires a mass due to the Anderson-Higgs mechanism. In this paper we derive the corresponding effective actions for the electromagnetic field in topological superconductors and topological confinement phases. In topological superconductors magnetic flux is confined and the photon acquires a topological mass through the BF mechanism: no symmetry breaking is involved, the ground state has topological order, and the transition is induced by quantum fluctuations. In topological confinement, instead, electric charge is linearly confined and the photon becomes a massive antisymmetric tensor via the Stueckelberg mechanism. Oblique confinement phases arise when the string condensate carries both magnetic and electric flux (dyonic strings). Such phases are characterized by a vortex quantum Hall effect potentially relevant for the dissipationless transport of information stored on vortices.
NASA Astrophysics Data System (ADS)
Lindlein, Norbert; Leuchs, Gerd
This chapter shall discuss the basics and the applications of geometrical optical methods in modern optics. Geometrical optics has a long tradition and some ideas are many centuries old. Nevertheless, the invention of modern personal computers which can perform several million floating-point operations in a second also revolutionized the methods of geometrical optics and so several analytical methods lost importance whereas numerical methods such as ray tracing became very important. Therefore, the emphasis in this chapter is also on modern numerical methods such as ray tracing and some other systematic methods such as the paraxial matrix theory.
Geometrical methods in soft condensed-matter physics
NASA Astrophysics Data System (ADS)
Kung, William
We propose a geometrical picture of understanding the thermodynamic and elastic properties of charged and fuzzy colloidal crystals, by analogy to foams, as well as perform a computational exercise to confirm a new universality class for long polymers with non-trivial topologies. By the foam analogy, we relate the problem of thermodynamic stability to the Kelvin's problem of partitioning space into equal-volume cells of minimal surface area. In particular, we consider the face-centered cubic (FCC), body-centered cubic (BCC) and the beta-tungsten (A15) lattices. We write down the free energy of these solid phases directly in terms of geometric and microscopic parameters of the system, and we derive the theoretical phase diagram of an experimental charged colloidal systems [Phys. Rev. Lett. 62, 1524 (1989)]. By considering deformations to the foam cells, we also compute the cubic elastic constants of these three lattices for charged and fuzzy colloids. In the polymer problem, we consider the critical behavior of polymers much longer than their persistence length, with built-in topological constraint in the form of Fuller's relation: Lk = Tw + Wr in a theta-solvent. We map the problem to the three-dimensional symmetric U( N)-Chern Simons theory as N → 0. To two-loop order, we find a new scaling regime for the topologically constrained polymers, with critical exponents that depend on the chemical potential for writhe which gives way to a fluctuation-induced first-order transition.
NASA Astrophysics Data System (ADS)
Tanda, Satoshi; Matsuyama, Toyoki; Oda, Migaku; Asano, Yasuhiro; Yakubo, Kousuke
2006-08-01
.]. Nanofibers of hydrogen storage alloy / I. Saita ... [et al.]. Synthesis of stable icosahedral quasicrystals in Zn-Sc based alloys and their magnetic properties / S. Kashimoto and T. Ishimasa. One-armed spiral wave excited by eam pressure in accretion disks in Be/X-Ray binaries / K. Hayasaki and A. T. Okazaki -- IV. Topological defects and excitations. Topological excitations in the ground state of charge density wave systems / P. Monceau. Soliton transport in nanoscale charge-density-wave systems / K. Inagaki, T. Toshima and S. Tanda. Topological defects in triplet superconductors UPt3, Sr[symbol]RuO[symbol], etc. / K. Maki ... [et al.]. Microscopic structure of vortices in type II superconductors / K. Machida ... [et al.]. Microscopic neutron investigation of the Abrikosov state of high-temperature superconductors / J. Mesot. Energy dissipation at nano-scale topological defects of high-Tc superconductors: microwave study / A. Maeda. Pressure induced topological phase transition in the heavy Fermion compound CeAl[symbol] / H. Miyagawa ... [et al.]. Explanation for the unusual orientation of LSCO square vortex lattice in terms of nodal superconductivity / M. Oda. Local electronic states in Bi[symbol]Sr[symbol]CaCu[symbol]O[symbol] / A. Hashimoto ... [et al.] -- V. Topology in quantum phenomena. Topological vortex formation in a Bose-Einstein condensate of alkali-metal atoms / M. Nakahara. Quantum phase transition of [symbol]He confined in nano-porous media / K. Shirahama, K. Yamamoto and Y. Shibayama. A new mean-field theory for Bose-Einstein condensates / T. Kita. Spin current in topological cristals / Y. Asano. Antiferromagnetic defects in non-magnetic hidden order of the heavy-electron system URu[symbol]Si[symbol] / H. Amitsuka, K. Tenya and M. Yokoyama. Magnetic-field dependences of thermodynamic quantities in the vortex state of Type-II superconductors / K. Watanabe, T. Kita and M. Arai. Three-magnon-mediated nuclear spin relaxation in quantum ferrimagnets of topological
NASA Astrophysics Data System (ADS)
Lu, Ying-Bo; Li, Y. H.; Ling, Z. C.; Cong, Wei-Yan; Zhang, Peng; Xin, Y. Q.; Yang, T. L.
2016-02-01
As transparent conducting oxides (TCOs), In2O3 in the high pressure phase attracts extensive research interests. Because physical properties are determined by the geometric structures, we investigate the electronic and optical properties of Zn/Sn codoped In2O3 materials (IZTO) being modulated by the bixbyite/corundum phase transition via Density Functional Theory calculations. For IZTO in high pressure phase, i.e. corundum phase, Sn/Zn dopant pair tends to form face-sharing ZnO6 and SnO6 octahedrons. The radius differences between Zn2+/Sn4+ dopants and In3+ host cations make Jahn-Teller effect occur and IZTO transform from bixbyite to corundum phase under a slight higher pressure than that of pure In2O3. Although Zn/Sn cosubstitution of In ions may increase the free carrier effective mass m * near the band edge, when IZTO crystal transforms to corundum phase, the more dense packing structure results in stronger cation s-orbital overlaps than in bixbyite phase, which makes m * recover to a smaller value. In addition, corundum IZTO has a larger indirect band gap and a high dopant solubility. So these investigations may open a new way to search for TCOs materials with low indium content.
NASA Astrophysics Data System (ADS)
Islam, Fhokrul; Pertsova, Anna; Mahani, Reza; Canali, Carlo
The breaking of time reversal symmetry in a topological insulator (TI) by magnetic doping is one of the most studied phenomena among the properties of Dirac materials. The robustness of the topological surface states (TSS) against magnetic impurities is of critical importance for spin-dependent transport in these systems. The interaction between TSS and magnetic impurities can open a gap, provided that the magnetic order is oriented normal to the surface of the TI. Such gap opening is crucial for realizing TI-based spintronic devices and for the observation of different fundamental phenomena, such as the anomalous quantum Hall effect. Using density functional theory as implemented in the WIEN2k ab-initio package, we have investigated the effect of the magnetization orientation on the gap opening at the Dirac point, for substitutional Mn and Fe impurities on the Bi2Se3 surface, and have calculated the associated single-ion anisotropy (SIA). We also have studied bulk SIA in order to compare the role played by TSS on the surface SIA.
NASA Astrophysics Data System (ADS)
Deng, Bei; Zhang, Yiou; Zhang, S. B.; Wang, Yayu; He, Ke; Zhu, Junyi
2016-08-01
The quantum anomalous Hall effect (QAHE) originates from a combination of the spin-orbital coupling and the breaking of time-reversal symmetry due to intrinsic ferromagnetic ordering and was recently observed in Cr and V doped magnetic topological insulators (TIs). However, it was only observed at extremely low temperatures due to the low ferromagnetic Curie temperature and the tiny magnetically induced gap. To fully understand the mechanism of the ferromagnetic ordering, thereby improving the ferromagnetism, we investigated 4 f transition metal doped B i2S e3 , using density functional theory approaches. We predict that Eu and Sm can introduce stable long-range ferromagnetic states in B i2S e3 , with large magnetic moments and low impurity disorders. Additionally, codoping is proposed to tune the Fermi level into the gap, which simultaneously improves the magnetic moment and the incorporation of magnetic ions. Our findings, thus, offer a step in facilitating the realization of QAHE in TI systems.
Thermodynamic and topological phase diagrams of correlated topological insulators
NASA Astrophysics Data System (ADS)
Zdulski, Damian; Byczuk, Krzysztof
2015-09-01
A definition of topological phases of density matrices is presented. The topological invariants in case of both noninteracting and interacting systems are extended to nonzero temperatures. The influence of electron interactions on topological insulators at finite temperatures is investigated. A correlated topological insulator is described by the Kane-Mele model, which is extended by the interaction term of the Falicov-Kimball type. Within the Hartree-Fock and the Hubbard I approximations, thermodynamic and topological phase diagrams are determined where the long-range order is included. The results show that correlation effects lead to a strong suppression of the existence of the nontrivial topological phase. In the homogeneous phase, we find a purely correlation driven phase transition into the topologically trivial Mott insulator.
NASA Astrophysics Data System (ADS)
Talman, Richard
1999-10-01
Mechanics for the nonmathematician-a modern approach For physicists, mechanics is quite obviously geometric, yet the classical approach typically emphasizes abstract, mathematical formalism. Setting out to make mechanics both accessible and interesting for nonmathematicians, Richard Talman uses geometric methods to reveal qualitative aspects of the theory. He introduces concepts from differential geometry, differential forms, and tensor analysis, then applies them to areas of classical mechanics as well as other areas of physics, including optics, crystal diffraction, electromagnetism, relativity, and quantum mechanics. For easy reference, Dr. Talman treats separately Lagrangian, Hamiltonian, and Newtonian mechanics-exploring their geometric structure through vector fields, symplectic geometry, and gauge invariance respectively. Practical perturbative methods of approximation are also developed. Geometric Mechanics features illustrative examples and assumes only basic knowledge of Lagrangian mechanics. Of related interest . . . APPLIED DYNAMICS With Applications to Multibody and Mechatronic Systems Francis C. Moon A contemporary look at dynamics at an intermediate level, including nonlinear and chaotic dynamics. 1998 (0-471-13828-2) 504 pp. MATHEMATICAL PHYSICS Applied Mathematics for Scientists and Engineers Bruce Kusse and Erik Westwig A comprehensive treatment of the mathematical methods used to solve practical problems in physics and engineering. 1998 (0-471-15431-8) 680 pp.
Perspective: Geometrically frustrated assemblies
NASA Astrophysics Data System (ADS)
Grason, Gregory M.
2016-09-01
This perspective will overview an emerging paradigm for self-organized soft materials, geometrically frustrated assemblies, where interactions between self-assembling elements (e.g., particles, macromolecules, proteins) favor local packing motifs that are incompatible with uniform global order in the assembly. This classification applies to a broad range of material assemblies including self-twisting protein filament bundles, amyloid fibers, chiral smectics and membranes, particle-coated droplets, curved protein shells, and phase-separated lipid vesicles. In assemblies, geometric frustration leads to a host of anomalous structural and thermodynamic properties, including heterogeneous and internally stressed equilibrium structures, self-limiting assembly, and topological defects in the equilibrium assembly structures. The purpose of this perspective is to (1) highlight the unifying principles and consequences of geometric frustration in soft matter assemblies; (2) classify the known distinct modes of frustration and review corresponding experimental examples; and (3) describe outstanding questions not yet addressed about the unique properties and behaviors of this broad class of systems.
Network topology of the desert rose
NASA Astrophysics Data System (ADS)
Hope, Sigmund; Kundu, Sumanta; Roy, Chandreyee; Manna, Subhrangshu; Hansen, Alex
2015-09-01
Desert roses are gypsum crystals that consist of intersecting disks. We determine their geometrical structure using computer assisted tomography. By mapping the geometrical structure onto a graph, the topology of the desert rose is analyzed and compared to a model based on diffusion limited aggregation. By comparing the topology, we find that the model gets a number of the features of the real desert rose right, whereas others do not fit so well.
Dziarmaga, Jacek; Zurek, Wojciech H.
2014-01-01
Kibble-Zurek mechanism (KZM) uses critical scaling to predict density of topological defects and other excitations created in second order phase transitions. We point out that simply inserting asymptotic critical exponents deduced from the immediate vicinity of the critical point to obtain predictions can lead to results that are inconsistent with a more careful KZM analysis based on causality – on the comparison of the relaxation time of the order parameter with the “time distance” from the critical point. As a result, scaling of quench-generated excitations with quench rates can exhibit behavior that is locally (i.e., in the neighborhood of any given quench rate) well approximated by the power law, but with exponents that depend on that rate, and that are quite different from the naive prediction based on the critical exponents relevant for asymptotically long quench times. Kosterlitz-Thouless scaling (that governs e.g. Mott insulator to superfluid transition in the Bose-Hubbard model in one dimension) is investigated as an example of this phenomenon. PMID:25091996
NASA Astrophysics Data System (ADS)
Schaper, Danielle; McElroy, Kyle; Calleja, Eduardo; Dai, Jixia; Li, Lijun; Lu, Wenjian; Sun, Yuping; Zhu, Xiangde
2014-03-01
Charged ordered states are becoming a common feature in the phase diagrams of correlated materials. In many cased there are indications that doping controlled quantum critical points between the CO state and others are related to interesting properties including superconductivity. An interesting test case is the ordered 2D CDW found in the transition metal dichalcogenides. We performed an analytical study on the dichalcogenides tantalum disulfide (TaS2) and tantalum diselenide (TaSe2) to observe how CDWs present in the material can be melted as disorder is introduced into the system via copper doping. Data was taken using a scanning tunneling microscope (STM) below the transition to the CDW state, both with and without copper dopants added. The resulting topographs were then analyzed to investigate the relationship between the phase and the amplitude of the disordered CDW. We found that the copper doping caused disorder in the CDW state characterized by phase wanderings and 2 π phase winding ``point defects'' in the CDW not present in the undoped parent compound. The locations of these point defects and windings were, in turn, found to have the characteristics of topological defects. Implications for studies of other disordered CO states seen in STM will be discussed.
Emergent geometric frustration of artificial magnetic skyrmion crystals
NASA Astrophysics Data System (ADS)
Ma, Fusheng; Reichhardt, C.; Gan, Weiliang; Reichhardt, C. J. Olson; Lew, Wen Siang
2016-10-01
Magnetic skyrmions have been receiving growing attention as potential information storage and magnetic logic devices since an increasing number of materials have been identified that support skyrmion phases. Explorations of artificial frustrated systems have led to new insights into controlling and engineering new emergent frustration phenomena in frustrated and disordered systems. Here, we propose a skyrmion spin ice, giving a unifying framework for the study of geometric frustration of skyrmion crystals (SCs) in a nonfrustrated artificial geometrical lattice as a consequence of the structural confinement of skyrmions in magnetic potential wells. The emergent ice rules from the geometrically frustrated SCs highlight a novel phenomenon in this skyrmion system: emergent geometrical frustration. We demonstrate how SC topology transitions between a nonfrustrated periodic configuration and a frustrated icelike ordering can also be realized reversibly. The proposed artificial frustrated skyrmion systems can be annealed into different ice phases with an applied current-induced spin-transfer torque, including a long-range ordered ice rule obeying ground state, as-relaxed random state, biased state, and monopole state. The spin-torque reconfigurability of the artificial skyrmion ice states, difficult to achieve in other artificial spin ice systems, is compatible with standard spintronic device fabrication technology, which makes the semiconductor industrial integration straightforward.
Topological string theory revisited I: The stage
NASA Astrophysics Data System (ADS)
Jia, Bei
2016-08-01
In this paper, we reformulate topological string theory using supermanifolds and supermoduli spaces, following the approach worked out by Witten (Superstring perturbation theory revisited, arXiv:1209.5461). We intend to make the construction geometrical in nature, by using supergeometry techniques extensively. The goal is to establish the foundation of studying topological string amplitudes in terms of integration over appropriate supermoduli spaces.
Geometrical Pumping with a Bose-Einstein Condensate.
Lu, H-I; Schemmer, M; Aycock, L M; Genkina, D; Sugawa, S; Spielman, I B
2016-05-20
We realized a quantum geometric "charge" pump for a Bose-Einstein condensate (BEC) in the lowest Bloch band of a novel bipartite magnetic lattice. Topological charge pumps in filled bands yield quantized pumping set by the global-topological-properties of the bands. In contrast, our geometric charge pump for a BEC occupying just a single crystal momentum state exhibits nonquantized charge pumping set by local-geometrical-properties of the band structure. Like topological charge pumps, for each pump cycle we observed an overall displacement (here, not quantized) and a temporal modulation of the atomic wave packet's position in each unit cell, i.e., the polarization. PMID:27258857
Geometrical Pumping with a Bose-Einstein Condensate.
Lu, H-I; Schemmer, M; Aycock, L M; Genkina, D; Sugawa, S; Spielman, I B
2016-05-20
We realized a quantum geometric "charge" pump for a Bose-Einstein condensate (BEC) in the lowest Bloch band of a novel bipartite magnetic lattice. Topological charge pumps in filled bands yield quantized pumping set by the global-topological-properties of the bands. In contrast, our geometric charge pump for a BEC occupying just a single crystal momentum state exhibits nonquantized charge pumping set by local-geometrical-properties of the band structure. Like topological charge pumps, for each pump cycle we observed an overall displacement (here, not quantized) and a temporal modulation of the atomic wave packet's position in each unit cell, i.e., the polarization.
Jagelská, Eva B; Brázda, Václav; Pecinka, Petr; Palecek, Emil; Fojta, Miroslav
2008-05-15
The tumour suppressor protein p53 is one of the most important factors regulating cell proliferation, differentiation and programmed cell death in response to a variety of cellular stress signals. P53 is a nuclear phosphoprotein and its biochemical function is closely associated with its ability to bind DNA in a sequence-specific manner and operate as a transcription factor. Using a competition assay, we investigated the effect of DNA topology on the DNA binding of human wild-type p53 protein. We prepared sets of topoisomers of plasmid DNA with and without p53 target sequences, differing in their internal symmetry. Binding of p53 to DNA increased with increasing negative superhelix density (-sigma). At -sigma < or = 0.03, the relative effect of DNA supercoiling on protein-DNA binding was similar for DNA containing both symmetrical and non-symmetrical target sites. On the other hand, at higher -sigma, target sites with a perfect inverted repeat sequence exhibited a more significant enhancement of p53 binding as a result of increasing levels of negative DNA supercoiling. For -sigma = 0.07, an approx. 3-fold additional increase in binding was observed for a symmetrical target site compared with a non-symmetrical target site. The p53 target sequences possessing the inverted repeat symmetry were shown to form a cruciform structure in sufficiently negative supercoiled DNA. We show that formation of cruciforms in DNA topoisomers at -sigma > or = 0.05 correlates with the extra enhancement of p53-DNA binding. PMID:18271758
NASA Astrophysics Data System (ADS)
Qing, Lu; Huai-Yong, Zhang; Yan, Cheng; Xiang-Rong, Chen; Guang-Fu, Ji
2016-02-01
The phase transition, elastic and electronic properties of three phases (phase I, II, and III) of Sb2Te3 are investigated by using the generalized gradient approximation (GGA) with the PBESOL exchange-correlation functional in the framework of density-functional theory. Some basic physical parameters, such as lattice constants, bulk modulus, shear modulus, Young’s modulus, Poisson’s ratio, acoustic velocity, and Debye temperature Θ are calculated. The obtained lattice parameters under various pressures are consistent with experimental data. Phase transition pressures are 9.4 GPa (I → II) and 14.1 GPa (II → III), which are in agreement with the experimental results. According to calculated elastic constants, we also discuss the ductile or brittle characters and elastic anisotropies of three phases. Phases I and III are brittle, while phase II is ductile. Of the three phases, phase II has the most serious degree of elastic anisotropy and phase III has the slightest one. Finally, we investigate the partial densities of states (PDOSs) of three phases and find that the three phases possess some covalent features. Project supported by the National Natural Science Foundation of China (Grant Nos. 11204192 and 11174214) and Jointly supported by the National Natural Science Foundation of China and the China Academy of Engineering Physics (NSAF) (Grant No. U1430117).
NASA Astrophysics Data System (ADS)
Schleich, K.; Witt, D. M.
Classically, all topologies are allowed as solutions to the Einstein equations. However, one does not observe any topological structures on medium range distance scales, that is scales that are smaller than the size of the observed universe but larger than the microscopic scales for which quantum gravity becomes important. Recently, Friedman, Schleich and Witt (1993) have proven that there is topological censorship on these medium range distance scales: the Einstein equations, locally positive energy, and local predictability of physics imply that any medium distance scale topological structures cannot be seen. More precisely we show that the topology of physically reasonable isolated systems is shrouded from distant observers, or in other words there is a topological censorship principle.
Lee, Yongjae; Kim, Sun Jin; Kao, Chi-Chang; Vogt, Thomas
2008-03-01
Two high-pressure phases of a potassium gallosilicate with a gismondine framework (K-GaSi-GIS) were characterized using Rietveld refinements of in-situ high-pressure, high-resolution synchrotron X-ray powder diffraction data. The observed response of the K-GaSi-GIS framework under hydrostatic pressure is a gradual flattening of the so-called "double crankshaft" structural chain units. At pressures below 1.0(1) GPa, additional water molecules from the hydrostatic pressure-transmitting medium are inserted into the potassium-water guest network ("pressure-induced hydration") resulting in a "super-hydrated" high-pressure phase I. As the flattening of the double crankshaft structural units in the GIS framework continues above 1.6 GPa, the ellipticity of the cross-linking 8-ring windows is reduced below a certain threshold, and a disordering of the potassium-water guest structure along the 8-ring channel, characteristic of a disordered high-pressure phase II, is observed. The concerted framework distortion and guest network disordering accommodates the increased hydration level while maintaining the seven-fold coordination environment of the potassium cations to framework oxygen atoms and water molecules. We have thus established the atomistic details of a guest-host order-disorder transition under pressure-induced hydration conditions in a zeolite with GIS framework and compared it to other zeolites during pressure-induced hydration. We find that the structural changes mediated by the extra-framework cations and their coordination environment under PIH conditions are at the core of these different mechanisms and are driving the changes in the ellipticity of pore openings, order-disorder and disorder-order transitions, and framework distortions. PMID:18266365
NASA Technical Reports Server (NTRS)
Grebowsky, G. J.
1982-01-01
Present LANDSAT data formats are reviewed to clarify how the geodetic location and registration capabilities were defined for P-tape products and RBV data. Since there is only one geometric model used in the master data processor, geometric location accuracy of P-tape products depends on the absolute accuracy of the model and registration accuracy is determined by the stability of the model. Due primarily to inaccuracies in data provided by the LANDSAT attitude management system, desired accuracies are obtained only by using ground control points and a correlation process. The verification of system performance with regards to geodetic location requires the capability to determine pixel positions of map points in a P-tape array. Verification of registration performance requires the capability to determine pixel positions of common points (not necessarily map points) in 2 or more P-tape arrays for a given world reference system scene. Techniques for registration verification can be more varied and automated since map data are not required. The verification of LACIE extractions is used as an example.
Second-quantized formulation of geometric phases
Deguchi, Shinichi; Fujikawa, Kazuo
2005-07-15
The level crossing problem and associated geometric terms are neatly formulated by the second-quantized formulation. This formulation exhibits a hidden local gauge symmetry related to the arbitrariness of the phase choice of the complete orthonormal basis set. By using this second-quantized formulation, which does not assume adiabatic approximation, a convenient exact formula for the geometric terms including off-diagonal geometric terms is derived. The analysis of geometric phases is then reduced to a simple diagonalization of the Hamiltonian, and it is analyzed both in the operator and path-integral formulations. If one diagonalizes the geometric terms in the infinitesimal neighborhood of level crossing, the geometric phases become trivial (and thus no monopole singularity) for arbitrarily large but finite time interval T. The integrability of Schroedinger equation and the appearance of the seemingly nonintegrable phases are thus consistent. The topological proof of the Longuet-Higgins' phase-change rule, for example, fails in the practical Born-Oppenheimer approximation where a large but finite ratio of two time scales is involved and T is identified with the period of the slower system. The difference and similarity between the geometric phases associated with level crossing and the exact topological object such as the Aharonov-Bohm phase become clear in the present formulation. A crucial difference between the quantum anomaly and the geometric phases is also noted.
NASA Astrophysics Data System (ADS)
Gonnelli, R. S.; Daghero, D.; Tortello, M.; Ummarino, G. A.; Bukowski, Z.; Karpinski, J.; Reuvekamp, P. G.; Kremer, R. K.; Profeta, G.; Suzuki, K.; Kuroki, K.
2016-05-01
Iron-based compounds (IBS) display a surprising variety of superconducting properties that seems to arise from the strong sensitivity of these systems to tiny details of the lattice structure. In this respect, systems that become superconducting under pressure, like CaFe2As2, are of particular interest. Here we report on the first directional point-contact Andreev-reflection spectroscopy (PCARS) measurements on CaFe2As2 crystals under quasi-hydrostatic pressure, and on the interpretation of the results using a 3D model for Andreev reflection combined with ab-initio calculations of the Fermi surface (within the density functional theory) and of the order parameter symmetry (within a random-phase-approximation approach in a ten-orbital model). The almost perfect agreement between PCARS results at different pressures and theoretical predictions highlights the intimate connection between the changes in the lattice structure, a topological transition in the holelike Fermi surface sheet, and the emergence on the same sheet of an order parameter with a horizontal node line.
Gonnelli, R. S.; Daghero, D.; Tortello, M.; Ummarino, G. A.; Bukowski, Z.; Karpinski, J.; Reuvekamp, P. G.; Kremer, R. K.; Profeta, G.; Suzuki, K.; Kuroki, K.
2016-01-01
Iron-based compounds (IBS) display a surprising variety of superconducting properties that seems to arise from the strong sensitivity of these systems to tiny details of the lattice structure. In this respect, systems that become superconducting under pressure, like CaFe2As2, are of particular interest. Here we report on the first directional point-contact Andreev-reflection spectroscopy (PCARS) measurements on CaFe2As2 crystals under quasi-hydrostatic pressure, and on the interpretation of the results using a 3D model for Andreev reflection combined with ab-initio calculations of the Fermi surface (within the density functional theory) and of the order parameter symmetry (within a random-phase-approximation approach in a ten-orbital model). The almost perfect agreement between PCARS results at different pressures and theoretical predictions highlights the intimate connection between the changes in the lattice structure, a topological transition in the holelike Fermi surface sheet, and the emergence on the same sheet of an order parameter with a horizontal node line. PMID:27216477
PREFACE: Geometrically frustrated magnetism Geometrically frustrated magnetism
NASA Astrophysics Data System (ADS)
Gardner, Jason S.
2011-04-01
Frustrated magnetism is an exciting and diverse field in condensed matter physics that has grown tremendously over the past 20 years. This special issue aims to capture some of that excitement in the field of geometrically frustrated magnets and is inspired by the 2010 Highly Frustrated Magnetism (HFM 2010) meeting in Baltimore, MD, USA. Geometric frustration is a broad phenomenon that results from an intrinsic incompatibility between some fundamental interactions and the underlying lattice geometry based on triangles and tetrahedra. Most studies have centred around the kagomé and pyrochlore based magnets but recent work has looked at other structures including the delafossite, langasites, hyper-kagomé, garnets and Laves phase materials to name a few. Personally, I hope this issue serves as a great reference to scientist both new and old to this field, and that we all continue to have fun in this very frustrated playground. Finally, I want to thank the HFM 2010 organizers and all the sponsors whose contributions were an essential part of the success of the meeting in Baltimore. Geometrically frustrated magnetism contents Spangolite: an s = 1/2 maple leaf lattice antiferromagnet? T Fennell, J O Piatek, R A Stephenson, G J Nilsen and H M Rønnow Two-dimensional magnetism and spin-size effect in the S = 1 triangular antiferromagnet NiGa2S4 Yusuke Nambu and Satoru Nakatsuji Short range ordering in the modified honeycomb lattice compound SrHo2O4 S Ghosh, H D Zhou, L Balicas, S Hill, J S Gardner, Y Qi and C R Wiebe Heavy fermion compounds on the geometrically frustrated Shastry-Sutherland lattice M S Kim and M C Aronson A neutron polarization analysis study of moment correlations in (Dy0.4Y0.6)T2 (T = Mn, Al) J R Stewart, J M Hillier, P Manuel and R Cywinski Elemental analysis and magnetism of hydronium jarosites—model kagome antiferromagnets and topological spin glasses A S Wills and W G Bisson The Herbertsmithite Hamiltonian: μSR measurements on single crystals
NASA Astrophysics Data System (ADS)
Trang, Chi Xuan; Wang, Zhiwei; Yamada, Keiko; Souma, Seigo; Sato, Takafumi; Takahashi, Takashi; Segawa, Kouji; Ando, Yoichi
2016-04-01
We report a systematic angle-resolved photoemission spectroscopy on topological insulator (TI) TlBi1 -xSbxTe2 which is bulk insulating at 0.5 ≲x ≲0.9 and undergoes a metal-insulator-metal transition with the Sb content x . We found that this transition is characterized by a systematic hole doping with increasing x , which results in the Fermi-level crossings of the bulk conduction and valence bands at x ˜0 and x ˜1 , respectively. The Dirac point of the topological surface state is gradually isolated from the valence-band edge, accompanied by a sign reversal of Dirac carriers. We also found that the Dirac velocity is the largest among known solid-solution TI systems. The TlBi1 -xSbxTe2 system thus provides an excellent platform for Dirac-cone engineering and device applications of TIs.
Rendering the Topological Spines
Nieves-Rivera, D.
2015-05-05
Many tools to analyze and represent high dimensional data already exits yet most of them are not flexible, informative and intuitive enough to help the scientists make the corresponding analysis and predictions, understand the structure and complexity of scientific data, get a complete picture of it and explore a greater number of hypotheses. With this in mind, N-Dimensional Data Analysis and Visualization (ND²AV) is being developed to serve as an interactive visual analysis platform with the purpose of coupling together a number of these existing tools that range from statistics, machine learning, and data mining, with new techniques, in particular with new visualization approaches. My task is to create the rendering and implementation of a new concept called topological spines in order to extend ND²AV's scope. Other existing visualization tools create a representation preserving either the topological properties or the structural (geometric) ones because it is challenging to preserve them both simultaneously. Overcoming such challenge by creating a balance in between them, the topological spines are introduced as a new approach that aims to preserve them both. Its render using OpenGL and C++ and is currently being tested to further on be implemented on ND²AV. In this paper I will present what are the Topological Spines and how they are rendered.
Broken symmetry and strangeness of the semiconductor impurity band metal-insulator transition.
Phillips, J C
1998-06-23
The filamentary model of the metal-insulator transition in randomly doped semiconductor impurity bands is geometrically equivalent to similar models for continuous transitions in dilute antiferromagnets and even to the lambda transition in liquid He, but the critical behaviors are different. The origin of these differences lies in two factors: quantum statistics and the presence of long range Coulomb forces on both sides of the transition in the electrical case. In the latter case, in addition to the main transition, there are two satellite transitions associated with disappearance of the filamentary structure in both insulating and metallic phases. These two satellite transitions were first identified by Fritzsche in 1958, and their physical origin is explained here in geometrical and topological terms that facilitate calculation of critical exponents.
Comprehensible Presentation of Topological Information
Weber, Gunther H.; Beketayev, Kenes; Bremer, Peer-Timo; Hamann, Bernd; Haranczyk, Maciej; Hlawitschka, Mario; Pascucci, Valerio
2012-03-05
Topological information has proven very valuable in the analysis of scientific data. An important challenge that remains is presenting this highly abstract information in a way that it is comprehensible even if one does not have an in-depth background in topology. Furthermore, it is often desirable to combine the structural insight gained by topological analysis with complementary information, such as geometric information. We present an overview over methods that use metaphors to make topological information more accessible to non-expert users, and we demonstrate their applicability to a range of scientific data sets. With the increasingly complex output of exascale simulations, the importance of having effective means of providing a comprehensible, abstract overview over data will grow. The techniques that we present will serve as an important foundation for this purpose.
Prediction of a strain-tunable 2D Topological Dirac semimetal in monolayers of black phosphorus
NASA Astrophysics Data System (ADS)
Zhang, Xiuwen; Liu, Qihang; Zunger, Alex; Theory Team
2015-03-01
N-dimensional Topological Nonmetals (TNM) such as N = 2D HgTe/CdTe quantum wells or N = 3D Bi2Se3 have a finite (often tiny) band gap between occupied and unoccupied bands, and show conductive Dirac cones in their N-1 dimensional geometric boundaries. On the other hand, examples of topological semimetals (TSM) are known for 3D solids (Cd3As2) where they have Dirac cones in the 3D system itself. Using density functional calculation of bands and the topological invariant Z2 we predict the existence of 2D topological Dirac semimetal in few monolayers of strain tuned black phosphorus (BP), with Dirac cones induced by band inversion. The band structures of few monolayers and bulk crystal of BP under a few percent biaxial and uniaxial strains were calculated using state-of-art electronic structure methods. The critical strain of the transition to TSM was found to decrease as the layer thickness increases. We will discuss the protection of the Dirac cones by the crystalline symmetry in the 2D TSM and the manipulation of crystalline symmetry, which induces further topological phase transitions. Supported by the NSF-DMREF-13-34170.
How Do Young Children Learn Geometric Concepts.
ERIC Educational Resources Information Center
Ohe, Pia
Twenty children (ages 5 and 6) from each of seven cultural groups (Caucasian, Black, Jewish, Puerto Rican, Chinese, Korean-American and native Korean) were given a copying task of 21 geometric shapes to test the cultural invariancy of Piaget's topological-projective-Euclidean concept acquisition sequence. All subjects were either middle or lower…
NASA Astrophysics Data System (ADS)
He, Yuan-Yao; Wu, Han-Qing; Meng, Zi Yang; Lu, Zhong-Yi
2016-05-01
Topological phase transitions in free fermion systems can be characterized by the closing of single-particle gap and the change in topological invariants. However, in the presence of electronic interactions, topological phase transitions can be more complicated. In paper I of this series [Phys. Rev. B 93, 195163 (2016), 10.1103/PhysRevB.93.195163], we have proposed an efficient scheme to evaluate the topological invariants based on the single-particle Green's function formalism. Here, in paper II, we demonstrate several interaction-driven topological phase transitions (TPTs) in two-dimensional (2D) interacting topological insulators (TIs) via large-scale quantum Monte Carlo (QMC) simulations, based on the scheme of evaluating topological invariants presented in paper I. Across these transitions, the defining symmetries of the TIs have been neither explicitly nor spontaneously broken. In the first two models, the topological invariants calculated from the Green's function formalism succeed in characterizing the topologically distinct phases and identifying interaction-driven TPTs. However, in the other two models, we find that the single-particle gap does not close and the topological invariants constructed from the single-particle Green's function acquire no change across the TPTs. Unexpected breakdown of the Green's function formalism in constructing the topological invariants is thus discovered. We thence classify the topological phase transitions in interacting TIs into two categories in practical computation: Those that have noninteracting correspondence can be characterized successfully by the topological invariants constructed from the Green's functions, while for the others that do not have noninteracting correspondence, the Green's function formalism experiences a breakdown, but more interesting and exciting phenomena, such as emergent collective critical modes at the transition, arise. Discussion on the success and breakdown of topological invariants
Topological insulators and superconductors
NASA Astrophysics Data System (ADS)
Teo, Jeffrey C. Y.
We study theoretical properties of robust low energy electronic excitations associated with topological insulators and superconductors. The bulk materials are described by non-interacting single particle band Hamiltonians with a finite excitation gap. Their topological phases are classifed according to symmetries and dimensions, characterized by discrete bulk invariants, and correspond to topologically protected gapless excitations bounded to boundaries, interfaces or other kinds of defects. In particular, we study the metallic surface states of the three dimensional topological insulator Bi1-- xSbx, critical edge transport behavior of quantum spin Hall insulators (QSHI) using point contact geometry, Majorana bound states in three dimensions and their resemblance to Ising statistics, and various gapless modes accompanying topological defects in insulators and superconductors. We illustrate the topological phase of Bi1-- xSbx by calculating its surface energy spectrum numerically from a previously proposed tight binding model. An odd number of surface Dirac cones occupy the surface Brillouin zone and exhibit the strong topological nature of the material. We investigate the critical conductance behavior of a point contact in QSHI using a spinful Luttinger liquid description along the edges. For weak interactions, a novel intermediate fixed point controls the pinch-off transition, and the universal crossover scaling function of conductance is extracted from the solvable limits for the Luttinger parameter g = 1 -- epsilon, g = 1/2 + epsilon, and g = 1/ 3 . Majorana fermions are studied as zero energy quasiparticle excitations associated with pointlike topological defects in 3D superconductors. The low energy modes are described phenomenologically in a Dirac-type Bogoliubov de Gennes (BdG) framework, and the Majorana bound states are shown to exhibit Ising non-Abelian statistics despite living in (3 + 1) dimensions. In particular, novel braidless operations are shown to
NASA Astrophysics Data System (ADS)
Yang, Zhaoju; Gao, Fei; Shi, Xihang; Lin, Xiao; Gao, Zhen; Chong, Yidong; Zhang, Baile
2015-03-01
The manipulation of acoustic wave propagation in fluids has numerous applications, including some in everyday life. Acoustic technologies frequently develop in tandem with optics, using shared concepts such as waveguiding and metamedia. It is thus noteworthy that an entirely novel class of electromagnetic waves, known as "topological edge states," has recently been demonstrated. These are inspired by the electronic edge states occurring in topological insulators, and possess a striking and technologically promising property: the ability to travel in a single direction along a surface without backscattering, regardless of the existence of defects or disorder. Here, we develop an analogous theory of topological fluid acoustics, and propose a scheme for realizing topological edge states in an acoustic structure containing circulating fluids. The phenomenon of disorder-free one-way sound propagation, which does not occur in ordinary acoustic devices, may have novel applications for acoustic isolators, modulators, and transducers.
Yang, Zhaoju; Gao, Fei; Shi, Xihang; Lin, Xiao; Gao, Zhen; Chong, Yidong; Zhang, Baile
2015-03-20
The manipulation of acoustic wave propagation in fluids has numerous applications, including some in everyday life. Acoustic technologies frequently develop in tandem with optics, using shared concepts such as waveguiding and metamedia. It is thus noteworthy that an entirely novel class of electromagnetic waves, known as "topological edge states," has recently been demonstrated. These are inspired by the electronic edge states occurring in topological insulators, and possess a striking and technologically promising property: the ability to travel in a single direction along a surface without backscattering, regardless of the existence of defects or disorder. Here, we develop an analogous theory of topological fluid acoustics, and propose a scheme for realizing topological edge states in an acoustic structure containing circulating fluids. The phenomenon of disorder-free one-way sound propagation, which does not occur in ordinary acoustic devices, may have novel applications for acoustic isolators, modulators, and transducers.
ERIC Educational Resources Information Center
Field, David; And Others
1992-01-01
Includes four articles: "Career Aspirations" (Field); "Making the Transition to a New Curriculum" (Baker, Householder); "How about a 'Work to School' Transition?" (Glasberg); and "Technological Improvisation: Bringing CNC to Woodworking" (Charles, McDuffie). (SK)
Signatures of topological Josephson junctions
NASA Astrophysics Data System (ADS)
Peng, Yang; Pientka, Falko; Berg, Erez; Oreg, Yuval; von Oppen, Felix
2016-08-01
Quasiparticle poisoning and diabatic transitions may significantly narrow the window for the experimental observation of the 4 π -periodic dc Josephson effect predicted for topological Josephson junctions. Here, we show that switching-current measurements provide accessible and robust signatures for topological superconductivity which persist in the presence of quasiparticle poisoning processes. Such measurements provide access to the phase-dependent subgap spectrum and Josephson currents of the topological junction when incorporating it into an asymmetric SQUID together with a conventional Josephson junction with large critical current. We also argue that pump-probe experiments with multiple current pulses can be used to measure the quasiparticle poisoning rates of the topological junction. The proposed signatures are particularly robust, even in the presence of Zeeman fields and spin-orbit coupling, when focusing on short Josephson junctions. Finally, we also consider microwave excitations of short topological Josephson junctions which may complement switching-current measurements.
Topological excitations in semiconductor heterostructures
Koushik, R.; Mukerjee, Subroto; Ghosh, Arindam; Baenninger, Matthias; Narayan, Vijay; Pepper, Michael; Farrer, Ian; Ritchie, David A.
2013-12-04
Topological defects play an important role in the melting phenomena in two-dimensions. In this work, we report experimental observation of topological defect induced melting in two-dimensional electron systems (2DES) in the presence of strong Coulomb interaction and disorder. The phenomenon is characterised by measurement of conductivity which goes to zero in a Berezinskii-Kosterlitz-Thouless like transition. Further evidence is provided via low-frequency conductivity noise measurements.
The classification of topological insulators and superconductors
NASA Astrophysics Data System (ADS)
Chiu, Ching-Kai; Stone, Michael; Hughes, Taylor
2011-03-01
We use the process of band crossings during quantum phase transitions to explain the periodic table of topological insulators and superconductors. This is achieved by showing how irreducible representations of the real and complex Clifford algebras are related to the 10 Altland-Zirnbauer symmetry classes of Hamiltonian matrices which are associated with time reversal, particle-hole, and chiral symmetries. The representation theory not only reveals why a unique topological invariant (0 ,Z2 , Z) exists for each specific symmetry class and dimension, but also shows the interplay between quantum phase transitions, topologically protected boundary modes, and topological invariants.
Luo, H.; Yan, K.; Pletikosic, I.; Xie, W.; Phelan, B. F.; Valla, T.; Cava, R. J.
2016-05-13
We report the characterization of the misfit compound (Pb1-xSnxSe2)1.16(TiSe2)2 for 0 ≤ x ≤ 0.6, in which a [100] rocksalt-structure bilayer of Pb1-xSnxSe, which is a topological crystalline insulator in bulk form, alternates with a double layer of the normally nonsuperconducting transition metal dichalcogenide TiSe2. The x dependence of Tc displays a weak dome-like shape with a maximum Tc of 4.5 K at x = 0.2; there is only a subtle change in Tc at the composition where the trivial to topological transition occurs in bulk Pb1-xSnxSe. We present the characterization of the superconductor at x = 0.4, for whichmore » the bulk Pb1-xSnxSe phase is in the topological crystalline insulator regime. For this material, the Sommerfeld parameter γ = 11.06 mJ mol-1 K-2, the Debye temperature ΘD = 161 K, the normalized specific heat jump value ΔC/γTc = 1.38 and the electron-phonon constant value γep = 0.72, suggesting that (Pb0.6Sn0.4Se)1.16(TiSe2)2 is a BCS-type weak coupling superconductor. This material may be of interest for probing the interaction of superconductivity with the surface states of a topological crystalline insulator.« less
NASA Astrophysics Data System (ADS)
Luo, Huixia; Yan, Kai; Pletikosic, Ivo's.; Xie, Weiwei; Phelan, Brendan F.; Valla, Tonica; Cava, Robert J.
2016-06-01
We report the characterization of the misfit compound (Pb1-xSnxSe2)1.16(TiSe2)2 for 0 ≤ x ≤ 0.6, in which a [100] rocksalt-structure bilayer of Pb1-xSnxSe, which is a topological crystalline insulator in bulk form, alternates with a double layer of the normally non-superconducting transition metal dichalcogenide TiSe2. The x dependence of Tc displays a weak dome-like shape with a maximum Tc of 4.5 K at x = 0.2; there is only a subtle change in Tc at the composition where the trivial to topological transition occurs in bulk Pb1-xSnxSe. We present the characterization of the superconductor at x = 0.4, for which the bulk Pb1-xSnxSe phase is in the topological crystalline insulator regime. For this material, the Sommerfeld parameter γ = 11.06 mJ mol-1 K-2, the Debye temperature ΘD = 161 K, the normalized specific heat jump value ΔC/γTc = 1.38 and the electron-phonon constant value λep = 0.72, suggesting that (Pb0.6Sn0.4Se)1.16(TiSe2)2 is a BCS-type weak coupling superconductor. This material may be of interest for probing the interaction of superconductivity with the surface states of a topological crystalline insulator.
Topologies on quantum topoi induced by quantization
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 quantum 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.
NASA Astrophysics Data System (ADS)
Hammerschmidt, T.; Bialon, A. F.; Pettifor, D. G.; Drautz, R.
2013-11-01
In steels and single-crystal superalloys the control of the formation of topologically close-packed (TCP) phases is critical for the performance of the material. The structural stability of TCP phases in multi-component transition-metal alloys may be rationalized in terms of the average valence-electron count \\bar {N} and the composition-dependent relative volume-difference \\overline {\\Delta V/V} . We elucidate the interplay of these factors by comparing density-functional theory calculations to an empirical structure map based on experimental data. In particular, we calculate the heat of formation for the TCP phases A15, C14, C15, C36, χ, μ and σ for all possible binary occupations of the Wyckoff positions. We discuss the isovalent systems V/Nb-Ta to highlight the role of atomic-size difference and observe the expected stabilization of C14/C15/C36/μ by \\overline {\\Delta V/V} at ΔN = 0 in V-Ta. In the systems V/Nb-Re, we focus on the well-known trend of A15 → σ → χ stability with increasing \\bar {N} and show that the influence of \\overline {\\Delta V/V} is too weak to stabilize C14/C15/C36/μ in Nb-Re. As an example for a significant influence of both \\bar {N} and \\overline {\\Delta V/V} , we also consider the systems Cr/Mo-Co. Here the sequence A15 → σ → χ is observed in both systems but in Mo-Co the large size-mismatch stabilizes C14/C15/C36/μ. We also include V/Nb-Co that cover the entire valence range of TCP stability and also show the stabilization of C14/C15/C36/μ. Moreover, the combination of a large volume-difference with a large mismatch in valence-electron count reduces the stability of the A15/σ/χ phases in Nb-Co as compared to V-Co. By comparison to non-magnetic calculations we also find that magnetism is of minor importance for the structural stability of TCP phases in Cr/Mo-Co and in V/Nb-Co.
Conifold transitions and five-brane condensation in M-theory on Spin(7) manifolds
NASA Astrophysics Data System (ADS)
Gukov, Sergei; Sparks, James; Tong, David
2003-02-01
We conjecture a topology-changing transition in M-theory on a non-compact asymptotically conical Spin(7) manifold, where a 5-sphere collapses and a Bbb CP2 bolt grows. We argue that the transition may be understood as the condensation of M5-branes wrapping S5. Upon reduction to ten dimensions, it has a physical interpretation as a transition of D6-branes lying on calibrated submanifolds of flat space. In yet another guise, it may be seen as a geometric transition between two phases of type IIA string theory on a G2 holonomy manifold with either wrapped D6-branes, or background Ramond-Ramond flux. This is the first non-trivial example of a topology-changing transition with only 1/16 supersymmetry.
NASA Astrophysics Data System (ADS)
Gilliland, Ronald L.
Transits of the planets Mercury and especially Venus have been exciting events in the development of astronomy over the past few hundred years. Just two years ago the first transiting extra-solar planet, HD 209458b, was discovered, and subsequent studies during transit have contributed fundamental new knowledge. From the photometric light curve during transit one obtains a basic confirmation that the radial velocity detected object is indeed a planet by allowing precise determination of its mass and radius relative to these stellar quantities. From study of spectroscopic changes during transit it has been possible to probe for individual components of the transiting planets atmosphere. Planet transits are likely to become a primary tool for detection of new planets, especially other Earth-like planets with the Kepler Discovery Mission. Looking ahead, the additional aperture of the James Webb Space Space Telescope promises to allow the first possibility of studying the atmosphere of extra-solar Earth-analogue planets, perhaps even providing the first evidence of direct relevance to the search for signs of life on other planets.
Exploring complex networks via topological embedding on surfaces.
Aste, Tomaso; Gramatica, Ruggero; Di Matteo, T
2012-09-01
We demonstrate that graphs embedded on surfaces are a powerful and practical tool to generate, to characterize, and to simulate networks with a broad range of properties. Any network can be embedded on a surface with sufficiently high genus and therefore the study of topologically embedded graphs is non-restrictive. We show that the local properties of the network are affected by the surface genus which determines the average degree, which influences the degree distribution, and which controls the clustering coefficient. The global properties of the graph are also strongly affected by the surface genus which is constraining the degree of interwovenness, changing the scaling properties of the network from large-world kind (small genus) to small- and ultrasmall-world kind (large genus). Two elementary moves allow the exploration of all networks embeddable on a given surface and naturally introduce a tool to develop a statistical mechanics description for these networks. Within such a framework, we study the properties of topologically embedded graphs which dynamically tend to lower their energy towards a ground state with a given reference degree distribution. We show that the cooling dynamics between high and low "temperatures" is strongly affected by the surface genus with the manifestation of a glass-like transition occurring when the distance from the reference distribution is low. We prove, with examples, that topologically embedded graphs can be built in a way to contain arbitrary complex networks as subgraphs. This method opens a new avenue to build geometrically embedded networks on hyperbolic manifolds.
NASA Astrophysics Data System (ADS)
Pankratov, D. L.; Nizamov, R. S.; Harisov, I. Zh
2016-06-01
The cause of a pipe clip during the setting of the pipe is determined on the basis of modeling. The method, which excludes the formation of a defect in a semi finished product by changing the configuration of the setting transition, is developed.
A geometric representation scheme suitable for shape optimization
NASA Technical Reports Server (NTRS)
Tortorelli, Daniel A.
1990-01-01
A geometric representation scheme is outlined which utilizes the natural design variable concept. A base configuration with distinct topological features is created. This configuration is then deformed to define components with similar topology but different geometry. The values of the deforming loads are the geometric entities used in the shape representation. The representation can be used for all geometric design studies; it is demonstrated here for structural optimization. This technique can be used in parametric design studies, where the system response is defined as functions of geometric entities. It can also be used in shape optimization, where the geometric entities of an original design are modified to maximize performance and satisfy constraints. Two example problems are provided. A cantilever beam is elongated to meet new design specifications and then optimized to reduce volume and satisfy stress constraints. A similar optimization problem is presented for an automobile crankshaft section. The finite element method is used to perform the analyses.
Emergence of magnetic topological states in topological insulators doped with magnetic impurities
NASA Astrophysics Data System (ADS)
Tran, Minh-Tien; Nguyen, Hong-Son; Le, Duc-Anh
2016-04-01
Emergence of the topological invariant and the magnetic moment in topological insulators doped with magnetic impurities is studied based on a mutual cooperation between the spin-orbit coupling of electrons and the spin exchange of these electrons with magnetic impurity moments. The mutual cooperation is realized based on the Kane-Mele model in the presence of magnetic impurities. The topological invariants and the spontaneous magnetization are self-consistently determined within the dynamical mean-field theory. We find different magnetic topological phase transitions, depending on the electron filling. At half filling an antiferromagnetic topological insulator, which exhibits the quantum spin Hall effect, exists in the phase region between the paramagnetic topological insulator and the trivially topological antiferromagnetic insulator. At quarter and three-quarter fillings, a ferromagnetic topological insulator, which exhibits the quantum anomalous Hall effect, occurs in the strong spin-exchange regime.
Network robustness: detecting topological quantum phases.
Chou, Chung-Pin
2014-12-17
Can the topology of a network that consists of many particles interacting with each other change in complexity when a phase transition occurs? The answer to this question is particularly interesting to understand the nature of the phase transitions if the distinct phases do not break any symmetry, such as topological phase transitions. Here we present a novel theoretical framework established by complex network analysis for demonstrating that across a transition point of the topological superconductors, the network space experiences a homogeneous-heterogeneous transition invisible in real space. This transition is nothing but related to the robustness of a network to random failures. We suggest that the idea of the network robustness can be applied to characterizing various phase transitions whether or not the symmetry is broken.
Learning topological maps: An alternative approach
Buecken, A.; Thrun, S.
1996-12-31
Our goal is autonomous real-time control of a mobile robot. In this paper we want to show a possibility to learn topological maps of a large-scale indoor environment autonomously. In the literature there are two paradigms how to store information on the environment of a robot: as a grid-based (geometric) or as a topological map. While grid-based maps are considerably easy to learn and maintain, topological maps are quite compact and facilitate fast motion-planning.
Semsarha, Farid; Raisali, Gholamreza; Goliaei, Bahram; Khalafi, Hossein
2016-05-01
In order to obtain the energy deposition pattern of ionizing radiation in the nanometric scale of genetic material and to investigate the different sensitivities of the DNA conformations, direct effects of (60)Co gamma rays on the three A, B and Z conformations of DNA have been studied. For this purpose, single-strand breaks (SSB), double-strand breaks (DSB), base damage (BD), hit probabilities and three microdosimetry quantities (imparted energy, mean chord length and lineal energy) in the mentioned DNA conformations have been calculated and compared by using GEometry ANd Tracking 4 (Geant4) toolkit. The results show that A-, B- and Z-DNA conformations have the highest yields of DSB (1.2 Gy(-1) Gbp(-1)), SSB (25.2 Gy(-1) Gbp(-1)) and BD (4.81 Gy(-1) Gbp(-1)), respectively. Based on the investigation of direct effects of radiation, it can be concluded that the DSB yield is largely correlated to the topological characteristics of DNA models, although the SSB yield is not. Moreover, according to the comparative results of the present study, a reliable candidate parameter for describing the relationship between DNA damage yields and geometry of DNA models in the theoretical radiation biology research studies would be the mean chord length (4 V/S) of the models.
Topological Mechanics of Origami and Kirigami.
Chen, Bryan Gin-Ge; Liu, Bin; Evans, Arthur A; Paulose, Jayson; Cohen, Itai; Vitelli, Vincenzo; Santangelo, C D
2016-04-01
Origami and kirigami have emerged as potential tools for the design of mechanical metamaterials whose properties such as curvature, Poisson ratio, and existence of metastable states can be tuned using purely geometric criteria. A major obstacle to exploiting this property is the scarcity of tools to identify and program the flexibility of fold patterns. We exploit a recent connection between spring networks and quantum topological states to design origami with localized folding motions at boundaries and study them both experimentally and theoretically. These folding motions exist due to an underlying topological invariant rather than a local imbalance between constraints and degrees of freedom. We give a simple example of a quasi-1D folding pattern that realizes such topological states. We also demonstrate how to generalize these topological design principles to two dimensions. A striking consequence is that a domain wall between two topologically distinct, mechanically rigid structures is deformable even when constraints locally match the degrees of freedom.
Topological Mechanics of Origami and Kirigami
NASA Astrophysics Data System (ADS)
Chen, Bryan Gin-ge; Liu, Bin; Evans, Arthur A.; Paulose, Jayson; Cohen, Itai; Vitelli, Vincenzo; Santangelo, C. D.
2016-04-01
Origami and kirigami have emerged as potential tools for the design of mechanical metamaterials whose properties such as curvature, Poisson ratio, and existence of metastable states can be tuned using purely geometric criteria. A major obstacle to exploiting this property is the scarcity of tools to identify and program the flexibility of fold patterns. We exploit a recent connection between spring networks and quantum topological states to design origami with localized folding motions at boundaries and study them both experimentally and theoretically. These folding motions exist due to an underlying topological invariant rather than a local imbalance between constraints and degrees of freedom. We give a simple example of a quasi-1D folding pattern that realizes such topological states. We also demonstrate how to generalize these topological design principles to two dimensions. A striking consequence is that a domain wall between two topologically distinct, mechanically rigid structures is deformable even when constraints locally match the degrees of freedom.
Topological Phenotypes in Complex Leaf Venation Networks
NASA Astrophysics Data System (ADS)
Ronellenfitsch, Henrik; Lasser, Jana; Daly, Douglas; Katifori, Eleni
2015-03-01
The leaves of vascular plants contain highly complex venation networks consisting of recursively nested, hierarchically organized loops. We analyze the topology of the venation of leaves from ca. 200 species belonging to ca. 10 families, defining topological metrics that quantify the hierarchical nestedness of the network cycles. We find that most of the venation variability can be described by a two dimensional phenotypic space, where one dimension consists of a linear combination of geometrical metrics and the other dimension of topological, previously uncharacterized metrics. We show how this new topological dimension in the phenotypic space significantly improves identification of leaves from fragments, by calculating a ``leaf fingerprint'' from the topology and geometry of the higher order veins. Further, we present a simple model suggesting that the topological phenotypic traits can be explained by noise effects and variations in the timing of higher order vein developmental events. This work opens the path to (a) new quantitative identification techniques for leaves which go beyond simple geometric traits such as vein density and (b) topological quantification of other planar or almost planar networks such as arterial vaculature in the neocortex and lung tissue.
Finite Topological Spaces as a Pedagogical Tool
ERIC Educational Resources Information Center
Helmstutler, Randall D.; Higginbottom, Ryan S.
2012-01-01
We propose the use of finite topological spaces as examples in a point-set topology class especially suited to help students transition into abstract mathematics. We describe how carefully chosen examples involving finite spaces may be used to reinforce concepts, highlight pathologies, and develop students' non-Euclidean intuition. We end with a…
Kodama, M; Murakami, M; Kodama, T
1999-08-01
The present study is an extension of our recent study in which we attempted statistical analysis of the data assembly of age-adjusted incidence rates (AAIRs) of a tumor without topological data manipulation for each of 20 individual tumors in scope, for each of 6 cancer registration areas in space, and for a period of early 1960's to mid 1980's in time. This time, a data assembly of log AAIR changes in time and space first passed through the process of topological data manipulation, and then underwent the sequential regression analysis so that we could assess the fitness of log AAIR changes either in space or in time to the equilibrium model of the law of mass action from the viewpoint of the interaction between oncogene activation and tumor suppressor gene inactivation. For the sake of comparison, the fitness of the cancer risk data to the equilibrium model was assessed in the framework of 3 sets of coordinates: a) the original (x org, y org) coordinates in which most of the log AAIR data assemblies in their data variations were classified as the oncogene activation type in the field of centripetal force (r seq=-1.000). b) The rect (X rect, Y rect) coordinates in which the log AAIR data assemblies were very often classified as the tumor suppressor gene inactivation type in the field of centrifugal force (r seq=+1.000). c) The para (X para, Y para) coordinates in which the log AAIR data assemblies were mostly classified as the intermediate type as regards the fitness to the equilibrium model. The rect-coordinates and the para-coordinates, 2 variants of angular rotation of the original coordinates, were so designed as to allow their X-axes to run each at a right angle and parallel to the regression line of the original pair data block. The results obtained were as follows: a) poor fitness of the log AAIR changes in space to the equilibrium model in the rect-coordinates was found in male breast cancer, male thyroid cancer, female esophageal cancer, female laryngeal
Identifying and Fostering Higher Levels of Geometric Thinking
ERIC Educational Resources Information Center
Škrbec, Maja; Cadež, Tatjana Hodnik
2015-01-01
Pierre M. Van Hiele created five levels of geometric thinking. We decided to identify the level of geometric thinking in the students in Slovenia, aged 9 to 11 years. The majority of students (60.7%) are at the transition between the zero (visual) level and the first (descriptive) level of geometric thinking. Nearly a third (31.7%) of students is…
Pollock, Christopher J; DeBeer, Serena
2015-11-17
A long-standing goal of inorganic chemists is the ability to decipher the geometric and electronic structures of chemical species. This is particularly true for the study of small molecule and biological catalysts, where this knowledge is critical for understanding how these molecules effect chemical transformations. Numerous techniques are available for this task, and collectively they have enabled detailed understanding of many complex chemical systems. Despite this battery of probes, however, challenges still remain, particularly when the structural question involves subtle perturbations of the ligands bound to a metal center, as is often the case during chemical reactions. It is here that, as an emerging probe of chemical structure, valence-to-core (VtC) X-ray emission spectroscopy (XES) holds promise. VtC XES begins with ionization of a 1s electron from a metal ion by high energy X-ray photons. Electrons residing in ligand-localized valence orbitals decay to fill the 1s hole, emitting fluorescent photons in the process; in this manner, VtC XES primarily probes the filled, ligand-based orbitals of a metal complex. This is in contrast to other X-ray based techniques, such as K-edge X-ray absorption and EXAFS, which probe the unoccupied d-manifold orbitals and atomic scatterers surrounding the metal, respectively. As a hard X-ray technique, VtC XES experiments can be performed on a variety of sample states and environments, enabling application to demanding systems, such as high pressure cells and dilute biological samples. VtC XES thus can offer unique insights into the geometric and electronic structures of inorganic complexes. In recent years, we have sought to use VtC XES in the study of inorganic and bioinorganic complexes; doing so, however, first required a thorough and detailed understanding of the information content of these spectra. Extensive experimental surveys of model compounds coupled to the insights provided by DFT calculated spectra of real and
Topological order parameters for interacting topological insulators.
Wang, Zhong; Qi, Xiao-Liang; Zhang, Shou-Cheng
2010-12-17
We propose a topological order parameter for interacting topological insulators, expressed in terms of the full Green's functions of the interacting system. We show that it is exactly quantized for a time-reversal invariant topological insulator, and it can be experimentally measured through the topological magneto-electric effect. This topological order parameter can be applied to both interacting and disordered systems, and used for determining their phase diagrams. PMID:21231609
Topological Aspects of Information Retrieval.
ERIC Educational Resources Information Center
Egghe, Leo; Rousseau, Ronald
1998-01-01
Discusses topological aspects of theoretical information retrieval, including retrieval topology; similarity topology; pseudo-metric topology; document spaces as topological spaces; Boolean information retrieval as a subsystem of any topological system; and proofs of theorems. (LRW)
Complex quantum network geometries: Evolution and phase transitions.
Bianconi, Ginestra; Rahmede, Christoph; Wu, Zhihao
2015-08-01
Networks are topological and geometric structures used to describe systems as different as the Internet, the brain, or the quantum structure of space-time. Here we define complex quantum network geometries, describing the underlying structure of growing simplicial 2-complexes, i.e., simplicial complexes formed by triangles. These networks are geometric networks with energies of the links that grow according to a nonequilibrium dynamics. The evolution in time of the geometric networks is a classical evolution describing a given path of a path integral defining the evolution of quantum network states. The quantum network states are characterized by quantum occupation numbers that can be mapped, respectively, to the nodes, links, and triangles incident to each link of the network. We call the geometric networks describing the evolution of quantum network states the quantum geometric networks. The quantum geometric networks have many properties common to complex networks, including small-world property, high clustering coefficient, high modularity, and scale-free degree distribution. Moreover, they can be distinguished between the Fermi-Dirac network and the Bose-Einstein network obeying, respectively, the Fermi-Dirac and Bose-Einstein statistics. We show that these networks can undergo structural phase transitions where the geometrical properties of the networks change drastically. Finally, we comment on the relation between quantum complex network geometries, spin networks, and triangulations.
Complex quantum network geometries: Evolution and phase transitions
NASA Astrophysics Data System (ADS)
Bianconi, Ginestra; Rahmede, Christoph; Wu, Zhihao
2015-08-01
Networks are topological and geometric structures used to describe systems as different as the Internet, the brain, or the quantum structure of space-time. Here we define complex quantum network geometries, describing the underlying structure of growing simplicial 2-complexes, i.e., simplicial complexes formed by triangles. These networks are geometric networks with energies of the links that grow according to a nonequilibrium dynamics. The evolution in time of the geometric networks is a classical evolution describing a given path of a path integral defining the evolution of quantum network states. The quantum network states are characterized by quantum occupation numbers that can be mapped, respectively, to the nodes, links, and triangles incident to each link of the network. We call the geometric networks describing the evolution of quantum network states the quantum geometric networks. The quantum geometric networks have many properties common to complex networks, including small-world property, high clustering coefficient, high modularity, and scale-free degree distribution. Moreover, they can be distinguished between the Fermi-Dirac network and the Bose-Einstein network obeying, respectively, the Fermi-Dirac and Bose-Einstein statistics. We show that these networks can undergo structural phase transitions where the geometrical properties of the networks change drastically. Finally, we comment on the relation between quantum complex network geometries, spin networks, and triangulations.
Transformable topological mechanical metamaterials
NASA Astrophysics Data System (ADS)
Rocklin, D. Zeb; Zhou, Shangnan; Sun, Kai; Mao, Xiaoming
We present a class of mechanical metamaterials characterized by a uniform soft deformation--a large, zero-energy homogeneous elastic deformation mode of the structure--that may be used to induce topological transitions and dramatically change mechanical and acoustic properties of the structure. We show that the existence of such a mode determines certain exotic mechanical and acoustic properties of the structure and its activation can reversibly alter and tune these properties. This serves as the basis for a design principle for mechanical metamaterials with tunable properties. When the structure's uniform mode is primarily dilational (shearing) its surface (bulk) possesses phonon modes with vanishing speed of sound. Maxwell lattices comprise a subclass of such material which, owing to their critical coordination number (four, in 2D), necessarily possess such a uniform zero mode, often termed a Guest mode, and which may be topologically polarized, such that zero modes are moved from one edge to another. We show that activating the deformation can alter the shear/dilational character of the mode and topologically polarize the structure, thereby altering the bulk and surface properties at no significant energy cost. arXiv:1510.06389 [cond-mat.soft] NWO, Delta Institute of Physics, ICAM fellowship (DZR) and NSF Grant PHY-1402971 at University of Michigan (KS).
EDITORIAL: Topological data analysis Topological data analysis
NASA Astrophysics Data System (ADS)
2011-12-01
Inverse problems can be defined as the area of mathematics that attempts to reconstruct a physical or mathematical object from derived data. Frequently, this means the evaluation of parameters or other numerical quantities (such as eigenvalues) that characterize or provide information about the system. There are, however, other aspects of a system that are important, but are not as readily summarized by numerical quantities. If one considers observations of diabetic patients (using metabolic quantities), one will find that the data breaks up into components, or pieces, corresponding to distinct forms of the disease. The decomposition of data sets into disjoint pieces, or clustering, is an aspect of the study of the shape of the data, albeit one that has been extensively studied. A more complex notion of shape appears in observations of a predator-prey system governed by a Lotka-Volterra equation. One would find that exact observations, consisting of (prey population, predator population) pairs, appear to lie along a simple closed curve in the plane. The fact that the data lies along such a closed curve is an important piece of information, since it suggests that the system displays recurrent behavior. If one did not know, a priori, that the system is governed by a Lotka-Volterra equation, then it would not be immediately obvious that the system is undergoing recurrent motion, and this deduction would constitute a significant insight. In this case, it is again the shape of the data, namely the fact that it lies on a simple closed curve, which is the key insight. Shape is a somewhat nebulous concept, which at first blush may be too intuitive to make precise mathematically, and describe quantitatively. Within pure mathematics, the disciplines of topology and differential geometry are designed exactly to address this problem. They provide explicit signatures which, in precise senses, quantify and describe the shape of a geometric object. In addition, they provide
EDITORIAL: Topological data analysis Topological data analysis
NASA Astrophysics Data System (ADS)
Epstein, Charles; Carlsson, Gunnar; Edelsbrunner, Herbert
2011-12-01
Inverse problems can be defined as the area of mathematics that attempts to reconstruct a physical or mathematical object from derived data. Frequently, this means the evaluation of parameters or other numerical quantities (such as eigenvalues) that characterize or provide information about the system. There are, however, other aspects of a system that are important, but are not as readily summarized by numerical quantities. If one considers observations of diabetic patients (using metabolic quantities), one will find that the data breaks up into components, or pieces, corresponding to distinct forms of the disease. The decomposition of data sets into disjoint pieces, or clustering, is an aspect of the study of the shape of the data, albeit one that has been extensively studied. A more complex notion of shape appears in observations of a predator-prey system governed by a Lotka-Volterra equation. One would find that exact observations, consisting of (prey population, predator population) pairs, appear to lie along a simple closed curve in the plane. The fact that the data lies along such a closed curve is an important piece of information, since it suggests that the system displays recurrent behavior. If one did not know, a priori, that the system is governed by a Lotka-Volterra equation, then it would not be immediately obvious that the system is undergoing recurrent motion, and this deduction would constitute a significant insight. In this case, it is again the shape of the data, namely the fact that it lies on a simple closed curve, which is the key insight. Shape is a somewhat nebulous concept, which at first blush may be too intuitive to make precise mathematically, and describe quantitatively. Within pure mathematics, the disciplines of topology and differential geometry are designed exactly to address this problem. They provide explicit signatures which, in precise senses, quantify and describe the shape of a geometric object. In addition, they provide
Global monopoles can change Universe's topology
NASA Astrophysics Data System (ADS)
Marunović, Anja; Prokopec, Tomislav
2016-05-01
If the Universe undergoes a phase transition, at which global monopoles are created or destroyed, topology of its spatial sections can change. More specifically, by making use of Myers' theorem, we show that, after a transition in which global monopoles form, spatial sections of a spatially flat, infinite Universe becomes finite and closed. This implies that global monopoles can change the topology of Universe's spatial sections (from infinite and open to finite and closed). Global monopoles cannot alter the topology of the space-time manifold.
Direct Measurement of Topological Numbers with Spins in Diamond.
Kong, Fei; Ju, Chenyong; Liu, Ying; Lei, Chao; Wang, Mengqi; Kong, Xi; Wang, Pengfei; Huang, Pu; Li, Zhaokai; Shi, Fazhan; Jiang, Liang; Du, Jiangfeng
2016-08-01
Topological numbers can characterize the transition between different topological phases, which are not described by Landau's paradigm of symmetry breaking. Since the discovery of the quantum Hall effect, more topological phases have been theoretically predicted and experimentally verified. However, it is still an experimental challenge to directly measure the topological numbers of various predicted topological phases. In this Letter, we demonstrate quantum simulation of topological phase transition of a quantum wire (QW), by precisely modulating the Hamiltonian of a single nitrogen-vacancy (NV) center in diamond. Deploying a quantum algorithm of finding eigenvalues, we reliably extract both the dispersion relations and topological numbers. This method can be further generalized to simulate more complicated topological systems. PMID:27541449
Direct Measurement of Topological Numbers with Spins in Diamond.
Kong, Fei; Ju, Chenyong; Liu, Ying; Lei, Chao; Wang, Mengqi; Kong, Xi; Wang, Pengfei; Huang, Pu; Li, Zhaokai; Shi, Fazhan; Jiang, Liang; Du, Jiangfeng
2016-08-01
Topological numbers can characterize the transition between different topological phases, which are not described by Landau's paradigm of symmetry breaking. Since the discovery of the quantum Hall effect, more topological phases have been theoretically predicted and experimentally verified. However, it is still an experimental challenge to directly measure the topological numbers of various predicted topological phases. In this Letter, we demonstrate quantum simulation of topological phase transition of a quantum wire (QW), by precisely modulating the Hamiltonian of a single nitrogen-vacancy (NV) center in diamond. Deploying a quantum algorithm of finding eigenvalues, we reliably extract both the dispersion relations and topological numbers. This method can be further generalized to simulate more complicated topological systems.
Direct Measurement of Topological Numbers with Spins in Diamond
NASA Astrophysics Data System (ADS)
Kong, Fei; Ju, Chenyong; Liu, Ying; Lei, Chao; Wang, Mengqi; Kong, Xi; Wang, Pengfei; Huang, Pu; Li, Zhaokai; Shi, Fazhan; Jiang, Liang; Du, Jiangfeng
2016-08-01
Topological numbers can characterize the transition between different topological phases, which are not described by Landau's paradigm of symmetry breaking. Since the discovery of the quantum Hall effect, more topological phases have been theoretically predicted and experimentally verified. However, it is still an experimental challenge to directly measure the topological numbers of various predicted topological phases. In this Letter, we demonstrate quantum simulation of topological phase transition of a quantum wire (QW), by precisely modulating the Hamiltonian of a single nitrogen-vacancy (NV) center in diamond. Deploying a quantum algorithm of finding eigenvalues, we reliably extract both the dispersion relations and topological numbers. This method can be further generalized to simulate more complicated topological systems.
Two-dimensional density-matrix topological fermionic phases: topological Uhlmann numbers.
Viyuela, O; Rivas, A; Martin-Delgado, M A
2014-08-15
We construct a topological invariant that classifies density matrices of symmetry-protected topological orders in two-dimensional fermionic systems. As it is constructed out of the previously introduced Uhlmann phase, we refer to it as the topological Uhlmann number n_{U}. With it, we study thermal topological phases in several two-dimensional models of topological insulators and superconductors, computing phase diagrams where the temperature T is on an equal footing with the coupling constants in the Hamiltonian. Moreover, we find novel thermal-topological transitions between two nontrivial phases in a model with high Chern numbers. At small temperatures we recover the standard topological phases as the Uhlmann number approaches to the Chern number.
Geometrical Pumping with a Bose-Einstein Condensate
NASA Astrophysics Data System (ADS)
Lu, H.-I.; Schemmer, M.; Aycock, L. M.; Genkina, D.; Sugawa, S.; Spielman, I. B.
2016-05-01
We realized a quantum geometric "charge" pump for a Bose-Einstein condensate (BEC) in the lowest Bloch band of a novel bipartite magnetic lattice. Topological charge pumps in filled bands yield quantized pumping set by the global—topological—properties of the bands. In contrast, our geometric charge pump for a BEC occupying just a single crystal momentum state exhibits nonquantized charge pumping set by local—geometrical—properties of the band structure. Like topological charge pumps, for each pump cycle we observed an overall displacement (here, not quantized) and a temporal modulation of the atomic wave packet's position in each unit cell, i.e., the polarization.
Topological Superconductivity in Dirac Semimetals
NASA Astrophysics Data System (ADS)
Sato, Masatoshi; Kobayashi, Shingo
Dirac semimetals host bulk band-touching Dirac points and a surface Fermi loop. We develop a theory of superconducting Dirac semimetals. Establishing a relation between the Dirac points and the surface Fermi loop, we clarify how the nontrivial topology of Dirac semimetals affects their superconducting state. We note that the unique orbital texture of Dirac points and a structural phase transition of the crystal favor symmetry-protected topological superconductivity with a quartet of surface Majorana fermions. We suggest the possible application of our theory to recently discovered superconducting states in Cd3As2.
Geometrical expression of excess entropy production.
Sagawa, Takahiro; Hayakawa, Hisao
2011-11-01
We derive a geometrical expression of the excess entropy production for quasistatic transitions between nonequilibrium steady states of Markovian jump processes, which can be exactly applied to nonlinear and nonequilibrium situations. The obtained expression is geometrical; the excess entropy production depends only on a trajectory in the parameter space, analogous to the Berry phase in quantum mechanics. Our results imply that vector potentials are needed to construct the thermodynamics of nonequilibrium steady states. PMID:22181372
NASA Technical Reports Server (NTRS)
Matias, A.; Garvin, J. B.; Sakimoto, S. E. H.
1998-01-01
One intriguing aspect of martian impact crater morphology is the change of crater cavity and ejecta characteristics from the mid-latitudes to the polar regions. This is thought to reflect differences in target properties such as an increasing presence of ice in the polar regions. Previous image-based efforts concerning martian crater morphology has documented some aspects of this, but has been hampered by the lack of adequate topography data. Recent Mars Orbiter Laser Altimeter (MOLA) topographic profiles provide a quantitative perspective for interpreting the detailed morphologies of martian crater cavities and ejecta morphology. This study is a preliminary effort to quantify the latitude-dependent differences in morphology with the goal of identifying target-dependent and crater modification effects from the combined of images and MOLA topography. We combine the available MOLA profiles and the corresponding Viking Mars Digital Image Mosaics (MDIMS), and high resolution Viking Orbiter images to focus on two transitional craters; one on the mid-latitudes, and one in the North Polar region. One MOLA pass (MGS Orbit 34) traverses the center of a 15.9 km diameter fresh complex crater located at 12.8degN 83.8degE on the Hesperian ridge plains unit (Hvr). Viking images, as well as MOLA data, show that this crater has well developed wall terraces and a central peak with 429 m of relative relief. Three MOLA passes have been acquired for a second impact crater, which is located at 69.5degN 41degE on the Vastitas Borealis Formation. This fresh rampart crater lacks terraces and central peak structures and it has a depth af 579 m. Correlation between images and MOLA topographic profiles allows us to construct basic facies maps of the craters. Eight main units were identified, four of which are common on both craters.
Crystallographic topology and its applications
Johnson, C.K.; Burnett, M.N.; Dunbar, W.D.
1996-10-01
Geometric topology and structural crystallography concepts are combined to define a new area we call Structural Crystallographic Topology, which may be of interest to both crystallographers and mathematicians. In this paper, we represent crystallographic symmetry groups by orbifolds and crystal structures by Morse - functions. The Morse function uses mildly overlapping Gaussian thermal-motion probability density functions centered on atomic sites to form a critical net with peak, pass, pale, and pit critical points joined into a graph by density gradient-flow separatrices. Critical net crystal structure drawings can be made with the ORTEP-III graphics pro- An orbifold consists of an underlying topological space with an embedded singular set that represents the Wyckoff sites of the crystallographic group. An orbifold for a point group, plane group, or space group is derived by gluing together equivalent edges or faces of a crystallographic asymmetric unit. The critical-net-on-orbifold model incorporates the classical invariant lattice complexes of crystallography and allows concise quotient-space topological illustrations to be drawn without the repetition that is characteristic of normal crystal structure drawings.
Topological crystalline insulators.
Fu, Liang
2011-03-11
The recent discovery of topological insulators has revived interest in the band topology of insulators. In this Letter, we extend the topological classification of band structures to include certain crystal point group symmetry. We find a class of three-dimensional "topological crystalline insulators" which have metallic surface states with quadratic band degeneracy on high symmetry crystal surfaces. These topological crystalline insulators are the counterpart of topological insulators in materials without spin-orbit coupling. Their band structures are characterized by new topological invariants. We hope this work will enlarge the family of topological phases in band insulators and stimulate the search for them in real materials.
Induced topological pressure for topological dynamical systems
Xing, Zhitao; Chen, Ercai
2015-02-15
In this paper, inspired by the article [J. Jaerisch et al., Stochastics Dyn. 14, 1350016, pp. 1-30 (2014)], we introduce the induced topological pressure for a topological dynamical system. In particular, we prove a variational principle for the induced topological pressure.
Geometry, topology, and string theory
Varadarajan, Uday
2003-07-10
A variety of scenarios are considered which shed light upon the uses and limitations of classical geometric and topological notions in string theory. The primary focus is on situations in which D-brane or string probes of a given classical space-time see the geometry quite differently than one might naively expect. In particular, situations in which extra dimensions, non-commutative geometries as well as other non-local structures emerge are explored in detail. Further, a preliminary exploration of such issues in Lorentzian space-times with non-trivial causal structures within string theory is initiated.
Topological Insulators from Electronic Superstructures
NASA Astrophysics Data System (ADS)
Sugita, Yusuke; Motome, Yukitoshi
2016-07-01
The possibility of realizing topological insulators by the spontaneous formation of electronic superstructures is theoretically investigated in a minimal two-orbital model including both the spin-orbit coupling and electron correlations on a triangular lattice. Using the mean-field approximation, we show that the model exhibits several different types of charge-ordered insulators, where the charge disproportionation forms a honeycomb or kagome superstructure. We find that the charge-ordered insulators in the presence of strong spin-orbit coupling can be topological insulators showing quantized spin Hall conductivity. Their band gap is dependent on electron correlations as well as the spin-orbit coupling, and even vanishes while showing the massless Dirac dispersion at the transition to a trivial charge-ordered insulator. Our results suggest a new route to realize and control topological states of quantum matter by the interplay between the spin-orbit coupling and electron correlations.
Topological approach of Jungian psychology.
Viret, Jacques
2010-09-01
In this work, we compare two global approaches which are usually considered as completely unconnected one with the other. The former is Thom's topology and the latter is Jung's psychology. More precisely, it seemed to us interesting to adapt some morphologies of Thom's catastrophe theory to some Jung's notions. Thus, we showed that the swallowtail, which is one of these morphologies, was able to describe geometrically the structural organisation of the psyche according to Jung, with its collective unconscious, personal unconscious and conscious. Moreover, we have correlated this morphology with Jung's evolutive processes like individualization and individuation. These comparisons incited us to think that some morphologies of Thom's catastrophe theory are the geometrical dealing of Jung's archetypes.
Topological approach of Jungian psychology.
Viret, Jacques
2010-09-01
In this work, we compare two global approaches which are usually considered as completely unconnected one with the other. The former is Thom's topology and the latter is Jung's psychology. More precisely, it seemed to us interesting to adapt some morphologies of Thom's catastrophe theory to some Jung's notions. Thus, we showed that the swallowtail, which is one of these morphologies, was able to describe geometrically the structural organisation of the psyche according to Jung, with its collective unconscious, personal unconscious and conscious. Moreover, we have correlated this morphology with Jung's evolutive processes like individualization and individuation. These comparisons incited us to think that some morphologies of Thom's catastrophe theory are the geometrical dealing of Jung's archetypes. PMID:20658172
Experimental Realizations of Magnetic Topological Insulator and Topological Crystalline Insulator
NASA Astrophysics Data System (ADS)
Xu, Suyang
2013-03-01
Over the past few years the experimental research on three-dimensional topological insulators have emerged as one of the most rapidly developing fields in condensed matter physics. In this talk, we report on two new developments in the field: The first part is on the dynamic interplay between ferromagnetism and the Z2 topological insulator state (leading to a magnetic topological insulator). We present our spin-resolved photoemission and magnetic dichroic experiments on MBE grown films where a hedgehog-like spin texture is revealed on the magnetically ordered surface of Mn-Bi2Se3 revealing a Berry's phase gradient in energy-momentum space of the crystal. A chemically/electrically tunable Berry's phase switch is further demonstrated via the tuning of the spin groundstate in Mn-Bi2Se3 revealed in our data (Nature Physics 8, 616 (2012)). The second part of this talk describes our experimental observation of a new topological phase of matter, namely a topological crystalline insulator where space group symmetries replace the role of time-reversal symmetry in an otherwise Z2 topological insulator predicted in theory. We experimentally investigate the possibility of a mirror symmetry protected topological phase transition in the Pb1-xSnxTe alloy system, which has long been known to contain an even number of band inversions based on band theory. Our experimental results show that at a composition below the theoretically predicted band inversion, the system is fully gapped, whereas in the band-inverted regime, the surface exhibits even number of spin-polarized Dirac cone states revealing mirror-protected topological order (Nature Communications 3, 1192 (2012)) distinct from that observed in Z2 topological insulators. We discuss future experimental possibilities opened up by these new developments in topological insulators research. This work is in collaboration with M. Neupane, C. Liu, N. Alidoust, I. Belopolski, D. Qian, D.M. Zhang, A. Richardella, A. Marcinkova, Q
Geometric Algebra for Physicists
NASA Astrophysics Data System (ADS)
Doran, Chris; Lasenby, Anthony
2007-11-01
Preface; Notation; 1. Introduction; 2. Geometric algebra in two and three dimensions; 3. Classical mechanics; 4. Foundations of geometric algebra; 5. Relativity and spacetime; 6. Geometric calculus; 7. Classical electrodynamics; 8. Quantum theory and spinors; 9. Multiparticle states and quantum entanglement; 10. Geometry; 11. Further topics in calculus and group theory; 12. Lagrangian and Hamiltonian techniques; 13. Symmetry and gauge theory; 14. Gravitation; Bibliography; Index.
Topological Z2 Gapless Photonic Crystals
NASA Astrophysics Data System (ADS)
Xie, Biye; Wang, Zidan
Topological properties of electronic materials with gapless band structure such as Topological Semimetals(TSMs) and Topological Metals(TMs) have drew lots of attention to both theoretical and experimental physicists recently. Although theoretical prediction of TSMs and TMs have been done well, experimental study of them is quite difficult to perform due to the fact that it is very difficult to control and design certain electronic materials. However, since the topological properties stem from the geometric feature, we can study them in Photonic Crystals(PhCs) which are much easy to be controlled and designed. Here we study 2-dimension PhCs consisting of gyrotropic materials with hexagonal structure. In the Brillouin corner, the dispersion relation has gapless points which are similar to Dirac Cones in electronic materials. We firstly derive the effective Hamiltonian of this system and show that if certain perturbation is added to this effective Hamiltonian, this system belongs to AII class according to Altland and Zirbauer topological classification and is described by a Z2 topological charge. Finally we also propose a way to detect this Z2 topological charge using momentum space Aharonov-Bohm interferometer which is firstly proposed by L.Duca and T.Li,etc.
Superlattice valley engineering for designer topological insulators.
Li, Xiao; Zhang, Fan; Niu, Qian; Feng, Ji
2014-09-30
A topological insulator is a novel state of quantum matter, characterized by symmetry-protected Dirac interfacial states within its bulk gap. Tremendous effort has been invested into the search for topological insulators. To date, the discovery of topological insulators has been largely limited to natural crystalline solids. Therefore, it is highly desirable to tailor-make various topological states of matter by design, starting with but a few accessible materials or elements. Here, we establish that valley-dependent dimerization of Dirac surface states can be exploited to induce topological quantum phase transitions, in a binary superlattice bearing symmetry-unrelated interfacial Dirac states. This mechanism leads to a rich phase diagram and allows for rational design of strong topological insulators, weak topological insulators, and topological crystalline insulators. Our ab initio simulations further demonstrate this mechanism in [111] and [110] superlattices of calcium and tin tellurides. While our results reveal a remarkable phase diagram for the binary superlattice, the mechanism is a general route to design various topological states.
Effective Topological Charge Cancelation Mechanism
Mesarec, Luka; Góźdź, Wojciech; Iglič, Aleš; Kralj, Samo
2016-01-01
Topological defects (TDs) appear almost unavoidably in continuous symmetry breaking phase transitions. The topological origin makes their key features independent of systems’ microscopic details; therefore TDs display many universalities. Because of their strong impact on numerous material properties and their significant role in several technological applications it is of strong interest to find simple and robust mechanisms controlling the positioning and local number of TDs. We present a numerical study of TDs within effectively two dimensional closed soft films exhibiting in-plane orientational ordering. Popular examples of such class of systems are liquid crystalline shells and various biological membranes. We introduce the Effective Topological Charge Cancellation mechanism controlling localised positional assembling tendency of TDs and the formation of pairs {defect, antidefect} on curved surfaces and/or presence of relevant “impurities” (e.g. nanoparticles). For this purpose, we define an effective topological charge Δmeff consisting of real, virtual and smeared curvature topological charges within a surface patch Δς identified by the typical spatially averaged local Gaussian curvature K. We demonstrate a strong tendency enforcing Δmeff → 0 on surfaces composed of Δς exhibiting significantly different values of spatially averaged K. For Δmeff ≠ 0 we estimate a critical depinning threshold to form pairs {defect, antidefect} using the electrostatic analogy. PMID:27250777
Effective Topological Charge Cancelation Mechanism
NASA Astrophysics Data System (ADS)
Mesarec, Luka; Góźdź, Wojciech; Iglič, Aleš; Kralj, Samo
2016-06-01
Topological defects (TDs) appear almost unavoidably in continuous symmetry breaking phase transitions. The topological origin makes their key features independent of systems’ microscopic details; therefore TDs display many universalities. Because of their strong impact on numerous material properties and their significant role in several technological applications it is of strong interest to find simple and robust mechanisms controlling the positioning and local number of TDs. We present a numerical study of TDs within effectively two dimensional closed soft films exhibiting in-plane orientational ordering. Popular examples of such class of systems are liquid crystalline shells and various biological membranes. We introduce the Effective Topological Charge Cancellation mechanism controlling localised positional assembling tendency of TDs and the formation of pairs {defect, antidefect} on curved surfaces and/or presence of relevant “impurities” (e.g. nanoparticles). For this purpose, we define an effective topological charge Δmeff consisting of real, virtual and smeared curvature topological charges within a surface patch Δς identified by the typical spatially averaged local Gaussian curvature K. We demonstrate a strong tendency enforcing Δmeff → 0 on surfaces composed of Δς exhibiting significantly different values of spatially averaged K. For Δmeff ≠ 0 we estimate a critical depinning threshold to form pairs {defect, antidefect} using the electrostatic analogy.
The topology of geology 2: Topological uncertainty
NASA Astrophysics Data System (ADS)
Thiele, Samuel T.; Jessell, Mark W.; Lindsay, Mark; Wellmann, J. Florian; Pakyuz-Charrier, Evren
2016-10-01
Uncertainty is ubiquitous in geology, and efforts to characterise and communicate it are becoming increasingly important. Recent studies have quantified differences between perturbed geological models to gain insight into uncertainty. We build on this approach by quantifying differences in topology, a property that describes geological relationships in a model, introducing the concept of topological uncertainty. Data defining implicit geological models were perturbed to simulate data uncertainties, and the amount of topological variation in the resulting model suite measured to provide probabilistic assessments of specific topological hypotheses, sources of topological uncertainty and the classification of possible model realisations based on their topology. Overall, topology was found to be highly sensitive to small variations in model construction parameters in realistic models, with almost all of the several thousand realisations defining distinct topologies. In particular, uncertainty related to faults and unconformities was found to have profound topological implications. Finally, possible uses of topology as a geodiversity metric and validation filter are discussed, and methods of incorporating topological uncertainty into physical models are suggested.
The topology of geology 1: Topological analysis
NASA Astrophysics Data System (ADS)
Thiele, Samuel T.; Jessell, Mark W.; Lindsay, Mark; Ogarko, Vitaliy; Wellmann, J. Florian; Pakyuz-Charrier, Evren
2016-10-01
Topology has been used to characterise and quantify the properties of complex systems in a diverse range of scientific domains. This study explores the concept and applications of topological analysis in geology. We have developed an automatic system for extracting first order 2D topological information from geological maps, and 3D topological information from models built with the Noddy kinematic modelling system, and equivalent analyses should be possible for other implicit modelling systems. A method is presented for describing the spatial and temporal topology of geological models using a set of adjacency relationships that can be expressed as a topology network, thematic adjacency matrix or hive diagram. We define three types of spatial topology (cellular, structural and lithological) that allow us to analyse different aspects of the geology, and then apply them to investigate the geology of the Hamersley Basin, Western Australia.
Persistent topology for cryo-EM data analysis.
Xia, Kelin; Wei, Guo-Wei
2015-08-01
In this work, we introduce persistent homology for the analysis of cryo-electron microscopy (cryo-EM) density maps. We identify the topological fingerprint or topological signature of noise, which is widespread in cryo-EM data. For low signal-to-noise ratio (SNR) volumetric data, intrinsic topological features of biomolecular structures are indistinguishable from noise. To remove noise, we employ geometric flows that are found to preserve the intrinsic topological fingerprints of cryo-EM structures and diminish the topological signature of noise. In particular, persistent homology enables us to visualize the gradual separation of the topological fingerprints of cryo-EM structures from those of noise during the denoising process, which gives rise to a practical procedure for prescribing a noise threshold to extract cryo-EM structure information from noise contaminated data after certain iterations of the geometric flow equation. To further demonstrate the utility of persistent homology for cryo-EM data analysis, we consider a microtubule intermediate structure Electron Microscopy Data (EMD 1129). Three helix models, an alpha-tubulin monomer model, an alpha-tubulin and beta-tubulin model, and an alpha-tubulin and beta-tubulin dimer model, are constructed to fit the cryo-EM data. The least square fitting leads to similarly high correlation coefficients, which indicates that structure determination via optimization is an ill-posed inverse problem. However, these models have dramatically different topological fingerprints. Especially, linkages or connectivities that discriminate one model from another, play little role in the traditional density fitting or optimization but are very sensitive and crucial to topological fingerprints. The intrinsic topological features of the microtubule data are identified after topological denoising. By a comparison of the topological fingerprints of the original data and those of three models, we found that the third model is
Persistent topology for cryo-EM data analysis.
Xia, Kelin; Wei, Guo-Wei
2015-08-01
In this work, we introduce persistent homology for the analysis of cryo-electron microscopy (cryo-EM) density maps. We identify the topological fingerprint or topological signature of noise, which is widespread in cryo-EM data. For low signal-to-noise ratio (SNR) volumetric data, intrinsic topological features of biomolecular structures are indistinguishable from noise. To remove noise, we employ geometric flows that are found to preserve the intrinsic topological fingerprints of cryo-EM structures and diminish the topological signature of noise. In particular, persistent homology enables us to visualize the gradual separation of the topological fingerprints of cryo-EM structures from those of noise during the denoising process, which gives rise to a practical procedure for prescribing a noise threshold to extract cryo-EM structure information from noise contaminated data after certain iterations of the geometric flow equation. To further demonstrate the utility of persistent homology for cryo-EM data analysis, we consider a microtubule intermediate structure Electron Microscopy Data (EMD 1129). Three helix models, an alpha-tubulin monomer model, an alpha-tubulin and beta-tubulin model, and an alpha-tubulin and beta-tubulin dimer model, are constructed to fit the cryo-EM data. The least square fitting leads to similarly high correlation coefficients, which indicates that structure determination via optimization is an ill-posed inverse problem. However, these models have dramatically different topological fingerprints. Especially, linkages or connectivities that discriminate one model from another, play little role in the traditional density fitting or optimization but are very sensitive and crucial to topological fingerprints. The intrinsic topological features of the microtubule data are identified after topological denoising. By a comparison of the topological fingerprints of the original data and those of three models, we found that the third model is
A topologically driven glass in ring polymers
NASA Astrophysics Data System (ADS)
Michieletto, Davide
2016-05-01
The static and dynamic properties of ring polymers in concentrated solutions remains one of the last deep unsolved questions in polymer physics. At the same time, the nature of the glass transition in polymeric systems is also not well understood. In this work, we study a novel glass transition in systems made of circular polymers by exploiting the topological constraints that are conjectured to populate concentrated solutions of rings. We show that such rings strongly interpenetrate through one another, generating an extensive network of topological interactions that dramatically affects their dynamics. We show that a kinetically arrested state can be induced by randomly pinning a small fraction of the rings. This occurs well above the classical glass transition temperature at which microscopic mobility is lost. Our work both demonstrates the existence of long-lived inter-ring penetrations and realizes a novel, topologically induced, glass transition.
Optical image encryption topology.
Yong-Liang, Xiao; Xin, Zhou; Qiong-Hua, Wang; Sheng, Yuan; Yao-Yao, Chen
2009-10-15
Optical image encryption topology is proposed based on the principle of random-phase encoding. Various encryption topological units, involving peer-to-peer, ring, star, and tree topologies, can be realized by an optical 6f system. These topological units can be interconnected to constitute an optical image encryption network. The encryption and decryption can be performed in both digital and optical methods.
Anomalous Topological Phases and Unpaired Dirac Cones in Photonic Floquet Topological Insulators.
Leykam, Daniel; Rechtsman, M C; Chong, Y D
2016-07-01
We propose a class of photonic Floquet topological insulators based on staggered helical lattices and an efficient numerical method for calculating their Floquet band structure. The lattices support anomalous Floquet topological insulator phases with vanishing Chern number and tunable topological transitions. At the critical point of the topological transition, the band structure hosts a single unpaired Dirac cone, which yields a variety of unusual transport effects: a discrete analogue of conical diffraction, weak antilocalization not limited by intervalley scattering, and suppression of Anderson localization. Unlike previous designs, the effective gauge field strength can be controlled via lattice parameters such as the interhelix distance, significantly reducing radiative losses and enabling applications such as switchable topological waveguiding.
Anomalous Topological Phases and Unpaired Dirac Cones in Photonic Floquet Topological Insulators
NASA Astrophysics Data System (ADS)
Leykam, Daniel; Rechtsman, M. C.; Chong, Y. D.
2016-07-01
We propose a class of photonic Floquet topological insulators based on staggered helical lattices and an efficient numerical method for calculating their Floquet band structure. The lattices support anomalous Floquet topological insulator phases with vanishing Chern number and tunable topological transitions. At the critical point of the topological transition, the band structure hosts a single unpaired Dirac cone, which yields a variety of unusual transport effects: a discrete analogue of conical diffraction, weak antilocalization not limited by intervalley scattering, and suppression of Anderson localization. Unlike previous designs, the effective gauge field strength can be controlled via lattice parameters such as the interhelix distance, significantly reducing radiative losses and enabling applications such as switchable topological waveguiding.
Evolutionary Optimization of a Geometrically Refined Truss
NASA Technical Reports Server (NTRS)
Hull, P. V.; Tinker, M. L.; Dozier, G. V.
2007-01-01
Structural optimization is a field of research that has experienced noteworthy growth for many years. Researchers in this area have developed optimization tools to successfully design and model structures, typically minimizing mass while maintaining certain deflection and stress constraints. Numerous optimization studies have been performed to minimize mass, deflection, and stress on a benchmark cantilever truss problem. Predominantly traditional optimization theory is applied to this problem. The cross-sectional area of each member is optimized to minimize the aforementioned objectives. This Technical Publication (TP) presents a structural optimization technique that has been previously applied to compliant mechanism design. This technique demonstrates a method that combines topology optimization, geometric refinement, finite element analysis, and two forms of evolutionary computation: genetic algorithms and differential evolution to successfully optimize a benchmark structural optimization problem. A nontraditional solution to the benchmark problem is presented in this TP, specifically a geometrically refined topological solution. The design process begins with an alternate control mesh formulation, multilevel geometric smoothing operation, and an elastostatic structural analysis. The design process is wrapped in an evolutionary computing optimization toolset.
Topological phase structure of entangled qudits
NASA Astrophysics Data System (ADS)
Khoury, A. Z.; Oxman, L. E.
2014-03-01
We discuss the appearance of fractional topological phases on cyclic evolutions of entangled qudits. The original result reported by Oxman and Khoury [Phys. Rev. Lett. 106, 240503 (2011), 10.1103/PhysRevLett.106.240503] is detailed and extended to qudits of different dimensions. The topological nature of the phase evolution and its restriction to fractional values are related to both the structure of the projective space of states and entanglement. For maximally entangled states of qudits with the same Hilbert-space dimension, the fractional geometric phases are the only ones attainable under local SU(d) operations, an effect that can be experimentally observed through conditional interference.
Topological classification of crystalline insulators with space group symmetry
Jadaun, Priyamvada; Xiao, Di; Niu, Q.; Banerjee, Sanjay K.
2013-01-01
We show that in crystalline insulators, space group symmetry alone gives rise to a topological classification based on the discretization of electric polarization. Using C3 rotational symmetry as an example, we first prove that the polarization is discretized into three distinct classes, i.e., it can only take three inequivalent values. We then prove that these classes are topologically distinct. Therefore, a Z3 topological classification exists, with polarization as a topological class index. A concrete tight-binding model is derived to demonstrate the Z3 topological phase transition. Using first-principles calculations, we identify graphene on a BN substrate as a possible candidate to realize these Z3 topological states. To complete our analysis, we extend the classification of band structures to all 17 two-dimensional space groups. This work will contribute to a complete theory of symmetry-conserved topological phases and also elucidate topological properties of graphenelike systems.
Exploring New Geometric Worlds
ERIC Educational Resources Information Center
Nirode, Wayne
2015-01-01
When students work with a non-Euclidean distance formula, geometric objects such as circles and segment bisectors can look very different from their Euclidean counterparts. Students and even teachers can experience the thrill of creative discovery when investigating these differences among geometric worlds. In this article, the author describes a…
NASA Astrophysics Data System (ADS)
Beck, Horst P.
2016-02-01
Referring to the experimental results of high pressure experiments of Léger et al. (1998) we have calculated the energies of all phases observed for CaCl2 within the DFT formalism using the VASP package, and we have retrieved enthalpies and transition pressures. All phases can be considerably compressed or dilated without much change in energy. This energetic "softness" could even be quantified. We classify the high temperature TiO2-type structure and the PbCl2-type one at highest pressures as the energetically "softest" ones and the SrI2-type one as the "hardest". We furthermore discuss the energy density (E/V) of the different phases and redefine it as a fictive cohesive pressure within these structures. Pursuing our earlier approaches we have analysed the charges of the atoms in the different CaCl2 phases and their change on compression or dilation. On comparing the gradients of the charge curves we define a sort of "charge hardness" which will generally depend on the type of cation-anion pair but also on their topological connection in the respective structures. We speculate that exhausting the "charge softness or hardness" of individual ions in such arrangements may initiate the structural reorganization at the transition pressures.
Topological defects in extended inflation
NASA Technical Reports Server (NTRS)
Copeland, Edmund J.; Kolb, Edward W.; Liddle, Andrew R.
1990-01-01
The production of topological defects, especially cosmic strings, in extended inflation models was considered. In extended inflation, the Universe passes through a first-order phase transition via bubble percolation, which naturally allows defects to form at the end of inflation. The correlation length, which determines the number density of the defects, is related to the mean size of bubbles when they collide. This mechanism allows a natural combination of inflation and large scale structure via cosmic strings.
Crystallographic parameters in geometrically and topologically close-packed superstructures
Knestaypin, Evgeny A. E-mail: 7mmm81@gmal.com; Morozov, Maksim M. E-mail: 7mmm81@gmal.com; Potekaev, Alexandr I.; Klopotov, Anatoly A.; Markova, Tatyana N.; Klopotov, Vladimir D.
2014-11-14
The structures of stoichiometric compositions AB, A{sub 2}B, and A{sub 3}B for structures, B19, L1{sub 0}, L1{sub 2}, D0{sub 19}, D0{sub 22}, D0{sub 23}, D0{sub 24}, A15, C14, C15 and C36 have been investigated based on the analysis of diagrams in coordinates of space-filling coefficients Ψ on superstructural compression ΔΩ/Ω. On the basis of the analysis of the abovementioned diagrams, the equation Ψ = f{sub 0}+f{sub 1}(ΔΩ/Ω) has been obtained, and coefficients f{sub 0} and f{sub 1} of the equation for the investigated structures have been determined. It has been established that values of coefficients f{sub 0} and f{sub 1} for Laves phases have higher values than for all other compounds.
Deformations of Geometric Structures in Topological Sigma Models
Bytsenko, A. A.
2010-11-25
We study a Lie algebra of formal vector fields W{sub n} with it application to the perturbative deformed holomorphic symplectic structure in the A-model, and a Calabi-Yau manifold with boundaries in the B-model. We show that equivalent classes of deformations are described by a Hochschild cohomology of the DG-algebra A = (A,Q), Q = {partial_derivative}-bar+{partial_derivative}{sub deform,} which is defined to be the cohomology of (-1){sup n}Q+d{sub Hoch}. Here {partial_derivative}-bar is the initial non-deformed BRST operator while {partial_derivative}{sub deform} is the deformed part whose algebra is a Lie algebra of linear vector fields gl{sub n}.
Correlation effects in two-dimensional topological insulators.
Hohenadler, M; Assaad, F F
2013-04-10
Topological insulators have become one of the most active research areas in condensed matter physics. This article reviews progress on the topic of electronic correlation effects in the two-dimensional case, with a focus on systems with intrinsic spin-orbit coupling and numerical results. Topics addressed include an introduction to the noninteracting case, an overview of theoretical models, correlated topological band insulators, interaction-driven phase transitions, topological Mott insulators and fractional topological states, correlation effects on helical edge states, and topological invariants of interacting systems.
Experimental Studies of Ferromagnetism in Topological Insulators
NASA Astrophysics Data System (ADS)
Checkelsky, Joseph
2014-03-01
Breaking of time reversal symmetry has proven to be an incisive method for experimentally drawing out the exotic nature of topological insulators. In particular, the introduction of magnetic dopants in to three dimensional topological insulators has led to the realization of theoretically predicted novel types of ferromagnetic order and a quantized version of the anomalous Hall effect. Here, I will present recent work on the synthesis and measurement of bulk and thin film topological insulators doped with 3 d transition metals. I will discuss the ferromagnetic order that arises in various systems and the associated electrical transport response of the surface modes.
Scaling theory of {{{Z}}_{2}} topological invariants
NASA Astrophysics Data System (ADS)
Chen, Wei; Sigrist, Manfred; Schnyder, Andreas P.
2016-09-01
For inversion-symmetric topological insulators and superconductors characterized by {{{Z}}2} topological invariants, two scaling schemes are proposed to judge topological phase transitions driven by an energy parameter. The scaling schemes renormalize either the phase gradient or the second derivative of the Pfaffian of the time-reversal operator, through which the renormalization group flow of the driving energy parameter can be obtained. The Pfaffian near the time-reversal invariant momentum is revealed to display a universal critical behavior for a great variety of models examined.
Topological influence and backaction between topological excitations
NASA Astrophysics Data System (ADS)
Kobayashi, Shingo; Tarantino, Nicolas; Ueda, Masahito
2014-03-01
Topological objects can influence each other if the underlying homotopy groups are non-Abelian. Under such circumstances, the topological charge of each individual object is no longer a conserved quantity and can be transformed to each other. Yet we can identify the conservation law by considering the backaction of topological influence. We develop a general theory of topological influence and backaction based on the commutators of the underlying homotopy groups. In the case of the topological influence of a half-quantum vortex on a point defect, we point out that the topological backaction from the point defect is a twisting of the vortex. The total twist of the vortex line compensates for the change in the point-defect charge to conserve the total charge. We use this theory to classify charge transfers in condensed matter systems and show that a non-Abelian charge transfer can be realized in a spin-2 Bose-Einstein condensate.
Emergence of topological and topological crystalline phases in TlBiS2 and TlSbS2.
Zhang, Qingyun; Cheng, Yingchun; Schwingenschlögl, Udo
2015-02-11
Using first-principles calculations, we investigate the band structure evolution and topological phase transitions in TlBiS2 and TlSbS2 under hydrostatic pressure as well as uniaxial and biaxial strain. The phase transitions are identified by parity analysis and by calculating the surface states. Zero, one, and four Dirac cones are found for the (111) surfaces of both TlBiS2 and TlSbS2 when the pressure grows, which confirms trivial-nontrivial-trivial phase transitions. The Dirac cones at the points are anisotropic with large out-of-plane component. TlBiS2 shows normal, topological, and topological crystalline insulator phases under hydrostatic pressure, thus being the first compound to exhibit a phase transition from a topological to a topological crystalline insulator.
Emergence of topological and topological crystalline phases in TlBiS2 and TlSbS2
Zhang, Qingyun; Cheng, Yingchun; Schwingenschlögl, Udo
2015-01-01
Using first-principles calculations, we investigate the band structure evolution and topological phase transitions in TlBiS2 and TlSbS2 under hydrostatic pressure as well as uniaxial and biaxial strain. The phase transitions are identified by parity analysis and by calculating the surface states. Zero, one, and four Dirac cones are found for the (111) surfaces of both TlBiS2 and TlSbS2 when the pressure grows, which confirms trivial-nontrivial-trivial phase transitions. The Dirac cones at the points are anisotropic with large out-of-plane component. TlBiS2 shows normal, topological, and topological crystalline insulator phases under hydrostatic pressure, thus being the first compound to exhibit a phase transition from a topological to a topological crystalline insulator. PMID:25669914
Linked topological colloids in a nematic host.
Martinez, Angel; Hermosillo, Leonardo; Tasinkevych, Mykola; Smalyukh, Ivan I
2015-04-14
Geometric shape and topology of constituent particles can alter many colloidal properties such as Brownian motion, self-assembly, and phase behavior. Thus far, only single-component building blocks of colloids with connected surfaces have been studied, although topological colloids, with constituent particles shaped as freestanding knots and handlebodies of different genus, have been recently introduced. Here we develop a topological class of colloids shaped as multicomponent links. Using two-photon photopolymerization, we fabricate colloidal microparticle analogs of the classic examples of links studied in the field of topology, the Hopf and Solomon links, which we disperse in nematic fluids that possess orientational ordering of anisotropic rod-like molecules. The surfaces of these particles are treated to impose tangential or perpendicular boundary conditions for the alignment of liquid crystal molecules, so that they generate a host of topologically nontrivial field and defect structures in the dispersing nematic medium, resulting in an elastic coupling between the linked constituents. The interplay between the topologies of surfaces of linked colloids and the molecular alignment field of the nematic host reveals that linking of particle rings with perpendicular boundary conditions is commonly accompanied by linking of closed singular defect loops, laying the foundations for fabricating complex composite materials with interlinking-based structural organization.
Linked topological colloids in a nematic host
Martinez, Angel; Hermosillo, Leonardo; Tasinkevych, Mykola; Smalyukh, Ivan I.
2015-01-01
Geometric shape and topology of constituent particles can alter many colloidal properties such as Brownian motion, self-assembly, and phase behavior. Thus far, only single-component building blocks of colloids with connected surfaces have been studied, although topological colloids, with constituent particles shaped as freestanding knots and handlebodies of different genus, have been recently introduced. Here we develop a topological class of colloids shaped as multicomponent links. Using two-photon photopolymerization, we fabricate colloidal microparticle analogs of the classic examples of links studied in the field of topology, the Hopf and Solomon links, which we disperse in nematic fluids that possess orientational ordering of anisotropic rod-like molecules. The surfaces of these particles are treated to impose tangential or perpendicular boundary conditions for the alignment of liquid crystal molecules, so that they generate a host of topologically nontrivial field and defect structures in the dispersing nematic medium, resulting in an elastic coupling between the linked constituents. The interplay between the topologies of surfaces of linked colloids and the molecular alignment field of the nematic host reveals that linking of particle rings with perpendicular boundary conditions is commonly accompanied by linking of closed singular defect loops, laying the foundations for fabricating complex composite materials with interlinking-based structural organization. PMID:25825765
NASA Astrophysics Data System (ADS)
Huang, Shin-Ming; Tsai, Wei-Feng; Chung, Chung-Hou; Mou, Chung-Yu
2016-02-01
The ground state of the large Hubbard U limit of a honeycomb lattice near half filling is known to be a singlet d +i d -wave superconductor. It is also known that this d +i d superconductor exhibits a chiral p +i p pairing locally at the Dirac cone, characterized by a 2 Z topological invariant. By constructing a dual transformation, we demonstrate that this 2 Z topological superconductor is equivalent to a collection of two topological ferromagnetic insulators. As a result of the duality, the topology of the electronic structures for a d +i d superconductor is controllable via the change of the chemical potential by tuning the gate voltage. In particular, instead of always being a chiral superconductor, we find that the d +i d superconductor undergoes a topological phase transition from a chiral superconductor to a quasihelical superconductor as the gap amplitude or the chemical potential decreases. The quasihelical superconducting phase is found to be characterized by a topological invariant in the pseudospin charge sector with vanishing both the Chern number and the spin Chern number. We further elucidate the topological phase transition by analyzing the relationship between the topological invariant and the rotation symmetry. Due to the angular momentum carried by the gap function and spin-orbit interactions, we show that by placing d +i d superconductors in proximity to ferromagnets, varieties of chiral superconducting phases characterized by higher Chern numbers can be accessed, providing a platform for hosting large numbers of Majorana modes at edges.
Robustness of topological quantum codes: Ising perturbation
NASA Astrophysics Data System (ADS)
Zarei, Mohammad Hossein
2015-02-01
We study the phase transition from two different topological phases to the ferromagnetic phase by focusing on points of the phase transition. To this end, we present a detailed mapping from such models to the Ising model in a transverse field. Such a mapping is derived by rewriting the initial Hamiltonian in a new basis so that the final model in such a basis has a well-known approximated phase transition point. Specifically, we consider the toric codes and the color codes on various lattices with Ising perturbation. Our results provide a useful table to compare the robustness of the topological codes and to explicitly show that the robustness of the topological codes depends on triangulation of their underlying lattices.
Geometric precipices in string cosmology
Kaloper, Nemanja; Watson, Scott
2008-03-15
We consider the effects of graviton multiplet fields on transitions between string gas phases. Focusing on the dilaton field, we show that it may obstruct transitions between different thermodynamic phases of the string gas, because the sign of its dimensionally reduced, T-duality invariant, part is conserved when the energy density of the Universe is positive. Thus, many interesting solutions for which this sign is positive end up in a future curvature singularity. Because of this, some of the thermodynamic phases of the usual gravitating string gases behave like superselection sectors. For example, a past-regular Hagedorn phase and an expanding Friedmann-Robertson-Walker (FRW) phase dominated by string momentum modes cannot be smoothly connected in the framework of string cosmology with positive sources. The singularity separates them like a geometric precipice in the moduli space, preventing the dynamics of the theory from bridging across. Sources which simultaneously violate the positivity of energy and null energy condition (NEC) could modify these conclusions. We provide a quantitative measure of positivity of energy and NEC violations that would be necessary for such transitions. These effects must dominate the Universe at the moment of transition, altering the standard gas pictures. At present, it is not known how to construct such sources from first principles in string theory.
Geometric intrinsic symmetries
Gozdz, A. Szulerecka, A.; Pedrak, A.
2013-08-15
The problem of geometric symmetries in the intrinsic frame of a many-body system (nucleus) is considered. An importance of symmetrization group notion is discussed. Ageneral structure of the intrinsic symmetry group structure is determined.
Protected gates for topological quantum field theories
NASA Astrophysics Data System (ADS)
Beverland, Michael E.; Buerschaper, Oliver; Koenig, Robert; Pastawski, Fernando; Preskill, John; Sijher, Sumit
2016-02-01
We study restrictions on locality-preserving unitary logical gates for topological quantum codes in two spatial dimensions. A locality-preserving operation is one which maps local operators to local operators — for example, a constant-depth quantum circuit of geometrically local gates, or evolution for a constant time governed by a geometrically local bounded-strength Hamiltonian. Locality-preserving logical gates of topological codes are intrinsically fault tolerant because spatially localized errors remain localized, and hence sufficiently dilute errors remain correctable. By invoking general properties of two-dimensional topological field theories, we find that the locality-preserving logical gates are severely limited for codes which admit non-abelian anyons, in particular, there are no locality-preserving logical gates on the torus or the sphere with M punctures if the braiding of anyons is computationally universal. Furthermore, for Ising anyons on the M-punctured sphere, locality-preserving gates must be elements of the logical Pauli group. We derive these results by relating logical gates of a topological code to automorphisms of the Verlinde algebra of the corresponding anyon model, and by requiring the logical gates to be compatible with basis changes in the logical Hilbert space arising from local F-moves and the mapping class group.
Topological boundary modes in jammed matter.
Sussman, Daniel M; Stenull, Olaf; Lubensky, T C
2016-07-13
Granular matter at the jamming transition is poised on the brink of mechanical stability, and hence it is possible that these random systems have topologically protected surface phonons. Studying two model systems for jammed matter, we find states that exhibit distinct mechanical topological classes, protected surface modes, and ubiquitous Weyl points. The detailed statistics of the boundary modes shed surprising light on the properties of the jamming critical point and help inform a common theoretical description of the detailed features of the transition. PMID:27345616
Descriptive Geometry and Geometric Modeling.
ERIC Educational Resources Information Center
Adams, J. Alan
1988-01-01
Describes experiences for engineering students to develop spatial awareness and reasoning capability. Describes geometric modeling, basic geometric concepts, operations, surface modeling, and conclusions. (YP)
NASA Technical Reports Server (NTRS)
Lieberman, R. N.
1972-01-01
Given a directed graph, a natural topology is defined and relationships between standard topological properties and graph theoretical concepts are studied. In particular, the properties of connectivity and separatedness are investigated. A metric is introduced which is shown to be related to separatedness. The topological notions of continuity and homeomorphism. A class of maps is studied which preserve both graph and topological properties. Applications involving strong maps and contractions are also presented.
Converting normal insulators into topological insulators via tuning orbital levels
NASA Astrophysics Data System (ADS)
Shi, Wu-Jun; Liu, Junwei; Xu, Yong; Xiong, Shi-Jie; Wu, Jian; Duan, Wenhui
2015-11-01
Tuning the spin-orbit coupling strength via foreign element doping and modifying bonding strength via strain engineering are the major routes to convert normal insulators to topological insulators. We here propose an alternative strategy to realize topological phase transition by tuning the orbital level. Following this strategy, our first-principles calculations demonstrate that a topological phase transition in the cubic perovskite-type compounds CsGeBr3 and CsSnBr3 could be facilitated by carbon substitutional doping. Such a unique topological phase transition predominantly results from the lower orbital energy of the carbon dopant, which can pull down the conduction bands and even induce band inversion. Beyond conventional approaches, our finding of tuning the orbital level may greatly expand the range of topologically nontrivial materials.
Electrically Tunable Magnetism in Magnetic Topological Insulators.
Wang, Jing; Lian, Biao; Zhang, Shou-Cheng
2015-07-17
The external controllability of the magnetic properties in topological insulators would be important both for fundamental and practical interests. Here we predict the electric-field control of ferromagnetism in a thin film of insulating magnetic topological insulators. The decrease of band inversion by the application of electric fields results in a reduction of magnetic susceptibility, and hence in the modification of magnetism. Remarkably, the electric field could even induce the magnetic quantum phase transition from ferromagnetism to paramagnetism. We further propose a transistor device in which the dissipationless charge transport of chiral edge states is controlled by an electric field. In particular, the field-controlled ferromagnetism in a magnetic topological insulator can be used for voltage based writing of magnetic random access memories in magnetic tunnel junctions. The simultaneous electrical control of magnetic order and chiral edge transport in such devices may lead to electronic and spintronic applications for topological insulators.
Mapping of Topological Quantum Circuits to Physical Hardware
NASA Astrophysics Data System (ADS)
Paler, Alexandru; Devitt, Simon J.; Nemoto, Kae; Polian, Ilia
2014-04-01
Topological quantum computation is a promising technique to achieve large-scale, error-corrected computation. Quantum hardware is used to create a large, 3-dimensional lattice of entangled qubits while performing computation requires strategic measurement in accordance with a topological circuit specification. The specification is a geometric structure that defines encoded information and fault-tolerant operations. The compilation of a topological circuit is one important aspect of programming a quantum computer, another is the mapping of the topological circuit into the operations performed by the hardware. Each qubit has to be controlled, and measurement results are needed to propagate encoded quantum information from input to output. In this work, we introduce an algorithm for mapping an topological circuit to the operations needed by the physical hardware. We determine the control commands for each qubit in the computer and the relevant measurements that are needed to track information as it moves through the circuit.
Topological Signatures in the Electronic Structure of Graphene Spirals
Avdoshenko, Stas M.; Koskinen, Pekka; Sevinçli, Haldun; Popov, Alexey A.; Rocha, Claudia G.
2013-01-01
Topology is familiar mostly from mathematics, but also natural sciences have found its concepts useful. Those concepts have been used to explain several natural phenomena in biology and physics, and they are particularly relevant for the electronic structure description of topological insulators and graphene systems. Here, we introduce topologically distinct graphene forms - graphene spirals - and employ density-functional theory to investigate their geometric and electronic properties. We found that the spiral topology gives rise to an intrinsic Rashba spin-orbit splitting. Through a Hamiltonian constrained by space curvature, graphene spirals have topologically protected states due to time-reversal symmetry. In addition, we argue that the synthesis of such graphene spirals is feasible and can be achieved through advanced bottom-up experimental routes that we indicate in this work. PMID:23568379
Mapping of topological quantum circuits to physical hardware.
Paler, Alexandru; Devitt, Simon J; Nemoto, Kae; Polian, Ilia
2014-01-01
Topological quantum computation is a promising technique to achieve large-scale, error-corrected computation. Quantum hardware is used to create a large, 3-dimensional lattice of entangled qubits while performing computation requires strategic measurement in accordance with a topological circuit specification. The specification is a geometric structure that defines encoded information and fault-tolerant operations. The compilation of a topological circuit is one important aspect of programming a quantum computer, another is the mapping of the topological circuit into the operations performed by the hardware. Each qubit has to be controlled, and measurement results are needed to propagate encoded quantum information from input to output. In this work, we introduce an algorithm for mapping an topological circuit to the operations needed by the physical hardware. We determine the control commands for each qubit in the computer and the relevant measurements that are needed to track information as it moves through the circuit. PMID:24722360
Topological computation based on direct magnetic logic communication
Zhang, Shilei; Baker, Alexander A.; Komineas, Stavros; Hesjedal, Thorsten
2015-01-01
Non-uniform magnetic domains with non-trivial topology, such as vortices and skyrmions, are proposed as superior state variables for nonvolatile information storage. So far, the possibility of logic operations using topological objects has not been considered. Here, we demonstrate numerically that the topology of the system plays a significant role for its dynamics, using the example of vortex-antivortex pairs in a planar ferromagnetic film. Utilising the dynamical properties and geometrical confinement, direct logic communication between the topological memory carriers is realised. This way, no additional magnetic-to-electrical conversion is required. More importantly, the information carriers can spontaneously travel up to ~300 nm, for which no spin-polarised current is required. The derived logic scheme enables topological spintronics, which can be integrated into large-scale memory and logic networks capable of complex computations. PMID:26508375
Geometrical optical illusionists.
Wade, Nicholas J
2014-01-01
Geometrical optical illusions were given this title by Oppel in 1855. Variants on such small distortions of visual space were illustrated thereafter, many of which bear the names of those who first described them. Some original forms of the geometrical optical illusions are shown together with 'perceptual portraits' of those who described them. These include: Roget, Chevreul, Fick, Zöllner, Poggendorff, Hering, Kundt, Delboeuf Mach, Helmholtz, Hermann, von Bezold, Müller-Lyer, Lipps, Thiéry, Wundt, Münsterberg, Ebbinghaus, Titchener, Ponzo, Luckiesh, Sander, Ehrenstein, Gregory, Heard, White, Shepard, and. Lingelbach. The illusions are grouped under the headings of orientation, size, the combination of size and orientation, and contrast. Early theories of illusions, before geometrical optical illusions were so named, are mentioned briefly.
Inflation from geometrical tachyons
Thomas, Steven; Ward, John
2005-10-15
We propose an alternative formulation of tachyon inflation using the geometrical tachyon arising from the time dependent motion of a BPS D3-brane in the background geometry due to k parallel NS5-branes arranged around a ring of radius R. Because of the fact that the mass of this geometrical tachyon field is {radical}(2/k) times smaller than the corresponding open-string tachyon mass, we find that the slow-roll conditions for inflation and the number of e-foldings can be satisfied in a manner that is consistent with an effective 4-dimensional model and with a perturbative string coupling. We also show that the metric perturbations produced at the end of inflation can be sufficiently small and do not lead to the inconsistencies that plague the open-string tachyon models. Finally we argue for the existence of a minimum of the geometrical tachyon potential which could give rise to a traditional reheating mechanism.
Geometrical optical illusionists.
Wade, Nicholas J
2014-01-01
Geometrical optical illusions were given this title by Oppel in 1855. Variants on such small distortions of visual space were illustrated thereafter, many of which bear the names of those who first described them. Some original forms of the geometrical optical illusions are shown together with 'perceptual portraits' of those who described them. These include: Roget, Chevreul, Fick, Zöllner, Poggendorff, Hering, Kundt, Delboeuf Mach, Helmholtz, Hermann, von Bezold, Müller-Lyer, Lipps, Thiéry, Wundt, Münsterberg, Ebbinghaus, Titchener, Ponzo, Luckiesh, Sander, Ehrenstein, Gregory, Heard, White, Shepard, and. Lingelbach. The illusions are grouped under the headings of orientation, size, the combination of size and orientation, and contrast. Early theories of illusions, before geometrical optical illusions were so named, are mentioned briefly. PMID:25507310
Geometrical optical illusionists.
Wade, Nicholas J
2014-01-01
Geometrical optical illusions were given this title by Oppel in 1855. Variants on such small distortions of visual space were illustrated thereafter, many of which bear the names of those who first described them. Some original forms of the geometrical optical illusions are shown together with 'perceptual portraits' of those who described them. These include: Roget, Chevreul, Fick, Zöllner, Poggendorff, Hering, Kundt, Delboeuf Mach, Helmholtz, Hermann, von Bezold, Müller-Lyer, Lipps, Thiéry, Wundt, Münsterberg, Ebbinghaus, Titchener, Ponzo, Luckiesh, Sander, Ehrenstein, Gregory, Heard, White, Shepard, and. Lingelbach. The illusions are grouped under the headings of orientation, size, the combination of size and orientation, and contrast. Early theories of illusions, before geometrical optical illusions were so named, are mentioned briefly. PMID:25420326
Bulk Topological Proximity Effect.
Hsieh, Timothy H; Ishizuka, Hiroaki; Balents, Leon; Hughes, Taylor L
2016-02-26
Existing proximity effects stem from systems with a local order parameter, such as a local magnetic moment or a local superconducting pairing amplitude. Here, we demonstrate that despite lacking a local order parameter, topological phases also may give rise to a proximity effect of a distinctively inverted nature. We focus on a general construction in which a topological phase is extensively coupled to a second system, and we argue that, in many cases, the inverse topological order will be induced on the second system. To support our arguments, we rigorously establish this "bulk topological proximity effect" for all gapped free-fermion topological phases and representative integrable models of interacting topological phases. We present a terrace construction which illustrates the phenomenological consequences of this proximity effect. Finally, we discuss generalizations beyond our framework, including how intrinsic topological order may also exhibit this effect.
Kalb, Jeffrey L.; Lee, David S.
2008-01-01
Emerging high-bandwidth, low-latency network technology has made network-based architectures both feasible and potentially desirable for use in satellite payload architectures. The selection of network topology is a critical component when developing these multi-node or multi-point architectures. This study examines network topologies and their effect on overall network performance. Numerous topologies were reviewed against a number of performance, reliability, and cost metrics. This document identifies a handful of good network topologies for satellite applications and the metrics used to justify them as such. Since often multiple topologies will meet the requirements of the satellite payload architecture under development, the choice of network topology is not easy, and in the end the choice of topology is influenced by both the design characteristics and requirements of the overall system and the experience of the developer.
Photonic Floquet topological insulators.
Rechtsman, Mikael C; Zeuner, Julia M; Plotnik, Yonatan; Lumer, Yaakov; Podolsky, Daniel; Dreisow, Felix; Nolte, Stefan; Segev, Mordechai; Szameit, Alexander
2013-04-11
Topological insulators are a new phase of matter, with the striking property that conduction of electrons occurs only on their surfaces. In two dimensions, electrons on the surface of a topological insulator are not scattered despite defects and disorder, providing robustness akin to that of superconductors. Topological insulators are predicted to have wide-ranging applications in fault-tolerant quantum computing and spintronics. Substantial effort has been directed towards realizing topological insulators for electromagnetic waves. One-dimensional systems with topological edge states have been demonstrated, but these states are zero-dimensional and therefore exhibit no transport properties. Topological protection of microwaves has been observed using a mechanism similar to the quantum Hall effect, by placing a gyromagnetic photonic crystal in an external magnetic field. But because magnetic effects are very weak at optical frequencies, realizing photonic topological insulators with scatter-free edge states requires a fundamentally different mechanism-one that is free of magnetic fields. A number of proposals for photonic topological transport have been put forward recently. One suggested temporal modulation of a photonic crystal, thus breaking time-reversal symmetry and inducing one-way edge states. This is in the spirit of the proposed Floquet topological insulators, in which temporal variations in solid-state systems induce topological edge states. Here we propose and experimentally demonstrate a photonic topological insulator free of external fields and with scatter-free edge transport-a photonic lattice exhibiting topologically protected transport of visible light on the lattice edges. Our system is composed of an array of evanescently coupled helical waveguides arranged in a graphene-like honeycomb lattice. Paraxial diffraction of light is described by a Schrödinger equation where the propagation coordinate (z) acts as 'time'. Thus the helicity of the
Photonic Floquet topological insulators.
Rechtsman, Mikael C; Zeuner, Julia M; Plotnik, Yonatan; Lumer, Yaakov; Podolsky, Daniel; Dreisow, Felix; Nolte, Stefan; Segev, Mordechai; Szameit, Alexander
2013-04-11
Topological insulators are a new phase of matter, with the striking property that conduction of electrons occurs only on their surfaces. In two dimensions, electrons on the surface of a topological insulator are not scattered despite defects and disorder, providing robustness akin to that of superconductors. Topological insulators are predicted to have wide-ranging applications in fault-tolerant quantum computing and spintronics. Substantial effort has been directed towards realizing topological insulators for electromagnetic waves. One-dimensional systems with topological edge states have been demonstrated, but these states are zero-dimensional and therefore exhibit no transport properties. Topological protection of microwaves has been observed using a mechanism similar to the quantum Hall effect, by placing a gyromagnetic photonic crystal in an external magnetic field. But because magnetic effects are very weak at optical frequencies, realizing photonic topological insulators with scatter-free edge states requires a fundamentally different mechanism-one that is free of magnetic fields. A number of proposals for photonic topological transport have been put forward recently. One suggested temporal modulation of a photonic crystal, thus breaking time-reversal symmetry and inducing one-way edge states. This is in the spirit of the proposed Floquet topological insulators, in which temporal variations in solid-state systems induce topological edge states. Here we propose and experimentally demonstrate a photonic topological insulator free of external fields and with scatter-free edge transport-a photonic lattice exhibiting topologically protected transport of visible light on the lattice edges. Our system is composed of an array of evanescently coupled helical waveguides arranged in a graphene-like honeycomb lattice. Paraxial diffraction of light is described by a Schrödinger equation where the propagation coordinate (z) acts as 'time'. Thus the helicity of the
Geometry and dynamics of one-norm geometric quantum discord
NASA Astrophysics Data System (ADS)
Huang, Zhiming; Qiu, Daowen; Mateus, Paulo
2016-01-01
We investigate the geometry of one-norm geometric quantum discord and present a geometric interpretation of one-norm geometric quantum discord for a class of two-qubit states. It is found that one-norm geometric quantum discord has geometric behavior different from that described in Lang and Caves (Phys Rev Lett 105:150501, 2010), Li et al. (Phys Rev A 83:022321, 2011) and Yao et al. (Phys Lett A 376:358-364, 2012). We also compare the dynamics of the one-norm geometric quantum discord and other measures of quantum correlations under correlated noise. It is shown that different decoherent channels bring different influences to quantum correlations measured by concurrence, entropic quantum discord and geometric quantum discord, which depend on the memory parameter and decoherence parameter. We lay emphasis on the behaviors such as entanglement sudden death and sudden transition of quantum discord. Finally, we study the dynamical behavior of one-norm geometric quantum discord in one-dimensional anisotropic XXZ model by utilizing the quantum renormalization group method. It is shown that the one-norm geometric quantum discord demonstrates quantum phase transition through renormalization group approach.
A quantum dot in topological insulator nanofilm.
Herath, Thakshila M; Hewageegana, Prabath; Apalkov, Vadym
2014-03-19
We introduce a quantum dot in topological insulator nanofilm as a bump at the surface of the nanofilm. Such a quantum dot can localize an electron if the size of the dot is large enough, ≳5 nm. The quantum dot in topological insulator nanofilm has states of two types, which belong to two ('conduction' and 'valence') bands of the topological insulator nanofilm. We study the energy spectra of such defined quantum dots. We also consider intraband and interband optical transitions within the dot. The optical transitions of the two types have the same selection rules. While the interband absorption spectra have multi-peak structure, each of the intraband spectra has one strong peak and a few weak high frequency satellites.
Statistical mechanics of topologically constrained DNA and nucleoprotein complexes
NASA Astrophysics Data System (ADS)
Giovan, Stefan Michael
A complex connection exists between the 3 dimensional topological state of DNA in living organisms and biological processes including gene expression, DNA replication, recombination and repair. A significant limitation in developing a detailed, quantitative understanding of this connection is due to a lack of rigorous methods to calculate statistical mechanical properties of DNA molecules with complex topologies, including supercoiling, looping and knotting. This dissertation's main focus is on developing such methods and applying them to realistic DNA and nucleoprotein models. In chapter 2, a method is presented to calculate free energies and J factors of protein mediated DNA loops by normal mode analysis (NMA). This method is similar to calculations performed previously but with several significant advances. We apply the method to the specific case of DNA looping mediated by Cre recombinase protein. J factors calculated by our method are compared to experimental measurements to extract geometric and elastic properties of the Cre-DNA synaptic complex. In particular, the results suggest the existence of a synaptic complex that is more flexible than previously expected and may be explained by a stable intermediate in the reaction pathway that deviates significantly from the planar crystal structure. Calculating free energies of DNA looping is difficult in general, especially when considering intermediate length scales such as plasmid sized DNA which may readily adopt multiple topological states. In chapter 3, a novel method is presented to obtain free energies of semiflexible biopolymers with fixed topologies and arbitrary ratios of contour length L to persistence length P. High accuracy is demonstrated by calculating free energies of specific DNA knots with L/P = 20 and L/P = 40, corresponding to DNA lengths of 3000 and 6000 base pairs, respectively. We then apply the method to study the free-energy landscape for a model of a synaptic nucleoprotein complex
Tasinkevych, Mykola; Campbell, Michael G; Smalyukh, Ivan I
2014-11-18
Topologically nontrivial field excitations, including solitonic, linked, and knotted structures, play important roles in physical systems ranging from classical fluids and liquid crystals, to electromagnetism, classic, and quantum field theories. These excitations can appear spontaneously during symmetry-breaking phase transitions. For example, in cosmological theories, cosmic strings may have formed knotted configurations influencing the Early Universe development, whereas in liquid crystals transient tangled defect lines were observed during isotropic-nematic transitions, eventually relaxing to defect-free states. Knotted and solitonic fields and defects were also obtained using optical manipulation, complex-shaped colloids, and frustrated cholesterics. Here we use confinement of nematic liquid crystal by closed surfaces with varied genus and perpendicular boundary conditions for a robust control of appearance and stability of such field excitations. Theoretical modeling and experiments reveal structure of defect lines as a function of the surface topology and material and geometric parameters, establishing a robust means of controlling solitonic, knotted, linked, and other field excitations. PMID:25369931
Tasinkevych, Mykola; Campbell, Michael G.; Smalyukh, Ivan I.
2014-01-01
Topologically nontrivial field excitations, including solitonic, linked, and knotted structures, play important roles in physical systems ranging from classical fluids and liquid crystals, to electromagnetism, classic, and quantum field theories. These excitations can appear spontaneously during symmetry-breaking phase transitions. For example, in cosmological theories, cosmic strings may have formed knotted configurations influencing the Early Universe development, whereas in liquid crystals transient tangled defect lines were observed during isotropic–nematic transitions, eventually relaxing to defect-free states. Knotted and solitonic fields and defects were also obtained using optical manipulation, complex-shaped colloids, and frustrated cholesterics. Here we use confinement of nematic liquid crystal by closed surfaces with varied genus and perpendicular boundary conditions for a robust control of appearance and stability of such field excitations. Theoretical modeling and experiments reveal structure of defect lines as a function of the surface topology and material and geometric parameters, establishing a robust means of controlling solitonic, knotted, linked, and other field excitations. PMID:25369931
Classification and characterization of topological insulators and superconductors
NASA Astrophysics Data System (ADS)
Mong, Roger
surface spectrum can be computed from bulk quantities. Specifically, we present an analytic prescription for computing the edge dispersion
Topological crystalline insulator nanostructures.
Shen, Jie; Cha, Judy J
2014-11-01
Topological crystalline insulators are topological insulators whose surface states are protected by the crystalline symmetry, instead of the time reversal symmetry. Similar to the first generation of three-dimensional topological insulators such as Bi₂Se₃ and Bi₂Te₃, topological crystalline insulators also possess surface states with exotic electronic properties such as spin-momentum locking and Dirac dispersion. Experimentally verified topological crystalline insulators to date are SnTe, Pb₁-xSnxSe, and Pb₁-xSnxTe. Because topological protection comes from the crystal symmetry, magnetic impurities or in-plane magnetic fields are not expected to open a gap in the surface states in topological crystalline insulators. Additionally, because they have a cubic structure instead of a layered structure, branched structures or strong coupling with other materials for large proximity effects are possible, which are difficult with layered Bi₂Se₃ and Bi₂Te₃. Thus, additional fundamental phenomena inaccessible in three-dimensional topological insulators can be pursued. In this review, topological crystalline insulator SnTe nanostructures will be discussed. For comparison, experimental results based on SnTe thin films will be covered. Surface state properties of topological crystalline insulators will be discussed briefly.
Geometric Series via Probability
ERIC Educational Resources Information Center
Tesman, Barry
2012-01-01
Infinite series is a challenging topic in the undergraduate mathematics curriculum for many students. In fact, there is a vast literature in mathematics education research on convergence issues. One of the most important types of infinite series is the geometric series. Their beauty lies in the fact that they can be evaluated explicitly and that…
NASA Technical Reports Server (NTRS)
Ives, David
1995-01-01
This paper presents a highly automated hexahedral grid generator based on extensive geometrical and solid modeling operations developed in response to a vision of a designer-driven one day turnaround CFD process which implies a designer-driven one hour grid generation process.
1500 System Geometric Dictionary.
ERIC Educational Resources Information Center
Peloquin, Paul V.
A general description is provided of the "geometric dictionary," a graphic display aid, used by the Computer-Assisted Instruction Laboratory at the Pennsylvania State University. The purpose of the description is to enable the reader to duplicate and use the dictionary on any cathode ray tube terminal of the IBM 1500 system. The major advantages…
ERIC Educational Resources Information Center
Smart, Julie; Marshall, Jeff
2007-01-01
Children possess a genuine curiosity for exploring the natural world around them. One third grade teacher capitalized on this inherent trait by leading her students on "A Geometric Scavenger Hunt." The four-lesson inquiry investigation described in this article integrates mathematics and science. Among the students' discoveries was the fact that…
Pragmatic geometric model evaluation
NASA Astrophysics Data System (ADS)
Pamer, Robert
2015-04-01
Quantification of subsurface model reliability is mathematically and technically demanding as there are many different sources of uncertainty and some of the factors can be assessed merely in a subjective way. For many practical applications in industry or risk assessment (e. g. geothermal drilling) a quantitative estimation of possible geometric variations in depth unit is preferred over relative numbers because of cost calculations for different scenarios. The talk gives an overview of several factors that affect the geometry of structural subsurface models that are based upon typical geological survey organization (GSO) data like geological maps, borehole data and conceptually driven construction of subsurface elements (e. g. fault network). Within the context of the trans-European project "GeoMol" uncertainty analysis has to be very pragmatic also because of different data rights, data policies and modelling software between the project partners. In a case study a two-step evaluation methodology for geometric subsurface model uncertainty is being developed. In a first step several models of the same volume of interest have been calculated by omitting successively more and more input data types (seismic constraints, fault network, outcrop data). The positions of the various horizon surfaces are then compared. The procedure is equivalent to comparing data of various levels of detail and therefore structural complexity. This gives a measure of the structural significance of each data set in space and as a consequence areas of geometric complexity are identified. These areas are usually very data sensitive hence geometric variability in between individual data points in these areas is higher than in areas of low structural complexity. Instead of calculating a multitude of different models by varying some input data or parameters as it is done by Monte-Carlo-simulations, the aim of the second step of the evaluation procedure (which is part of the ongoing work) is to
Topological structure of dictionary graphs
NASA Astrophysics Data System (ADS)
Fukś, Henryk; Krzemiński, Mark
2009-09-01
We investigate the topological structure of the subgraphs of dictionary graphs constructed from WordNet and Moby thesaurus data. In the process of learning a foreign language, the learner knows only a subset of all words of the language, corresponding to a subgraph of a dictionary graph. When this subgraph grows with time, its topological properties change. We introduce the notion of the pseudocore and argue that the growth of the vocabulary roughly follows decreasing pseudocore numbers—that is, one first learns words with a high pseudocore number followed by smaller pseudocores. We also propose an alternative strategy for vocabulary growth, involving decreasing core numbers as opposed to pseudocore numbers. We find that as the core or pseudocore grows in size, the clustering coefficient first decreases, then reaches a minimum and starts increasing again. The minimum occurs when the vocabulary reaches a size between 103 and 104. A simple model exhibiting similar behavior is proposed. The model is based on a generalized geometric random graph. Possible implications for language learning are discussed.
Geometric Aspects of Quantum Hall States
NASA Astrophysics Data System (ADS)
Gromov, Andrey
Explanation of the quantization of the Hall conductance at low temperatures in strong magnetic field is one of the greatest accomplishments of theoretical physics of the end of the 20th century. Since the publication of the Laughlin's charge pumping argument condensed matter theorists have come a long way to topological insulators, classification of noninteracting (and sometimes interacting) topological phases of matter, non-abelian statistics, Majorana zero modes in topological superconductors and topological quantum computation---the framework for "error-free'' quantum computation. While topology was very important in these developments, geometry has largely been neglected. We explore the role of space-time symmetries in topological phases of matter. Such symmetries are responsible for the conservation of energy, momentum and angular momentum. We will show that if these symmetries are maintained (at least on average) then in addition to Hall conductance there are other, in principle, measurable transport coefficients that are quantized and sensitive to topological phase transition. Among these coefficients are non-dissipative viscosity of quantum fluids, known as Hall viscosity; thermal Hall conductance, and a recently discovered coefficient---orbital spin variance. All of these coefficients can be computed as linear responses to variations of geometry of a physical sample. We will show how to compute these coefficients for a variety of abelian and non-abelian quantum Hall states using various analytical tools: from RPA-type perturbation theory to non-abelian Chern-Simons-Witten effective topological quantum field theory. We will explain how non-Riemannian geometry known as Newton-Cartan (NC) geometry arises in the computation of momentum and energy transport in non-relativistic gapped systems. We use this geometry to derive a number of thermodynamic relations and stress the non-relativistic nature of condensed matter systems. NC geometry is also useful in the
Universal Geometric Path to a Robust Majorana Magic Gate
NASA Astrophysics Data System (ADS)
Karzig, Torsten; Oreg, Yuval; Refael, Gil; Freedman, Michael H.
2016-07-01
A universal quantum computer requires a full set of basic quantum gates. With Majorana bound states one can form all necessary quantum gates in a topologically protected way, bar one. In this paper, we present a scheme that achieves the missing, so-called, π /8 magic phase gate without the need of fine-tuning for distinct physical realizations. The scheme is based on the manipulation of geometric phases described by a universal protocol and converges exponentially with the number of steps in the geometric path. Furthermore, our magic gate proposal relies on the most basic hardware previously suggested for topologically protected gates, and can be extended to an any-phase gate, where π /8 is substituted by any α .
Cubic topological Kondo insulators.
Alexandrov, Victor; Dzero, Maxim; Coleman, Piers
2013-11-27
Current theories of Kondo insulators employ the interaction of conduction electrons with localized Kramers doublets originating from a tetragonal crystalline environment, yet all Kondo insulators are cubic. Here we develop a theory of cubic topological Kondo insulators involving the interaction of Γ(8) spin quartets with a conduction sea. The spin quartets greatly increase the potential for strong topological insulators, entirely eliminating the weak topological phases from the diagram. We show that the relevant topological behavior in cubic Kondo insulators can only reside at the lower symmetry X or M points in the Brillouin zone, leading to three Dirac cones with heavy quasiparticles.
Electric-magnetic duality and the geometric Langlands program
NASA Astrophysics Data System (ADS)
Kapustin, Anton; Witten, Edward
The geometric Langlands program can be described in a natural way bycompactifying on a Riemann surface C a twisted version of EUN=4 super Yang-Mills theory in four dimensions. The keyingredients are electric-magnetic duality of gauge theory, mirrorsymmetry of sigma-models, branes, Wilson and 't Hooft operators,and topological field theory. Seemingly esoteric notions of thegeometric Langlands program, such as Hecke eigensheaves and D-modules, arise naturally from the physics.
Destroying a topological quantum bit by condensing Ising vortices.
Hao, Zhihao; Inglis, Stephen; Melko, Roger
2014-12-09
The imminent realization of topologically protected qubits in fabricated systems will provide not only an elementary implementation of fault-tolerant quantum computing architecture, but also an experimental vehicle for the general study of topological order. The simplest topological qubit harbours what is known as a Z2 liquid phase, which encodes information via a degeneracy depending on the system's topology. Elementary excitations of the phase are fractionally charged objects called spinons, or Ising flux vortices called visons. At zero temperature, a Z2 liquid is stable under deformations of the Hamiltonian until spinon or vison condensation induces a quantum-phase transition destroying the topological order. Here we use quantum Monte Carlo to study a vison-induced transition from a Z2 liquid to a valence-bond solid in a quantum dimer model on the kagome lattice. Our results indicate that this critical point is beyond the description of the standard Landau paradigm.
Superfluidity in topologically nontrivial flat bands
NASA Astrophysics Data System (ADS)
Peotta, Sebastiano; Törmä, Päivi
2015-11-01
Topological invariants built from the periodic Bloch functions characterize new phases of matter, such as topological insulators and topological superconductors. The most important topological invariant is the Chern number that explains the quantized conductance of the quantum Hall effect. Here we provide a general result for the superfluid weight Ds of a multiband superconductor that is applicable to topologically nontrivial bands with nonzero Chern number C. We find that the integral over the Brillouin-zone of the quantum metric, an invariant calculated from the Bloch functions, gives the superfluid weight in a flat band, with the bound Ds>=|C|. Thus, even a flat band can carry finite superfluid current, provided the Chern number is nonzero. As an example, we provide Ds for the time-reversal invariant attractive Harper-Hubbard model that can be experimentally tested in ultracold gases. In general, our results establish that a topologically nontrivial flat band is a promising concept for increasing the critical temperature of the superconducting transition.
Superfluidity in topologically nontrivial flat bands.
Peotta, Sebastiano; Törmä, Päivi
2015-11-20
Topological invariants built from the periodic Bloch functions characterize new phases of matter, such as topological insulators and topological superconductors. The most important topological invariant is the Chern number that explains the quantized conductance of the quantum Hall effect. Here we provide a general result for the superfluid weight Ds of a multiband superconductor that is applicable to topologically nontrivial bands with nonzero Chern number C. We find that the integral over the Brillouin-zone of the quantum metric, an invariant calculated from the Bloch functions, gives the superfluid weight in a flat band, with the bound Ds⩾|C|. Thus, even a flat band can carry finite superfluid current, provided the Chern number is nonzero. As an example, we provide Ds for the time-reversal invariant attractive Harper-Hubbard model that can be experimentally tested in ultracold gases. In general, our results establish that a topologically nontrivial flat band is a promising concept for increasing the critical temperature of the superconducting transition.
Superfluidity in topologically nontrivial flat bands
Peotta, Sebastiano; Törmä, Päivi
2015-01-01
Topological invariants built from the periodic Bloch functions characterize new phases of matter, such as topological insulators and topological superconductors. The most important topological invariant is the Chern number that explains the quantized conductance of the quantum Hall effect. Here we provide a general result for the superfluid weight Ds of a multiband superconductor that is applicable to topologically nontrivial bands with nonzero Chern number C. We find that the integral over the Brillouin-zone of the quantum metric, an invariant calculated from the Bloch functions, gives the superfluid weight in a flat band, with the bound Ds⩾|C|. Thus, even a flat band can carry finite superfluid current, provided the Chern number is nonzero. As an example, we provide Ds for the time-reversal invariant attractive Harper–Hubbard model that can be experimentally tested in ultracold gases. In general, our results establish that a topologically nontrivial flat band is a promising concept for increasing the critical temperature of the superconducting transition. PMID:26586543
The topological Anderson insulator phase in the Kane-Mele model.
Orth, Christoph P; Sekera, Tibor; Bruder, Christoph; Schmidt, Thomas L
2016-04-05
It has been proposed that adding disorder to a topologically trivial mercury telluride/cadmium telluride (HgTe/CdTe) quantum well can induce a transition to a topologically nontrivial state. The resulting state was termed topological Anderson insulator and was found in computer simulations of the Bernevig-Hughes-Zhang model. Here, we show that the topological Anderson insulator is a more universal phenomenon and also appears in the Kane-Mele model of topological insulators on a honeycomb lattice. We numerically investigate the interplay of the relevant parameters, and establish the parameter range in which the topological Anderson insulator exists. A staggered sublattice potential turns out to be a necessary condition for the transition to the topological Anderson insulator. For weak enough disorder, a calculation based on the lowest-order Born approximation reproduces quantitatively the numerical data. Our results thus considerably increase the number of candidate materials for the topological Anderson insulator phase.
The topological Anderson insulator phase in the Kane-Mele model.
Orth, Christoph P; Sekera, Tibor; Bruder, Christoph; Schmidt, Thomas L
2016-01-01
It has been proposed that adding disorder to a topologically trivial mercury telluride/cadmium telluride (HgTe/CdTe) quantum well can induce a transition to a topologically nontrivial state. The resulting state was termed topological Anderson insulator and was found in computer simulations of the Bernevig-Hughes-Zhang model. Here, we show that the topological Anderson insulator is a more universal phenomenon and also appears in the Kane-Mele model of topological insulators on a honeycomb lattice. We numerically investigate the interplay of the relevant parameters, and establish the parameter range in which the topological Anderson insulator exists. A staggered sublattice potential turns out to be a necessary condition for the transition to the topological Anderson insulator. For weak enough disorder, a calculation based on the lowest-order Born approximation reproduces quantitatively the numerical data. Our results thus considerably increase the number of candidate materials for the topological Anderson insulator phase. PMID:27045779
The topological Anderson insulator phase in the Kane-Mele model
Orth, Christoph P.; Sekera, Tibor; Bruder, Christoph; Schmidt, Thomas L.
2016-01-01
It has been proposed that adding disorder to a topologically trivial mercury telluride/cadmium telluride (HgTe/CdTe) quantum well can induce a transition to a topologically nontrivial state. The resulting state was termed topological Anderson insulator and was found in computer simulations of the Bernevig-Hughes-Zhang model. Here, we show that the topological Anderson insulator is a more universal phenomenon and also appears in the Kane-Mele model of topological insulators on a honeycomb lattice. We numerically investigate the interplay of the relevant parameters, and establish the parameter range in which the topological Anderson insulator exists. A staggered sublattice potential turns out to be a necessary condition for the transition to the topological Anderson insulator. For weak enough disorder, a calculation based on the lowest-order Born approximation reproduces quantitatively the numerical data. Our results thus considerably increase the number of candidate materials for the topological Anderson insulator phase. PMID:27045779
The topological Anderson insulator phase in the Kane-Mele model
NASA Astrophysics Data System (ADS)
Orth, Christoph P.; Sekera, Tibor; Bruder, Christoph; Schmidt, Thomas L.
2016-04-01
It has been proposed that adding disorder to a topologically trivial mercury telluride/cadmium telluride (HgTe/CdTe) quantum well can induce a transition to a topologically nontrivial state. The resulting state was termed topological Anderson insulator and was found in computer simulations of the Bernevig-Hughes-Zhang model. Here, we show that the topological Anderson insulator is a more universal phenomenon and also appears in the Kane-Mele model of topological insulators on a honeycomb lattice. We numerically investigate the interplay of the relevant parameters, and establish the parameter range in which the topological Anderson insulator exists. A staggered sublattice potential turns out to be a necessary condition for the transition to the topological Anderson insulator. For weak enough disorder, a calculation based on the lowest-order Born approximation reproduces quantitatively the numerical data. Our results thus considerably increase the number of candidate materials for the topological Anderson insulator phase.
Irreducible many-body correlations in topologically ordered systems
NASA Astrophysics Data System (ADS)
Liu, Yang; Zeng, Bei; Zhou, D. L.
2016-02-01
Topologically ordered systems exhibit large-scale correlation in their ground states, which may be characterized by quantities such as topological entanglement entropy. We propose that the concept of irreducible many-body correlation (IMC), the correlation that cannot be implied by all local correlations, may also be used as a signature of topological order. In a topologically ordered system, we demonstrate that for a part of the system with holes, the reduced density matrix exhibits IMCs which become reducible when the holes are removed. The appearance of these IMCs then represents a key feature of topological phase. We analyze the many-body correlation structures in the ground state of the toric code model in external magnetic fields, and show that the topological phase transition is signaled by the IMCs.
Condensation of lattice defects and melting transitions in quantum Hall phases
NASA Astrophysics Data System (ADS)
Cho, Gil Young; Parrikar, Onkar; You, Yizhi; Leigh, Robert G.; Hughes, Taylor L.
2015-01-01
Motivated by recent progress in understanding the interplay between lattice and electronic topological phases, we consider quantum-melting transitions of weak quantum liquid crystals, a crystal and a nematic phase, in which electrons form a quantum Hall state. In certain classes of Chern band insulators and quantum Hall phases, it has been previously demonstrated that there are topological Chern-Simons terms such as a Hall viscosity term and a gravitational Chern-Simons term for local lattice deformations. The Chern-Simons terms can induce anyonic statistics for the topological lattice defects and, furthermore, dress the defects with certain symmetry quantum numbers. On the other hand, the melting transitions of such liquid-crystalline orders are driven by the condensation of lattice defects. Based on these observations, we show how the topological terms can change the nature of the proximate disordered phases of the quantum liquid-crystalline phases. We derive and study the effective dual field theories for the liquid-crystalline phases with the geometric Chern-Simons terms, and carefully examine the symmetry quantum numbers and statistics of defects. We show that a crystal may go through a continuous phase transition into another crystal with the different discrete translational symmetries because the dislocation, the topological defect in the crystal, carries nonzero crystal momentum due to the Hall viscosity term. For the nematic phase, the disclination will condense at the phase transition to the isotropic phase, and we show that the isotropic phase may support a deconfined fractionally charged excitation due to the Wen-Zee term, and thus the isotropic phase and the nematic phase have different electromagnetic Hall responses.