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.
Geometric Hall effects in topological insulator heterostructures
NASA Astrophysics Data System (ADS)
Yasuda, K.; Wakatsuki, R.; Morimoto, T.; Yoshimi, R.; Tsukazaki, A.; Takahashi, K. S.; Ezawa, M.; Kawasaki, M.; Nagaosa, N.; Tokura, Y.
2016-06-01
Geometry, both in momentum and in real space, plays an important role in the electronic dynamics of condensed matter systems. Among them, the Berry phase associated with nontrivial geometry can be an origin of the transverse motion of electrons, giving rise to various geometric effects such as the anomalous, spin and topological Hall effects. Here, we report two unconventional manifestations of Hall physics: a sign-reversal of the anomalous Hall effect, and the emergence of a topological Hall effect in magnetic/non-magnetic topological insulator heterostructures, Crx(Bi1-ySby)2-xTe3/(Bi1-ySby)2Te3. The sign-reversal in the anomalous Hall effect is driven by a Rashba splitting at the bulk bands, which is caused by the broken spatial inversion symmetry. Instead, the topological Hall effect arises in a wide temperature range below the Curie temperature, in a region where the magnetic-field dependence of the Hall resistance largely deviates from the magnetization. Its origin is assigned to the formation of a Néel-type skyrmion induced by the Dzyaloshinskii-Moriya interaction.
Topological rewriting and the geometrization of programming
NASA Astrophysics Data System (ADS)
Giavitto, Jean-Louis; Spicher, Antoine
2008-07-01
Spatial computing is an emerging field that recognizes the importance of explicitly handling spatial relationships at three levels: computer architectures, programming languages and applications. In this context, we present MGS, an experimental programming language where data structures are fields on abstract spaces. In MGS, fields are transformed using rules. We show that this approach is able to unify, at least for programming purposes, several computational models like Lindenmayer systems and cellular automata. The MGS notions of topological collection and transformation are formalized using concepts developed in algebraic topology. We propose to use transformations in order to implement a discrete version of some differential operators. These transformations satisfy a Stokes-like theorem. This result constitutes a geometric view of programming where data are handled like fields in physics. The relevance of this approach for the design of autonomic software systems is discussed in the conclusion.
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
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.
Effective Theory of Floquet Topological Transitions
NASA Astrophysics Data System (ADS)
Kundu, Arijit; Fertig, H. A.; Seradjeh, Babak
2014-12-01
We develop a theory of topological transitions in a Floquet topological insulator, using graphene irradiated by circularly polarized light as a concrete realization. We demonstrate that a hallmark signature of such transitions in a static system, i.e., metallic bulk transport with conductivity of order e2/h , is substantially suppressed at some Floquet topological transitions in the clean system. We determine the conditions for this suppression analytically and confirm our results in numerical simulations. Remarkably, introducing disorder dramatically enhances this transport by several orders of magnitude.
Effective theory of Floquet topological transitions.
Kundu, Arijit; Fertig, H A; Seradjeh, Babak
2014-12-01
We develop a theory of topological transitions in a Floquet topological insulator, using graphene irradiated by circularly polarized light as a concrete realization. We demonstrate that a hallmark signature of such transitions in a static system, i.e., metallic bulk transport with conductivity of order e^{2}/h, is substantially suppressed at some Floquet topological transitions in the clean system. We determine the conditions for this suppression analytically and confirm our results in numerical simulations. Remarkably, introducing disorder dramatically enhances this transport by several orders of magnitude. PMID:25526148
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
Kuprat, A.; George, D.
1998-12-01
When modeling deformation of geometrically complex regions, unstructured tetrahedral meshes provide the flexibility necessary to track interfaces as they change geometrically and topologically. In the class of time-dependent simulations considered in this paper, multimaterial interfaces are represented by sets of triangular facets, and motion of the interfaces is controlled by physical considerations. The motion of interior points in the conforming tetrahedral mesh (i.e., points not on interfaces) is arbitrary and may be chosen to produce good element shapes. In the context of specified boundary motion driven by physical considerations, they have found that a rather large glossary of mesh changes is required to allow the simulation to survive all the transitions of interface geometry and topology that occur during time evolution. This paper will describe mesh changes required to maintain good element quality as the geometry evolves, as well as mesh changes required to capture changes i n topology that occur when material regions collapse or pinch off. This paper will present a detailed description of mesh changes necessary for capturing the aforementioned geometrical and topological changes, as implemented in the code GRAIN3D, and will provide examples from a metallic grain growth simulation in which the normal velocity of the grain boundary is proportional to mean curvature.
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. PMID:25391961
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.
Geometric Transitions and Dynamical SUSY Breaking
Aganagic, Mina; Beem, Christopher; Kachru, Shamit; /UC, Berkeley /SLAC
2007-10-01
We show that the physics of D-brane theories that exhibit dynamical SUSY breaking due to stringy instanton effects is well captured by geometric transitions, which recast the non-perturbative superpotential as a classical flux superpotential. This allows for simple engineering of Fayet, Polonyi, O'Raifeartaigh, and other canonical models of supersymmetry breaking in which an exponentially small scale of breaking can be understood either as coming from stringy instantons or as arising from the classical dynamics of fluxes.
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.
Tran, Lisa; Lavrentovich, Maxim O; Beller, Daniel A; Li, Ningwei; Stebe, Kathleen J; Kamien, Randall D
2016-06-28
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. PMID:27222582
Understanding topological phase transition in monolayer transition metal dichalcogenides
NASA Astrophysics Data System (ADS)
Choe, Duk-Hyun; Sung, Ha-Jun; Chang, K. J.
2016-03-01
Despite considerable interest in layered transition metal dichalcogenides (TMDs), such as M X2 with M =(Mo ,W ) and X =(S ,Se ,Te ) , the physical origin of their topological nature is still poorly understood. In the conventional view of topological phase transition (TPT), the nontrivial topology of electron bands in TMDs is caused by the band inversion between metal d - and chalcogen p -orbital bands where the former is pulled down below the latter. Here, we show that, in TMDs, the TPT is entirely different from the conventional speculation. In particular, M S2 and M S e2 exhibits the opposite behavior of TPT such that the chalcogen p -orbital band moves down below the metal d -orbital band. More interestingly, in M T e2 , the band inversion occurs between the metal d -orbital bands. Our findings cast doubts on the common view of TPT and provide clear guidelines for understanding the topological nature in new topological materials to be discovered.
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.
Topological classification of dynamical phase transitions
NASA Astrophysics Data System (ADS)
Vajna, Szabolcs; Dóra, Balázs
2015-04-01
We study the nonequilibrium time evolution of a variety of one-dimensional (1D) and two-dimensional (2D) systems (including SSH model, Kitaev-chain, Haldane model, p +i p superconductor, etc.) following a sudden quench. We prove analytically that topology-changing quenches are always followed by nonanalytical temporal behavior of return rates (logarithm of the Loschmidt echo), referred to as dynamical phase transitions (DPTs) in the literature. Similarly to edge states in topological insulators, DPTs can be classified as being topologically protected or not. In 1D systems the number of topologically protected nonequilibrium time scales are determined by the difference between the initial and final winding numbers, while in 2D systems no such relation exists for the Chern numbers. The singularities of dynamical free energy in the 2D case are qualitatively different from those of the 1D case; the cusps appear only in the first time derivative.
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
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.
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.
Topological phase transition of a Josephson junction and its dynamics
NASA Astrophysics Data System (ADS)
Hutasoit, Jimmy; Marciani, Marco; Tarasinski, Brian; Beenakker, Carlo
A Josephson junction formed by a superconducting ring interrupted by a semiconductor nanowire can realize a zero-dimensional class D topological superconductor. By coupling the Josephson junction to a ballistic wire and altering the strength of the coupling, one can drive this topological superconductor through a topological phase transition. We study the compressibility of the junction as a probe of the topological phase transition. We also study the dynamics of the phase transition by studying the current pulse injected into the wire.
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
Quantum algorithms for topological and geometric analysis of data
NASA Astrophysics Data System (ADS)
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.
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
NASA Astrophysics Data System (ADS)
Qin, Wei; Zhang, Zhenyu
2014-12-01
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.
Topological transitions in carbon nanotube networks via nanoscale confinement.
Somu, Sivasubramanian; Wang, Hailong; Kim, Younglae; Jaberansari, Laila; Hahm, Myung Gwan; Li, Bo; Kim, Taehoon; Xiong, Xugang; Jung, Yung Joon; Upmanyu, Moneesh; Busnaina, Ahmed
2010-07-27
Efforts aimed at large-scale integration of nanoelectronic devices that exploit the superior electronic and mechanical properties of single-walled carbon nanotubes (SWCNTs) remain limited by the difficulties associated with manipulation and packaging of individual SWNTs. Alternative approaches based on ultrathin carbon nanotube networks (CNNs) have enjoyed success of late with the realization of several scalable device applications. However, precise control over the network electronic transport is challenging due to (i) an often uncontrollable interplay between network coverage and its detailed topology and (ii) the inherent electrical heterogeneity of the constituent SWNTs. In this article, we use template-assisted fluidic assembly of SWCNT networks to explore the effect of geometric confinement on the network topology. Heterogeneous SWCNT networks dip-coated onto submicrometer wide ultrathin polymer channels become increasingly aligned with decreasing channel width and thickness. Experimental-scale coarse-grained computations of interacting SWCNTs show that the effect is a reflection of a topology that is no longer dependent on the network density, which in turn emerges as a robust knob that can induce semiconductor-to-metallic transitions in the network response. Our study demonstrates the effectiveness of directed assembly on channels with varying degrees of confinement as a simple tool to tailor the conductance of the otherwise heterogeneous network, opening up the possibility of robust large-scale CNN-based devices. PMID:20695518
Topological phase transition in 2D porous media flows
NASA Astrophysics Data System (ADS)
Waisbord, Nicolas; Stoop, Norbert; Kantsler, Vasily; Guasto, Jeffrey S.; Dunkel, Jorn; Guasto Team; Dunkel Team; Kantsler Team
2015-11-01
Since the establishment of Darcy's law, analysis of porous-media flows has focused primarily on linking macroscopic transport properties, such as mean flow rate and dispersion, to the pore statistics of the material matrix. Despite intense efforts to understand the fluid velocity statistics from the porous-media structure, a qualitative and quantitative connection remains elusive. Here, we combine precisely controlled experiments with theory to quantify how geometric disorder in the matrix affects the flow statistics and transport in a quasi-2D microfluidic channel. Experimentally measured velocity fields for a range of different microstructure configurations are found to be in excellent agreement with large-scale numerical simulations. By successively increasing the matrix disorder, we study the transition from periodic flow structures to transport networks consisting of extended high-velocity channels. Morse-Smale complex analysis of the flow patterns reveals a topological phase transition that is linked to a qualitative change in the physical transport properties. This work demonstrates that topological flow analysis provides a mathematically well-defined, broadly applicable framework for understanding and quantifying fluid transport in complex geometries.
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.
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.
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.
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.
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. PMID:27152805
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.
Exploring percolative landscapes: Infinite cascades of geometric phase transitions.
Timonin, P N; Chitov, Gennady Y
2016-01-01
The evolution of many kinetic processes in 1+1 (space-time) dimensions results in 2D 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. PMID:26871019
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.
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 driven by electron-phonon interaction
NASA Astrophysics Data System (ADS)
Saha, Kush; Garate, Ion
2014-03-01
We study the effect of electron-phonon interactions in the band topology of Dirac insulators, both at zero and finite temperature. Elaborating on recent theoretical work, we determine how and when phonons can drive a trivial insulator into a topological insulating phase. As an application, we evaluate the temperature-dependence of the critical thickness for the topological transition in CdTe/HgTe quantum wells.
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.
Topological phase transition on honeycomb lattice with third neighbor hooping
NASA Astrophysics Data System (ADS)
Chen, Yao-Hua; Hung, Hsiang-Hsuan; Ting, C. S.
2014-03-01
The topological phases originating in spin-orbital coupling systems have attracted great attention in modern condensed matter physics. Many interesting phenomena have been found in recent theoretical and experimental works, such as the integer and fractional quantum Hall effect, topological band insulator, topological Mott insulator, and topological superconductor. We have investigated the topological phase transition on honeycomb lattice with third neighbor hooping by employing the cellular dynamical mean-field theory combining with the continuous-time Monte Carlo method. The non-trivial topological insulator can be found by observing the spin Chern number directly, and the effects of the third neighbor hopping and interaction are also discussed. Furthermore, we also provide the whole phase diagram for interaction, third neighbor hopping, and temperature. This work is supported by the Texas Center for Superconductivity at the University of Houston and by the Robert A. Welch Foundation under Grant No. E-1146.
Scaling and Topological Phase Transitions: Energy vs. Entropy
NASA Astrophysics Data System (ADS)
Wang, Yuting; Gulden, Tobias; Janas, Michael; Kamenev, Alex
The critical point of a topological phase transition is described by a conformal field theory. Finite-size corrections give rise to a scaling function away from criticality for both energy and entanglement entropy of the system. While in the past the scaling function for the usual von Neumann entropy was found to be equal for the trivial and the topological side of the transition, we find that the scaling functions for energy and Renyi entropy with α > 1 are different for the two sides. This provides an easy tool to distinguish between the trivial and topological phases near criticality.
Topological phase transition driven by a spatially periodic potential
NASA Astrophysics Data System (ADS)
Fu, Bo; Zheng, Huaixiu; Li, Qunxiang; Shi, Qinwei; Yang, Jinlong
2014-12-01
We propose a simple approach to realize a topological phase transition using a spatial periodic potential. As an example, we examine the electronic structures of HgTe/CdTe quantum wells, and demonstrate that their band structures can be effectively manipulated by the periodic potential. At a critical potential, we find that a conventional band insulator undergoes a topological phase transition into a quantum spin Hall system, which is characterized by an abrupt change of the spin Chern number and emerging edge states. Our proposal provides an interesting way to dynamically turn on or off topologically protected edge states for application in switching devices.
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.
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
Electron Topological Transitions of 31/2 Kind in Metals
NASA Astrophysics Data System (ADS)
Mikitik, G. P.; Sharlai, Yu. V.
2016-06-01
We consider electron topological transitions associated with certain points of band-contact lines in metals. These transitions are 31/2 kind according to the classification of Lifshits and are widespread in metals with inversion symmetry and a weak spin-orbit interaction. The 31/2 -order transitions can be detected with the magnetic susceptibility. As an example, we consider these transitions in graphite.
Observation of topological transitions in interacting quantum circuits
NASA Astrophysics Data System (ADS)
Roushan, Pedram
2015-03-01
Topology, despite its mathematical abstractness, often manifests itself in physics and plays a pivotal role in our understanding of natural phenomena. Notable examples include the discoveries of topological phases in condensed matter systems which have 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 inadequate for studying such properties at a fundamental level. Here, we employ the exquisite control afforded by superconducting quantum circuits to directly investigate topological properties of quantum spin systems. The essence of our approach is to infer local curvature by measuring the deflection of quantum trajectories topological properties are then revealed from a quantum analog of the Gauss-Bonnet theorem. We benchmark our technique by constructing the topological phase diagram of the celebrated Haldane model. The nature of the individual phases is revealed by visualizing their microscopic spin texture and evolution across the transition. Furthermore, we demonstrate the power of our method in studying the topology of interacting quantum systems, utilizing a novel qubit architecture which enables control over every term in a two-qubit Hamiltonian. We discovered an interaction-driven topological phase, whose emergence is understood by fully exploring the parameter-space of the Hamiltonian. Our work establishes a generalizable experimental platform to study fundamental aspects of topological phenomena in quantum systems. NSF Grants: DMR-0907039 and DMR-1029764.
Topology changing transitions in supersymmetric linear σ-models
NASA Astrophysics Data System (ADS)
Ryang, Shijong
1995-02-01
We analyze the two-dimensional supersymmetric linear σ-model with U(1) gauge symmetries that includes a Calabi-Yau phase and a possible Landau-Ginzburg phase. We demonstrate the topology changing transitions among the generic vacua of various linear σ-models. In the supersymmetric transition the determinantal contraction naturally arises.
NASA Astrophysics Data System (ADS)
Varney, Michael C. M.; Jenness, Nathan J.; Smalyukh, Ivan I.
2014-02-01
Despite the recent progress in physical control and manipulation of various condensed matter, atomic, and particle systems, including individual atoms and photons, our ability to control topological defects remains limited. Recently, controlled generation, spatial translation, and stretching of topological point and line defects have been achieved using laser tweezers and liquid crystals as model defect-hosting systems. However, many modes of manipulation remain hindered by limitations inherent to optical trapping. To overcome some of these limitations, we integrate holographic optical tweezers with a magnetic manipulation system, which enables fully holonomic manipulation of defects by means of optically and magnetically controllable colloids used as "handles" to transfer forces and torques to various liquid crystal defects. These colloidal handles are magnetically rotated around determined axes and are optically translated along three-dimensional pathways while mechanically attached to defects, which, combined with inducing spatially localized nematic-isotropic phase transitions, allow for geometrically unrestricted control of defects, including previously unrealized modes of noncontact manipulation, such as the twisting of disclination clusters. These manipulation capabilities may allow for probing topological constraints and the nature of defects in unprecedented ways, providing the foundation for a tabletop laboratory to expand our understanding of the role defects play in fields ranging from subatomic particle physics to early-universe cosmology.
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.
Disorder induced topological transition in graphene with random adatoms
NASA Astrophysics Data System (ADS)
Castro, Eduardo; López-Sancho, María; Vozmediano, María
2015-03-01
Abstract One of the first proposals for a two-dimensional topological insulator was made for graphene, the so called Kane-Mele model, but the very low spin-orbit coupling makes this phase undetectable. It has been suggested that randomly depositing certain heavy adatoms can amplify the effect by many orders, and that a dilute concentration should be enough to open a detectable topological gap. Still lacking, however, is a precise determination of the critical density of random adatoms based in the evolution of the topological index. Based in a finite size analysis of the topological index as a function of the density of randomly distributed adatoms, and also on the localization properties of the system accessed through the Lyapunov exponent, we not only determine the critical density but also establish the nature of this peculiar topological transition. EC acknowledge the financial support of FCT-Portugal through Grant No. EXPL/FIS-NAN/1720/2013.
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.
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.
Experimental observation of topological transitions in interacting multispin systems
NASA Astrophysics Data System (ADS)
Luo, Zhihuang; Lei, Chao; Li, Jun; Nie, Xinfang; Li, Zhaokai; Peng, Xinhua; Du, Jiangfeng
2016-05-01
Topologically ordered phase has emerged as one of most exciting concepts that not only broadens our understanding of phases of matter, but also has been found to have potential application in fault-tolerant quantum computation. The direct measurement of topological properties, however, is still a challenge, especially in interacting quantum system. Here we realize two to four spin one-dimensional Heisenberg chains using nuclear magnetic resonance simulators and observe interaction-induced topological transitions, where Berry curvature in the parameter space of Hamiltonian is probed by means of dynamical response and then the first Chern number is extracted by integrating the curvature over the closed surface. The utilized experimental method provides a powerful means to explore topological phenomena in quantum systems with many-body interactions.
Geometric phase for a neutral particle in the presence of a topological defect
NASA Astrophysics Data System (ADS)
Bakke, K.; Nascimento, J. R.; Furtado, C.
2008-09-01
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.
NASA Astrophysics Data System (ADS)
Narita, Kohei; Okada, Susumu
2016-04-01
We used density functional theory to study the geometric and electronic structure of dimerized and one-dimensionally polymerized corannulene as ultra-narrow graphene ribbons with corrugation and topological defects. Our computations reveal that the relative stability and electronic structure of dimerized and polymerized corannulene are sensitive to the intermolecular covalent networks. The energy gap between the highest occupied and lowest unoccupied states of corannulene dimers is narrower than that of isolated corannulene. The corannulene polymers are semiconductors with a direct energy gap of about 1 eV depending on intermolecular bonds. The polymers possess moderate mechanical stiffness having Young's moduli of 200 GPa.
NASA Astrophysics Data System (ADS)
Wu, Wei; Xu, Jing-Bo
2016-06-01
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.
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
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.
Approaching a topological phase transition in Majorana nanowires
NASA Astrophysics Data System (ADS)
Mishmash, Ryan V.; Aasen, David; Higginbotham, Andrew P.; Alicea, Jason
2016-06-01
Recent experiments have produced mounting evidence of Majorana zero modes in nanowire-superconductor hybrids. Signatures of an expected topological phase transition accompanying the onset of these modes nevertheless remain elusive. We investigate a fundamental question concerning this issue: Do well-formed Majorana modes necessarily entail a sharp phase transition in these setups? Assuming reasonable parameters, we argue that finite-size effects can dramatically smooth this putative transition into a crossover, even in systems large enough to support well-localized Majorana modes. We propose overcoming such finite-size effects by examining the behavior of low-lying excited states through tunneling spectroscopy. In particular, the excited-state energies exhibit characteristic field and density dependence, and scaling with system size, that expose an approaching topological phase transition. We suggest several experiments for extracting the predicted behavior. As a useful byproduct, the protocols also allow one to measure the wire's spin-orbit coupling directly in its superconducting environment.
Electron topological transitions of 3½ kind in beryllium
NASA Astrophysics Data System (ADS)
Mikitik, G. P.; Sharlai, Yu. V.
2015-12-01
An analysis of known experimental literature data on the temperature dependence of magnetic susceptibility of beryllium. It is shown that this dependence can be explained if we take into account that beryllium has an electron topological transition of 3½ kind near the Fermi level.
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.
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. PMID:26780658
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.
Phase transitions on random lattices: how random is topological disorder?
Barghathi, Hatem; Vojta, Thomas
2014-09-19
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)/(2d) 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. PMID:25279615
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.
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
Majorana Correlation as a Signature of a Topological Phase Transition
NASA Astrophysics Data System (ADS)
Nag, Amit; Sau, Jay D.
2015-03-01
Spin orbit coupled semiconductor nanowires in proximity to ordinary S wave superconductor exhibit a topological phase which supports Majorana fermions at the two ends of the nanowire. A signature of Majorana fermions would be a zero bias conductance peak. Indeed such a peak has been observed in recent experiments but at the same time alternate non topological mechanisms have been suggested to explain appearance of the zero bias peak. Here we demonstrate that the zero bias conductance peak from Majorana fermions must appear in a correlated way between the two ends. We analyze how this peculiarity can be used as a signature of the topological phase transition linked to the appearance of Majorana modes and thus can be used to experimentally distinguish between competing theoretical mechanisms. We acknowledge support from Physics Frontier Center and Maryland Startup Fund.
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.
Thermally-driven electronic topological transition in FeTi
Yang, F. C.; Munoz, Jorge A.; Hellman, O.; Mauger, L.; Lucas, M; Tracy, Sally J.; Stone, Matthew B; Abernathy, Douglas L; Xiao, Yuming; Fultz, B.
2016-01-01
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 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 M5- phonon mode, and an adiabatic electron-phonon interaction with an unusual temperature dependence.
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
Loss-induced topological transition of dispersion in metamaterials
NASA Astrophysics Data System (ADS)
Yu, Kun; Guo, Zhiwei; Jiang, Haitao; Chen, Hong
2016-05-01
Topological transition of dispersion in anisotropic metamaterials, in which isofrequency contour changes from a closed ellipsoid to an open hyperboloid, is usually realized by changing the sign of one component of permittivity (ɛ) or permeability (μ) from positive to negative. However, we show that topological transition of dispersion can occur by tuning the imaginary part of ɛ(μ) while fixing the real part of ɛ(μ). By adding different lumped resistors into two-dimensional transmission-line-based metamaterials, we just tune the imaginary part of μ at a fixed frequency. With the increase of loss, we measure the different emission patterns from a point source in the metamaterials to observe the changing process of isofrequency contours.
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.
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.
Novel Quantum Criticality in Two Dimensional Topological Phase transitions
NASA Astrophysics Data System (ADS)
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.
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
Topological-distance-dependent transition in flocks with binary interactions
NASA Astrophysics Data System (ADS)
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 n th 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 tc, 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.
Dirac point movement and topological phase transition in patterned graphene
NASA Astrophysics Data System (ADS)
Dvorak, Marc; Wu, Zhigang
2015-02-01
The honeycomb lattice of graphene is characterized by linear dispersion and pseudospin chirality of fermions on the Dirac cones. If lattice anisotropy is introduced, the Dirac cones stay intact but move in reciprocal space. Dirac point movement can lead to a topological transition from semimetal to semiconductor when two inequivalent Dirac points merge, an idea that has attracted significant research interest. However, such movement normally requires unrealistically high lattice anisotropy. Here we show that anisotropic defects can break the C3 symmetry of graphene, leading to Dirac point drift in the Brillouin zone. Additionally, the long-range order in periodically patterned graphene can induce intervalley scattering between two inequivalent Dirac points, resulting in a semimetal-to-insulator topological phase transition. The magnitude and direction of Dirac point drift are predicted analytically, which are consistent with our first-principles electronic structure calculations. Thus, periodically patterned graphene can be used to study the fascinating physics associated with Dirac point movement and the corresponding phase transition.The honeycomb lattice of graphene is characterized by linear dispersion and pseudospin chirality of fermions on the Dirac cones. If lattice anisotropy is introduced, the Dirac cones stay intact but move in reciprocal space. Dirac point movement can lead to a topological transition from semimetal to semiconductor when two inequivalent Dirac points merge, an idea that has attracted significant research interest. However, such movement normally requires unrealistically high lattice anisotropy. Here we show that anisotropic defects can break the C3 symmetry of graphene, leading to Dirac point drift in the Brillouin zone. Additionally, the long-range order in periodically patterned graphene can induce intervalley scattering between two inequivalent Dirac points, resulting in a semimetal-to-insulator topological phase transition. The
Galvanomagnetic phenomena in organic conductors under topological phase transition
NASA Astrophysics Data System (ADS)
Galbova, O.; Peschansky, V. G.; Stepanenko, D. I.
2015-07-01
The magnetoresistance of layered organic conductors with a multisheet Fermi surface (FS) is studied theoretically under conditions of the Lifshitz topological transition, where the FS topology may change in response to external effects acting on the conductor, such as pressure or doping with impurity atoms. Using as an example the Fermi surface consisting of a cylinder and two planes, which are slightly corrugated along the projection of the momentum pz=p n along the normal to the layers n, we analyze the magnetic-field dependence of the resistance and the Hall field in a strong external magnetic field H, where the cyclotron frequency ωc of the conduction electrons is much higher than their collision frequency 1/τ. In the immediate vicinity of the topological transition, where the distance between the different sheets of the FS becomes small, an electron can move from one sheet of the FS to another with the probability w due to the magnetic breakdown. In this case, a quadratic increase of the electric resistance across the layers with magnetic field, which occurs in the absence of the magnetic breakdown, is replaced by a linear dependence on H for w ≥γ=1 /ωcτ , and then reaches saturation for (1 -w )≤γ . The Hall field depends substantially on the probability of a magnetic breakdown, but in the case of ωcτ≫1 , its asymptote is independent of τ for all values of w. At w = 1, the quasi-planar sheets of the Fermi surface touch the corrugated cylinders, and under further perturbation acting on the conductor, there occurs a break of a flat sheet along the line of contact. As a result, separate sections of the flat FS sheet together with the cut halves of the corrugated cylinder form a new corrugated cylinder with the sign of charge carriers reversed. This is not the only scenario of the Lifshitz topological transition. Studies of the Hall effect will allow us to obtain further important information on the nature of changes in the topological structure of
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.
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
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. PMID:21173475
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.
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 transitions for lattice bosons in a magnetic field
Huber, Sebastian D.; Lindner, Netanel H.
2011-01-01
The Hall response provides an important characterization of strongly correlated phases of matter. We study the Hall conductivity of interacting bosons on a lattice subjected to a magnetic field. We show that for any density or interaction strength, the Hall conductivity is characterized by an integer. We find that the phase diagram is intersected by topological transitions between different values of this integer. These transitions lead to surprising effects, including sign reversal of the Hall conductivity and extensive regions in the phase diagram where it acquires a negative sign, which implies that flux flow is reversed in these regions—vortices there flow upstream. Our findings have immediate applications to a wide range of phenomena in condensed matter physics, which are effectively described in terms of lattice bosons. PMID:22109548
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.
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.
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 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
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.
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.
Schutter, J. de; Bruyninckx, H.; Dutre, S.; Geeter, J. de; Katupitiya, J.; Demey, S.; Lefebvre, T.
1999-12-01
This paper uses (linearized) Kalman filters to estimate first-order geometric parameters (i.e., orientation of contact normals and location of contact points) that occur in force-controlled compliant motions. The time variance of these parameters is also estimated. In addition, transitions between contact situations can be monitored. The contact between the manipulated object and its environment is general, i.e., multiple contacts can occur at the same time, and both the topology and the geometry of each single contact are arbitrary. The two major theoretical contributions are (1) the integration of the general contact model, developed previously by the authors, into a state-space form suitable for recursive processing; and (2) the use of the reciprocity constraint between ideal contact forces and motion freedoms as the measurement equation of the Kalman filter. The theory is illustrated by full 3-D experiments. The approach of this paper allows a breakthrough in the state of the art dominated by the classical, orthogonal contact models of Mason that can only cope with a limited (albeit important) subset of all possible contact situations.
Wu, Wei; Luo, Da-Wei; Xu, Jing-Bo
2014-06-28
We investigate the phenomenon of double sudden transitions in geometric quantum correlations for a system consisting of a bare qubit and a qubit locally coupled to its finite-temperature heat environment with an Ohmic spectrum in the framework of stochastic description. Moreover, we explore the possibility of protecting the geometric discord between the two qubits and prolonging the time during which the geometric discord remains constant by applying Bang-Bang pulses.
NASA Astrophysics Data System (ADS)
Saraiva, J.; Lousada, M.; Pina, P.; Bandeira, L.; Vieira, G.
2012-04-01
Polygonal terrain patterns commonly occur in periglacial regions of the Earth, where seasonal processes of freezing and thawing cause the soil to expand and contract, leading to the formation and growth of cracks. Understanding the formation of this type of networks on the Earth and tracing their evolution (including differentiating ages of formation) can provide us with many insights into the history of similar patterns on Mars, in whose surface they occupy vast extensions, most likely due to the presence of frozen water in the soil. Thus, analogue studies of this type of structure on the Earth are important. In this work, we describe the geometric and topologic characteristics of a number of networks of ice-wedge polygons occurring in a coastal valley, the Adventdalen, on the Norwegian archipelago of Svalbard, in the Arctic, at 78° N. The aim of the study is to try and find the similarities and differences between them and to relate those with factors such as soil characteristics and topography. Given the logistic problems in conducting a complete on site study of all those networks, spread out over many kilometers, the study was conducted through the analysis of remotely sensed imagery: 53 images (four-band RGB+NIR and 0.2 m/pixel of spatial resolution), acquired by the Norwegian Polar Institute in 2009 during their aerial photogrammetric campaign, were purchased and processed. They were orthorectified with an ASTER Global Digital Elevation Model (a product of METI and NASA). Polygonal networks were identified and digitized into a GIS. They occupy a total area of almost 10 km2. The areas covered by the individual networks studied range between 4x103 and 106 m2. Individual polygon sizes vary widely, from 6 to 7x103 m2, with an average of 300 m2. The variation is less pronounced for the networks that are most clearly traceable in the images (which reduces typical errors such as those that create large polygons occupying the area of several smaller ones that go
NASA Astrophysics Data System (ADS)
Jiang, Qi; Zeng, Huidan; Liu, Zhao; Ren, Jing; Chen, Guorong; Wang, Zhaofeng; Sun, Luyi; Zhao, Donghui
2013-09-01
Sodium borophosphate glasses exhibit intriguing mixed network former effect, with the nonlinear compositional dependence of their glass transition temperature as one of the most typical examples. In this paper, we establish the widely applicable topological constraint model of sodium borophosphate mixed network former glasses to explain the relationship between the internal structure and nonlinear changes of glass transition temperature. The application of glass topology network was discussed in detail in terms of the unified methodology for the quantitative distribution of each coordinated boron and phosphorus units and glass transition temperature dependence of atomic constraints. An accurate prediction of composition scaling of the glass transition temperature was obtained based on topological constraint model.
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.
Topological quantum phase transitions and edge states in spin-orbital coupled Fermi gases
Zhou, Tao; Gao, Yi; Wang, Z. D.
2014-01-01
We study superconducting states in the presence of spin-orbital coupling and Zeeman field. It is found that a phase transition from a Fulde-Ferrell-Larkin-Ovchinnikov state to the topological superconducting state occurs upon increasing the spin-orbital coupling. The nature of this topological phase transition and its critical property are investigated numerically. Physical properties of the topological superconducting phase are also explored. Moreover, the local density of states is calculated, through which the topological feature may be tested experimentally. PMID:24918901
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
2015-01-01
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. PMID:25882717
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
2015-01-01
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. PMID:25882717
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
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.
Liang; Ioannidis; Chatzis
2000-01-01
This article presents a versatile, rigorous, and efficient methodology for extracting various geometric and topological parameters of 3D discrete porous media. The new approach takes advantage of the morphological skeleton of the pore structure-a lower dimensional representation of the pore space akin to the topological "deformation retract". The skeleton is derived by a fully parallel thinning algorithm that fulfils two essential requirements: it generates a medial axis and preserves the connectivity of the pore space. Topological analysis is accomplished by classifying all skeleton points as node or link (branch) points according to the concept of lambda-adjacency in 3D discrete space. In this manner, node coordination number and link length distributions are directly obtained from the skeleton. Pore necks (throats) are identified through a search for minima in the hydraulic radius of individual pore space channels outlined by skeleton links. In addition to the determination of the size distribution of the constrictions (pore necks) that control nonwetting phase invasion, improved estimates of the distributions of effective hydraulic and electric conductivity of individual pore space channels are obtained. Furthermore, erection of planes at the location of pore necks results in partitioning of the pore space into its constituent pores. This enables the characterization of the pore space in terms of a pore volume distribution. The new methodology is illustrated by application to a regular cubic pore network and irregularly shaped 2D and 3D pore networks generated by stochastic simulation. In the latter case, important new results are obtained concerning the sensitivity of geometric and topological properties of the microstructure to the parameters of stochastic simulation, namely, the porosity and correlation function. It is found that model porous media reconstructed from the same porosity and correlation function can exhibit marked differences in geometry and
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
Topological defects from first-order gauge theory phase transitions
NASA Astrophysics Data System (ADS)
Donaire, M.
2006-12-01
We investigate the mechanism by which topological defects form in first-order phase transitions with a charged-order parameter. We show how thick superconductor vortices and heavy cosmic strings form by trapping of magnetic flux. In an external magnetic field, intermediate objects such as strips and membranes of magnetic flux and chains of single winding defects are produced. At non-zero temperature, a variety of spontaneous defects of different winding numbers arise. In cosmology, our results mean that the magnetic flux thermal fluctuations get trapped in a primordial multi-tension string network. The mechanism may also apply to the production of cosmic-like strings in brane collisions. In a thin type-I superconductor film, flux strips are found to be meta-stable while thick vortices are stable up to some critical value of the winding number which increases with the thickness of the film. In addition, a non-dissipative Josephson-like current is obtained across the strips of quantized magnetic flux.
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.
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
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.
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. PMID:26440940
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
Non-local Optical Topological Transitions and Critical States in Electromagnetic Metamaterials
NASA Astrophysics Data System (ADS)
Ishii, Satoshi; Narimanov, Evgenii
2015-12-01
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.
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.
Topology-driven quantum phase transitions in time-reversal-invariant anyonic quantum liquids
NASA Astrophysics Data System (ADS)
Gils, Charlotte; Trebst, Simon; Kitaev, Alexei; Ludwig, Andreas W. W.; Troyer, Matthias; Wang, Zhenghan
2009-11-01
Indistinguishable particles in two dimensions can be characterized by anyonic quantum statistics, which is more general than that of bosons or fermions. Anyons emerge as quasiparticles in fractional quantum Hall states and in certain frustrated quantum magnets. Quantum liquids of anyons show degenerate ground states, where the degeneracy depends on the topology of the underlying surface. Here, we present a new type of continuous quantum phase transition in such anyonic quantum liquids, which is driven by quantum fluctuations of the topology. The critical state connecting two anyonic liquids on surfaces with different topologies is reminiscent of the notion of a `quantum foam' with fluctuations on all length scales. This exotic quantum phase transition arises in a microscopic model of interacting anyons for which we present an exact solution in a linear geometry. We introduce an intuitive physical picture of this model that unifies string nets and loop gases, and provide a simple description of topological quantum phases and their phase transitions.
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.
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.
New geometric transition as origin of particle production in time-dependent backgrounds
NASA Astrophysics Data System (ADS)
Kim, Sang Pyo
2013-10-01
By extending the quantum evolution of a scalar field in time-dependent backgrounds to the complex-time plane and transporting the in-vacuum along a closed path, we argue that the geometric transition from the simple pole at infinity determines the multi-pair production depending on the winding number. We apply the geometric transition to Schwinger mechanism in the time-dependent vector potential for a constant electric field and to Gibbons-Hawking particle production in the planar coordinates of a de Sitter space.
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.
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.
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.
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.
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.
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.
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.
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
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.
Wigner-Poisson statistics of topological transitions in a Josephson junction.
Beenakker, C W J; Edge, J M; Dahlhaus, J P; Pikulin, D I; Mi, Shuo; Wimmer, M
2013-07-19
The phase-dependent bound states (Andreev levels) of a Josephson junction can cross at the Fermi level if the superconducting ground state switches between even and odd fermion parity. The level crossing is topologically protected, in the absence of time-reversal and spin-rotation symmetry, irrespective of whether the superconductor itself is topologically trivial or not. We develop a statistical theory of these topological transitions in an N-mode quantum-dot Josephson junction by associating the Andreev level crossings with the real eigenvalues of a random non-Hermitian matrix. The number of topological transitions in a 2π phase interval scales as √[N], and their spacing distribution is a hybrid of the Wigner and Poisson distributions of random-matrix theory. PMID:23909353
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.
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.
NASA Astrophysics Data System (ADS)
Suramlishvili, Nugzar; Eggers, Jens; Fontelos, Marco
2014-11-01
We are concerned with singularities of the shock fronts of converging perturbed shock waves. Our considerations are based on Whitham's theory of geometrical shock dynamics. The recently developed method of local analysis is applied in order to determine generic singularities. In this case the solutions of partial differential equations describing the geometry of the shock fronts are presented as families of smooth maps with state variables and the set of control parameters dependent on Mach number, time and initial conditions. The space of control parameters of the singularities is analysed, the unfoldings describing the deformations of the canonical germs of shock front singularities are found and corresponding bifurcation diagrams are constructed. Research is supported by the Leverhulme Trust, Grant Number RPG-2012-568.
Cheng, Bingqing; Ngan, Alfonso H W
2013-04-28
Molecular dynamics simulations of small Cu nanoparticles using three different interatomic potentials at rising temperature indicate that small nanoparticles can undergo solid-solid structural transitions through a direct geometrical conversion route. The direct geometrical conversion can happen for cuboctahedral nanoparticles, which turn into an icosahedra shape: one diagonal of the square faces contracts, and the faces are folded along the diagonal to give rise to two equilateral triangles. The transition is a kinetic process that cannot be fully explained through an energetic point of view. It has low activation energy and fast reaction time in the simulations. The transition mechanism is via the transmission of shear waves initiated from the particle surface and does not involve dislocation activity. PMID:23635145
NASA Astrophysics Data System (ADS)
Cheng, Bingqing; Ngan, Alfonso H. W.
2013-04-01
Molecular dynamics simulations of small Cu nanoparticles using three different interatomic potentials at rising temperature indicate that small nanoparticles can undergo solid-solid structural transitions through a direct geometrical conversion route. The direct geometrical conversion can happen for cuboctahedral nanoparticles, which turn into an icosahedra shape: one diagonal of the square faces contracts, and the faces are folded along the diagonal to give rise to two equilateral triangles. The transition is a kinetic process that cannot be fully explained through an energetic point of view. It has low activation energy and fast reaction time in the simulations. The transition mechanism is via the transmission of shear waves initiated from the particle surface and does not involve dislocation activity.
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.
Pressure-induced phase transition in Bi2Se3 at 3 GPa: electronic topological transition or not?
Bera, Achintya; Pal, Koushik; Muthu, D V S; Waghmare, U V; Sood, A K
2016-03-16
In recent years, a low pressure transition around P3 GPa exhibited by the A2B3-type 3D topological insulators is attributed to an electronic topological transition (ETT) for which there is no direct evidence either from theory or experiments. We address this phase transition and other transitions at higher pressure in bismuth selenide (Bi2Se3) using Raman spectroscopy at pressure up to 26.2 GPa. We see clear Raman signatures of an isostructural phase transition at P2.4 GPa followed by structural transitions at ∼ 10 GPa and 16 GPa. First-principles calculations reveal anomalously sharp changes in the structural parameters like the internal angle of the rhombohedral unit cell with a minimum in the c/a ratio near P3 GPa. While our calculations reveal the associated anomalies in vibrational frequencies and electronic bandgap, the calculated Z2 invariant and Dirac conical surface electronic structure remain unchanged, showing that there is no change in the electronic topology at the lowest pressure transition. PMID:26881905
Pressure-induced phase transition in Bi2Se3 at 3 GPa: electronic topological transition or not?
NASA Astrophysics Data System (ADS)
Bera, Achintya; Pal, Koushik; Muthu, D. V. S.; Waghmare, U. V.; Sood, A. K.
2016-03-01
In recent years, a low pressure transition around P∼ 3 GPa exhibited by the {{A}2}{{B}3} -type 3D topological insulators is attributed to an electronic topological transition (ETT) for which there is no direct evidence either from theory or experiments. We address this phase transition and other transitions at higher pressure in bismuth selenide (Bi2Se3) using Raman spectroscopy at pressure up to 26.2 GPa. We see clear Raman signatures of an isostructural phase transition at P∼ 2.4 GPa followed by structural transitions at ∼10 GPa and 16 GPa. First-principles calculations reveal anomalously sharp changes in the structural parameters like the internal angle of the rhombohedral unit cell with a minimum in the c/a ratio near P∼ 3 GPa. While our calculations reveal the associated anomalies in vibrational frequencies and electronic bandgap, the calculated {{{Z}}2} invariant and Dirac conical surface electronic structure remain unchanged, showing that there is no change in the electronic topology at the lowest pressure transition.
Disorder-induced structural transitions in topological insulating Ge-Sb-Te compounds
NASA Astrophysics Data System (ADS)
Kim, Jeongwoo; Jhi, Seung-Hoon
2015-05-01
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 Ge2Sb2Te5 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.
Topological phase transition of a fractal spin system: The relevance of the network complexity
NASA Astrophysics Data System (ADS)
Torres, Felipe; Rogan, José; Kiwi, Miguel; Valdivia, Juan Alejandro
2016-05-01
A new type of collective excitations, due to the topology of a complex random network that can be characterized by a fractal dimension DF, is investigated. We show analytically that these excitations generate phase transitions due to the non-periodic topology of the DF > 1 complex network. An Ising system, with long range interactions, is studied in detail to support the claim. The analytic treatment is possible because the evaluation of the partition function can be decomposed into closed factor loops, in spite of the architectural complexity. The removal of the infrared divergences leads to an unconventional phase transition, with spin correlations that are robust against thermal fluctuations.
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
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.
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.
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.
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
Observation of a transition from a topologically ordered to a spontaneously broken symmetry phase
NASA Astrophysics Data System (ADS)
Samkharadze, N.; Schreiber, K. A.; Gardner, G. C.; Manfra, M. J.; Fradkin, E.; Csáthy, G. A.
2016-02-01
Until the late 1980s, phases of matter were understood in terms of Landau’s symmetry-breaking theory. Following the discovery of the quantum Hall effect, the introduction of a second class of phases, those with topological order, was necessary. Phase transitions within the first class of phases involve a change in symmetry, whereas those between topological phases require a change in topological order. However, in rare cases, transitions may occur between the two classes, in which the vanishing of the topological order is accompanied by the emergence of a broken symmetry. Here, we report the existence of such a transition in a two-dimensional electron gas hosted by a GaAs/AlGaAs crystal. When tuned by hydrostatic pressure, the ν = 5/2 fractional quantum Hall state, believed to be a prototypical non-Abelian topological phase, gives way to a quantum Hall nematic phase. Remarkably, this nematic phase develops spontaneously, in the absence of any externally applied symmetry-breaking fields.
Thick-brane solutions and topology change transition on black hole backgrounds
Czinner, Viktor G.
2010-07-15
We consider static, axisymmetric, thick-brane solutions on higher-dimensional, spherically symmetric black hole backgrounds. It was found recently [V. G. Czinner and A. Flachi, Phys. Rev. D 80, 104017 (2009).], that in cases in which the thick brane has more than two spacelike dimensions, perturbative approaches break down around the corresponding thin solutions for Minkowski-type topologies. This behavior is a consequence of the fact that thin solutions are not smooth at the axis, and for a general discussion of possible phase transitions in the system, one needs to use a nonperturbative approach. In the present paper, we provide an exact, numerical solution of the problem both for black hole- and Minkowski-type topologies with an arbitrary number of brane and bulk dimensions. We also illustrate a topology change transition in the system for a five-dimensional brane embedded in a six-dimensional bulk.
Khirevich, Siarhei; Höltzel, Alexandra; Seidel-Morgenstern, Andreas; Tallarek, Ulrich
2012-11-01
At low column-to-particle diameter (or aspect) ratio (d(c)/d(p)) the kinetic column performance is dominated by the transcolumn disorder that arises from the morphological gradient between the more homogeneous, looser packed wall region and the random, dense core. For a systematic analysis of this morphology-dispersion relation we computer-generated a set of confined sphere packings varying three parameters: aspect ratio (d(c)/d(p)=10-30), bed porosity (ɛ=0.40-0.46), and packing homogeneity. Plate height curves were received from simulation of hydrodynamic dispersion in the packings over a wide range of reduced velocities (v=0.5-500). Geometrical measures derived from radial porosity and velocity profiles were insufficient as morphological descriptors of the plate height data. After Voronoi tessellation of the packings, topological information was obtained from the statistical moments of the free Voronoi volume (V(free)) distributions. The radial profile of the standard deviation of the V(free) distributions in the form of an integral measure was identified as a quantitative scalar measure for the transcolumn disorder. The first morphology-dispersion correlation for confined sphere packings deepens our understanding of how the packing microstructure determines the kinetic column performance. PMID:23000179
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.
2015-01-01
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).
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
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
Role of Topological Defects in the Phase Transition of the Three-Dimensional Heisenberg Model.
NASA Astrophysics Data System (ADS)
Lau, Manhot
The role of topological point defects (hedgehogs) in the phase transition of the classical Heisenberg model in three dimensions is investigated by using Monte Carlo simulations. Simulations of the behavior of the defects near the phase transition show that the number density of defects increases sharply and defect pairs with separations comparable to the sample size begin to appear as the temperature is increased through the transition temperature. In simulations in a restricted ensemble in which spin configurations containing defects are not allowed, the system appears to remain ordered at all temperatures. Simulations in which the spin-spin interaction is set equal to zero and the number density of defects is controlled by varying a 'chemical potential' term indicate that the system is ordered if the number density of defect pairs is sufficiently small. These results show that topological defects play a crucial role in the three-dimensional Heisenberg transition in the sense that configurations containing defect pairs are necessary for the transition from the ferromagnetic to paramagnetic phase to occur. Such a conclusion is also consistent with a Renormalization Group study of the O(n) model, which suggests that topological defects should be explicitly taken into account for a correct description of the critical behavior in models including the three-dimensional Heisenberg model.
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.
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.
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.
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.
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.
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
Tunable Topological Phononic Crystals
NASA Astrophysics Data System (ADS)
Chen, Ze-Guo; Wu, Ying
2016-05-01
Topological insulators first observed in electronic systems have inspired many analogues in photonic and phononic crystals in which remarkable one-way propagation edge states are supported by topologically nontrivial band gaps. Such band gaps can be achieved by breaking the time-reversal symmetry to lift the degeneracy associated with Dirac cones at the corners of the Brillouin zone. Here, we report on our construction of a phononic crystal exhibiting a Dirac-like cone in the Brillouin zone center. We demonstrate that simultaneously breaking the time-reversal symmetry and altering the geometric size of the unit cell result in a topological transition that we verify by the Chern number calculation and edge-mode analysis. We develop a complete model based on the tight binding to uncover the physical mechanisms of the topological transition. Both the model and numerical simulations show that the topology of the band gap is tunable by varying both the velocity field and the geometric size; such tunability may dramatically enrich the design and use of acoustic topological insulators.
Topology of the postperovskite phase transition and mantle dynamics
Monnereau, Marc; Yuen, David A.
2007-01-01
The postperovskite (ppv) phase transition occurs in the deep mantle close to the core–mantle boundary (CMB). For this reason, we must include in the dynamical considerations both the Clapeyron slope and the temperature intercept, Tint, which is the temperature of the phase transition at the CMB pressure. For a CMB temperature greater than Tint, there is a double crossing of the phase boundary by the geotherms associated with the descending flow. We have found a great sensitivity of the shape of the ppv surface due to the CMB from variations of various parameters such as the amount of internal heating, the Clapeyron slope, and the temperature intercept. Three-dimensional spherical models of mantle convection that can satisfy the seismological constraints depend on the Clapeyron slope. At moderate value, 8 MPa/K, the best fit is found with a core heat flow amounting for 40% of the total heat budget (≈15 TW), whereas for 10 MPa/K the agreement is for a lower core heat flow (20%, ≈7.5 TW). In all cases, these solutions correspond to a temperature intercept 200 K lower than the CMB temperature. These models have holes of perovskite adjacent to ppv in regions of hot upwellings. PMID:17483485
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)
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.
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.
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.
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.
Prediction of topological phase transition in X2-SiGe monolayers.
Juarez-Mosqueda, Rosalba; Ma, Yandong; Heine, Thomas
2016-02-01
Quantum spin Hall (QSH) insulators exhibit a bulk insulting gap and metallic edge states characterized by nontrivial topology. Here, we used first-principles calculations to investigate the electronic and topological properties of halogenated silicon germanide (X2-SiGe, with X = F, Cl, and Br) monolayers, which we found to be trivial semiconductors with energy band gaps ranging from 500 meV to 900 meV. Interestingly, we found that under 8% strain, X2-SiGe monolayers behave as QSH insulators with global band gaps between 53 meV and 123 meV. The underlying mechanism of the topological phase transition is the strain-induced s-p band inversion. The nontrivial topological features for the strained X2-SiGe monolayers were further confirmed by the presence of topologically protected edge states that form a single Dirac cone in the middle of the bulk band gaps. Therefore, our results reveal that this new family of QSH insulators is promising for room temperature applications in spintronics and quantum computation devices. PMID:26758453
A geometric entropy detecting the Erdös-Rényi phase transition
NASA Astrophysics Data System (ADS)
Franzosi, Roberto; Felice, Domenico; Mancini, Stefano; Pettini, Marco
2015-07-01
We propose a method to associate a differentiable Riemannian manifold to a generic many-degrees-of-freedom discrete system which is not described by a Hamiltonian function. Then, in analogy with classical statistical mechanics, we introduce an entropy as the logarithm of the volume of the manifold. The geometric entropy so defined is able to detect a paradigmatic phase transition occurring in random graphs theory: the appearance of the “giant component” according to the Erdös-Rényi theorem.
Temperature-driven transition from a semiconductor to a topological insulator
NASA Astrophysics Data System (ADS)
Wiedmann, Steffen; Jost, Andreas; Thienel, Cornelius; Brüne, Christoph; Leubner, Philipp; Buhmann, Hartmut; Molenkamp, Laurens W.; Maan, J. C.; Zeitler, Uli
2015-05-01
We report on a temperature-induced transition from a conventional semiconductor to a two-dimensional topological insulator investigated by means of magnetotransport experiments on HgTe/CdTe quantum well structures. At low temperatures, we are in the regime of the quantum spin Hall effect and observe an ambipolar quantized Hall resistance by tuning the Fermi energy through the bulk band gap. At room temperature, we find electron and hole conduction that can be described by a classical two-carrier model. Above the onset of quantized magnetotransport at low temperature, we observe a pronounced linear magnetoresistance that develops from a classical quadratic low-field magnetoresistance if electrons and holes coexist. Temperature-dependent bulk band structure calculations predict a transition from a conventional semiconductor to a topological insulator in the regime where the linear magnetoresistance occurs.
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
Realizing a topological transition in a non-Hermitian quantum walk with circuit QED
NASA Astrophysics Data System (ADS)
Huang, Yizhou; Yin, Zhang-qi; Yang, W. L.
2016-08-01
We extend the non-Hermitian one-dimensional quantum walk model [Phys. Rev. Lett. 102, 065703 (2009), 10.1103/PhysRevLett.102.065703] by taking the dephasing effect into account. We prove that the feature of topological transition does not change even when dephasing between the sites within units is present. The potential experimental observation of our theoretical results in the circuit QED system consisting of superconducting qubit coupled to a superconducting resonator mode is discussed and numerically simulated. The results clearly show a topological transition in quantum walk and display the robustness of such a system to the decay and dephasing of qubits. We also discuss how to extend this model to higher dimension in the circuit QED system.
Topological phase transitions on a triangular optical lattice with non-Abelian gauge fields
NASA Astrophysics Data System (ADS)
Iskin, M.
2016-03-01
We study the mean-field BCS-BEC evolution of a uniform Fermi gas on a single-band triangular lattice and construct its ground-state phase diagrams, showing a wealth of topological quantum phase transitions between gapped and gapless superfluids that are induced by the interplay of an out-of-plane Zeeman field and a generic non-Abelian gauge field.
A geometric frequency-magnitude scaling transition: Measuring b = 1.5 for large earthquakes
NASA Astrophysics Data System (ADS)
Yoder, Mark R.; Holliday, James R.; Turcotte, Donald L.; Rundle, John B.
2012-04-01
We identify two distinct scaling regimes in the frequency-magnitude distribution of global earthquakes. Specifically, we measure the scaling exponent b = 1.0 for "small" earthquakes with 5.5 < m < 7.6 and b = 1.5 for "large" earthquakes with 7.6 < m < 9.0. This transition at mt = 7.6, can be explained by geometric constraints on the rupture. In conjunction with supporting literature, this corroborates theories in favor of fully self-similar and magnitude independent earthquake physics. We also show that the scaling behavior and abrupt transition between the scaling regimes imply that earthquake ruptures have compact shapes and smooth rupture-fronts.
Li, Xin; Zou, Qi; Ågren, Hans
2015-08-27
We present a density functional theory study on the thermal bistability of a number of photochromic diarylethenes, with emphasis on the free energy barrier of the ground-state ring-opening process. We found that the free energy barrier is correlated with the geometrical and vibrational character of the transition state, in particular the distance between the two reactive carbon atoms, the out-of-plane angles of the methyl groups at the reactive carbon atoms, and the imaginary vibrational frequency. Based on these relationships we propose a linear fitting expression for the free energy barrier in terms of the three aforementioned transition-state quantities and obtained a correlation coefficient of R(2) = 0.971. In this way quantum chemical calculations may provide insight and structure-property relationships, which can be applied in the development of novel photochromic materials. PMID:26267793
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
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.
NASA Astrophysics Data System (ADS)
Wang, Ya-Ping; Ji, Wei-Xiao; Zhang, Chang-Wen; Li, Ping; Li, Feng; Ren, Miao-Juan; Chen, Xin-Lian; Yuan, Min; Wang, Pei-Ji
2016-02-01
Discovery of two-dimensional (2D) topological insulator such as group-V films initiates challenges in exploring exotic quantum states in low dimensions. Here, we perform first-principles calculations to study the geometric and electronic properties in 2D arsenene monolayer with hydrogenation (HAsH). We predict a new σ-type Dirac cone related to the px,y orbitals of As atoms in HAsH, dependent on in-plane tensile strain. Noticeably, the spin-orbit coupling (SOC) opens a quantum spin Hall (QSH) gap of 193 meV at the Dirac cone. A single pair of topologically protected helical edge states is established for the edges, and its QSH phase is confirmed with topological invariant Z2 = 1. We also propose a 2D quantum well (QW) encapsulating HAsH with the h-BN sheet on each side, which harbors a nontrivial QSH state with the Dirac cone lying within the band gap of cladding BN substrate. These findings provide a promising innovative platform for QSH device design and fabrication operating at room temperature.
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
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
Domain-size heterogeneity in the Ising model: Geometrical and thermal transitions.
de la Rocha, André R; de Oliveira, Paulo Murilo C; Arenzon, Jeferson J
2015-04-01
A measure of cluster size heterogeneity (H), introduced by Lee et al. [Phys. Rev. E 84, 020101 (2011)] in the context of explosive percolation, was recently applied to random percolation and to domains of parallel spins in the Ising and Potts models. It is defined as the average number of different domain sizes in a given configuration and a new exponent was introduced to explain its scaling with the size of the system. In thermal spin models, however, physical clusters take into account the temperature-dependent correlation between neighboring spins and encode the critical properties of the phase transition. We here extend the measure of H to these clusters and, moreover, present new results for the geometric domains for both d=2 and 3. We show that the heterogeneity associated with geometric domains has a previously unnoticed double peak, thus being able to detect both the thermal and percolative transitions. An alternative interpretation for the scaling of H that does not introduce a new exponent is also proposed. PMID:25974445
Domain-size heterogeneity in the Ising model: Geometrical and thermal transitions
NASA Astrophysics Data System (ADS)
de la Rocha, André R.; de Oliveira, Paulo Murilo C.; Arenzon, Jeferson J.
2015-04-01
A measure of cluster size heterogeneity (H ), introduced by Lee et al. [Phys. Rev. E 84, 020101 (2011), 10.1103/PhysRevE.84.020101] in the context of explosive percolation, was recently applied to random percolation and to domains of parallel spins in the Ising and Potts models. It is defined as the average number of different domain sizes in a given configuration and a new exponent was introduced to explain its scaling with the size of the system. In thermal spin models, however, physical clusters take into account the temperature-dependent correlation between neighboring spins and encode the critical properties of the phase transition. We here extend the measure of H to these clusters and, moreover, present new results for the geometric domains for both d =2 and 3. We show that the heterogeneity associated with geometric domains has a previously unnoticed double peak, thus being able to detect both the thermal and percolative transitions. An alternative interpretation for the scaling of H that does not introduce a new exponent is also proposed.
NASA Astrophysics Data System (ADS)
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.
2015-06-01
Three-dimensional Dirac semimetals (DSMs) are materials that have massless Dirac 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 in materials that exhibit both superconductivity and topological surface states. Here we show that 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 Z2=-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 Z2 invariant.
NASA Astrophysics Data System (ADS)
Lau, Man-Hot; Dasgupta, Chandan
1989-04-01
The role of topological point defects (hedgehogs) in the phase transition of the classical Heisenberg model in three dimensions is investigated by using Monte Carlo simulations. Simulations of the behavior of the defects near the phase transition show that the number density of defects increases sharply and defect pairs with separations comparable to the sample size begin to appear as the temperature is increased through the transition temperature. In simulations in a restricted ensemble in which spin configurations containing defects are not allowed, the system appears to remain ordered at all temperatures. Simulations in which the spin-spin interaction is set equal to zero and the number density of defects is controlled by varying a ``chemical potential'' term indicate that the system is ordered if the number density of defect pairs is sufficiently small. These results show that topological defects play a crucial role in the three-dimensional Heisenberg transition in the sense that configurations containing defect pairs are necessary for the transition from the ferromagnetic to the paramagnetic phase to occur.
Topological black holes in pure Gauss-Bonnet gravity and phase transitions
NASA Astrophysics Data System (ADS)
Aránguiz, Ligeia; Kuang, Xiao-Mei; Miskovic, Olivera
2016-03-01
We study charged, static, topological black holes in pure Gauss-Bonnet gravity in asymptotically AdS space. As in general relativity, the theory possesses a unique nondegenerate AdS vacuum. It also admits charged black hole solutions which asymptotically behave as the Reissner-Nordström AdS black hole. We discuss black hole thermodynamics of these black holes. Then we study phase transitions in a dual quantum field theory in four dimensions, with the Stückelberg scalar field as an order parameter. We find in the probe limit that the black hole can develop hair below some critical temperature, which suggests a phase transition. Depending on the scalar coupling constants, the phase transition can be first or second order. Analysis of the free energy reveals that, comparing the two solutions, the hairy state is energetically favorable, thus a phase transition will occur in a dual field theory.
Autore, Marta; Giorgianni, Flavio; D' Apuzzo, Fausto; Di Gaspare, Alessandra; Lo Vecchio, Irene; Brahlek, Matthew; Koirala, Nikesh; Oh, Seongshik; Schade, Urlich; Ortolani, Michele; Lupi, Stefano
2016-02-28
A 3D Topological Insulator (TI) is an intrinsically stratified electronic material characterized by an insulating bulk and Dirac free electrons at the interface with vacuum or another dielectric. In this paper, we investigate, through terahertz (THz) spectroscopy, the plasmon excitation of Dirac electrons on thin films of (Bi1-xInx)2Se3 TI patterned in the form of a micro-ribbon array, across a Quantum Phase Transition (QPT) from the topological to a trivial insulating phase. The latter is achieved by In doping onto the Bi-site and is characterized by massive electrons at the surface. While the plasmon frequency is nearly independent of In content, the plasmon width undergoes a sudden broadening across the QPT, perfectly mirroring the single particle (free electron) behavior as measured on the same films. This strongly suggests that the topological protection from backscattering characterizing Dirac electrons in the topological phase extends also to their plasmon excitations. PMID:26852877
NASA Astrophysics Data System (ADS)
Autore, Marta; Giorgianni, Flavio; D'Apuzzo, Fausto; di Gaspare, Alessandra; Lo Vecchio, Irene; Brahlek, Matthew; Koirala, Nikesh; Oh, Seongshik; Schade, Urlich; Ortolani, Michele; Lupi, Stefano
2016-02-01
A 3D Topological Insulator (TI) is an intrinsically stratified electronic material characterized by an insulating bulk and Dirac free electrons at the interface with vacuum or another dielectric. In this paper, we investigate, through terahertz (THz) spectroscopy, the plasmon excitation of Dirac electrons on thin films of (Bi1-xInx)2Se3 TI patterned in the form of a micro-ribbon array, across a Quantum Phase Transition (QPT) from the topological to a trivial insulating phase. The latter is achieved by In doping onto the Bi-site and is characterized by massive electrons at the surface. While the plasmon frequency is nearly independent of In content, the plasmon width undergoes a sudden broadening across the QPT, perfectly mirroring the single particle (free electron) behavior as measured on the same films. This strongly suggests that the topological protection from backscattering characterizing Dirac electrons in the topological phase extends also to their plasmon excitations.A 3D Topological Insulator (TI) is an intrinsically stratified electronic material characterized by an insulating bulk and Dirac free electrons at the interface with vacuum or another dielectric. In this paper, we investigate, through terahertz (THz) spectroscopy, the plasmon excitation of Dirac electrons on thin films of (Bi1-xInx)2Se3 TI patterned in the form of a micro-ribbon array, across a Quantum Phase Transition (QPT) from the topological to a trivial insulating phase. The latter is achieved by In doping onto the Bi-site and is characterized by massive electrons at the surface. While the plasmon frequency is nearly independent of In content, the plasmon width undergoes a sudden broadening across the QPT, perfectly mirroring the single particle (free electron) behavior as measured on the same films. This strongly suggests that the topological protection from backscattering characterizing Dirac electrons in the topological phase extends also to their plasmon excitations. Electronic
Topology-changing first order phase transition and the dynamics of flavor
Albash, Tameem; Filev, Veselin; Johnson, Clifford V.; Kundu, Arnab
2008-03-15
In studying the dynamics of large N{sub c}, SU(N{sub c}) gauge theory at finite temperature with fundamental quark flavors in the quenched approximation, we observe a first order phase transition. A quark condensate forms at finite quark mass, and the value of the condensate varies smoothly with the quark mass for generic regions in parameter space. At a particular value of the quark mass, there is a finite discontinuity in the condensate's vacuum expectation value, corresponding to a first order phase transition. We study the gauge theory via its string dual formulation using the AdS/CFT conjecture, the string dual being the near-horizon geometry of N{sub c} D3-branes at finite temperature, AdS{sub 5}-SchwarzschildxS{sup 5}, probed by a D7-brane. The D7-brane has topology R{sup 4}xS{sup 3}xS{sup 1} and allowed solutions correspond to either the S{sup 3} or the S{sup 1} shrinking away in the interior of the geometry. The phase transition represents a jump between branches of solutions having these two distinct D-brane topologies. The transition also appears in the meson spectrum.
Kim, Jinsu; Lee, Kyujoon; Takabatake, Toshiro; Kim, Hanchul; Kim, Miyoung; Jung, Myung-Hwa
2015-01-01
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. PMID:25974047
Kim, Jinsu; Lee, Kyujoon; Takabatake, Toshiro; Kim, Hanchul; Kim, Miyoung; Jung, Myung-Hwa
2015-01-01
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. PMID:25974047
NASA Astrophysics Data System (ADS)
Setiawan, F.; Sengupta, Krishnendu; Spielman, Ian; Sau, Jay
2015-03-01
We theoretically study the dynamics of topological phase transition in one-dimensional (1D) spin-orbit coupled (SOC) Fermi gases with attractive interaction as a means of detecting the phase transition. The transition from conventional (trivial) superfluid to topological superfluid phase happens as the intensity of the Raman lasers (Zeeman field) is ramped above the critical value. To minimize effect of heating, we propose to ramp from a conventional superfluid phase through the topological phase transition and back. We calculate the momentum distribution of the atoms after the ramp by solving the time-dependent Bogoliubov-de Gennes (BdG) equations self-consistently with the initial state of the Fermi gas being the thermal state. We show that the phase transition can be detected by measuring the scaling of the momentum distribution with the ramp rate. This work is supported by NSF-JQI-PFC and ARO-Atomtronics-MURI.
NASA Astrophysics Data System (ADS)
Ma, Fengxian; Gao, Guoping; Jiao, Yalong; Gu, Yuantong; Bilic, Ante; Zhang, Haijun; Chen, Zhongfang; Du, Aijun
2016-02-01
Single layered transition metal dichalcogenides have attracted tremendous research interest due to their structural phase diversities. By using a global optimization approach, we have discovered a new phase of transition metal dichalcogenides (labelled as T''), which is confirmed to be energetically, dynamically and kinetically stable by our first-principles calculations. The new T'' MoS2 phase exhibits an intrinsic quantum spin Hall (QSH) effect with a nontrivial gap as large as 0.42 eV, suggesting that a two-dimensional (2D) topological insulator can be achieved at room temperature. Most interestingly, there is a topological phase transition simply driven by a small tensile strain of up to 2%. Furthermore, all the known MX2 (M = Mo or W; X = S, Se or Te) monolayers in the new T'' phase unambiguously display similar band topologies and strain controlled topological phase transitions. Our findings greatly enrich the 2D families of transition metal dichalcogenides and offer a feasible way to control the electronic states of 2D topological insulators for the fabrication of high-speed spintronics devices.Single layered transition metal dichalcogenides have attracted tremendous research interest due to their structural phase diversities. By using a global optimization approach, we have discovered a new phase of transition metal dichalcogenides (labelled as T''), which is confirmed to be energetically, dynamically and kinetically stable by our first-principles calculations. The new T'' MoS2 phase exhibits an intrinsic quantum spin Hall (QSH) effect with a nontrivial gap as large as 0.42 eV, suggesting that a two-dimensional (2D) topological insulator can be achieved at room temperature. Most interestingly, there is a topological phase transition simply driven by a small tensile strain of up to 2%. Furthermore, all the known MX2 (M = Mo or W; X = S, Se or Te) monolayers in the new T'' phase unambiguously display similar band topologies and strain controlled topological
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.
Geometric-phase atom optics and interferometry
NASA Astrophysics Data System (ADS)
Zygelman, B.
2015-10-01
We illustrate how geometric gauge forces and topological phase effects emerge in atomic and molecular systems without employing assumptions that rely on adiabaticity. We show how geometric magnetism may be harnessed to engineer novel quantum devices including a velocity sieve, a component in mass spectrometers, for neutral atoms. We introduce and outline a possible experimental setup that demonstrates topological interferometry for neutral spin-1/2 systems. For that two-level system, we study the transition from Abelian to non-Abelian behavior and explore its relation to the molecular Aharonov-Bohm effect.
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
Structural properties of Sb2S3 under pressure: evidence of an electronic topological transition
NASA Astrophysics Data System (ADS)
Efthimiopoulos, Ilias; Buchan, Cienna; Wang, Yuejian
2016-04-01
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.
Topological transition and edge states in HgTe quantum wells from first principles
NASA Astrophysics Data System (ADS)
Küfner, Sebastian; Bechstedt, Friedhelm
2014-05-01
(HgTe)N(CdTe)M(110) and (001) superlattices are studied by means of ab initio calculations versus the thickness of the HgTe quantum wells (QWs). The used approximate quasiparticle theory including spin-orbit coupling (SOC) gives the correct band ordering, band gap, and SOC splitting for bulk HgTe and CdTe. The resulting band discontinuities indicate confinement also for occupied states. In agreement with earlier k .p calculations and experiments we find a topological transition from the topological nontrivial quantum spin Hall state into a trivial insulator with decreasing QW thickness. The spatial localization near the interfaces and the spin polarization are demonstrated for the edge states for QWs with thicknesses near the critical one. They do not depend on the QW orientation and are therefore topologically protected. Below the critical QW thickness, the trivial insulator exhibits drastic confinement effects with a significant gap opening. We show that the inclusion of inversion symmetry, the nonaxial rotation symmetry of the QWs, and the real QW barriers lead to some agreement but also significant deviations from the predictions within toy models. The deviations concern the critical thickness, the number and localization of edge states, and the possibility to find QW subbands between edge states.
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.
NASA Astrophysics Data System (ADS)
Liu, Jin Hua; Wang, Hai Tao
2015-10-01
Topological quantum phase transitions are numerically investigated in a spin-1/2 dimerized and frustrated Heisenberg chain by using infinite matrix product state representation with the infinite time evolving block decimation method. Quantum fidelity approach is employed to detect the degenerate ground states and quantum phase transitions. By calculating the long-range string order parameters, we find two topological Haldane phases characterized by two long-range string orders. Also, continuous and discontinuous behaviors of von Neumann entropy show that phase transitions between two topological Haldane phases are topologically continuous and discontinuous quantum phase transitions. For the topologically continuous phase transition, the central charge at the critical point is obtained as c = 1, which means that the topologically continuous quantum phase transition belongs to the Gaussian universality class.
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
Symmetry-protected topological phases and transition in a frustrated spin-1/2 XXZ chain
NASA Astrophysics Data System (ADS)
Ueda, Hiroshi; Onoda, Shigeki
2014-12-01
A frustrated spin-1/2 XXZ zigzag chain relevant to Rb2Cu2Mo3O12 is revisited in the light of symmetry-protected topological (SPT) phases. Using a density-matrix renormalization group method for infinite systems, we identify projective representations for four distinct time-reversal invariant SPT phases; two parity-symmetric dimer phases near the Heisenberg and XX limits and two parity-broken vector-chiral (VC) dimer phases in between. A small bond alternation in the nearest-neighbor ferromagnetic exchange coupling induces a direct SPT transition between the two distinct VC dimer phases. It is also found numerically that two Berezinskii-Kosterlitz-Thouless transitions, which occur from the gapless to the two distinct gapped VC phases in the case of δ =0 , meet each other in the case of δ >0 at a Gaussian criticality of the same Tomonaga-Luttinger parameter value as in the SU(2)-symmetric case.
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
NASA Astrophysics Data System (ADS)
Lai, Hsin-Hua; Hung, Hsiang-Hsuan
2015-02-01
Time-reversal symmetric topological insulator (TI) is a novel state of matter that a bulk-insulating state carries dissipationless spin transport along the surfaces, embedded by the Z2 topological invariant. In the noninteracting limit, this exotic state has been intensively studied and explored with realistic systems, such as HgTe/(Hg, Cd)Te quantum wells. On the other hand, electronic correlation plays a significant role in many solid-state systems, which further influences topological properties and triggers topological phase transitions. Yet an interacting TI is still an elusive subject and most related analyses rely on the mean-field approximation and numerical simulations. Among the approaches, the mean-field approximation fails to predict the topological phase transition, in particular at intermediate interaction strength without spontaneously breaking symmetry. In this paper, we develop an analytical approach based on a combined perturbative and self-consistent mean-field treatment of interactions that is capable of capturing topological phase transitions beyond either method when used independently. As an illustration of the method, we study the effects of short-ranged interactions on the Z2 TI phase, also known as the quantum spin Hall (QSH) phase, in three generalized versions of the Kane-Mele (KM) model at half-filling on the honeycomb lattice. The results are in excellent agreement with quantum Monte Carlo (QMC) calculations on the same model and cannot be reproduced by either a perturbative treatment or a self-consistent mean-field treatment of the interactions. Our analytical approach helps to clarify how the symmetries of the one-body terms of the Hamiltonian determine whether interactions tend to stabilize or destabilize a topological phase. Moreover, our method should be applicable to a wide class of models where topological transitions due to interactions are in principle possible, but are not correctly predicted by either perturbative or self
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
Ma, Fengxian; Gao, Guoping; Jiao, Yalong; Gu, Yuantong; Bilic, Ante; Zhang, Haijun; Chen, Zhongfang; Du, Aijun
2016-03-01
Single layered transition metal dichalcogenides have attracted tremendous research interest due to their structural phase diversities. By using a global optimization approach, we have discovered a new phase of transition metal dichalcogenides (labelled as T''), which is confirmed to be energetically, dynamically and kinetically stable by our first-principles calculations. The new T'' MoS2 phase exhibits an intrinsic quantum spin Hall (QSH) effect with a nontrivial gap as large as 0.42 eV, suggesting that a two-dimensional (2D) topological insulator can be achieved at room temperature. Most interestingly, there is a topological phase transition simply driven by a small tensile strain of up to 2%. Furthermore, all the known MX2 (M = Mo or W; X = S, Se or Te) monolayers in the new T'' phase unambiguously display similar band topologies and strain controlled topological phase transitions. Our findings greatly enrich the 2D families of transition metal dichalcogenides and offer a feasible way to control the electronic states of 2D topological insulators for the fabrication of high-speed spintronics devices. PMID:26620395
Topological phase transition and unexpected mass acquisition of Dirac fermion in TlBi(S1-xSex)2
NASA Astrophysics Data System (ADS)
Niu, Chengwang; Dai, Ying; Zhu, Yingtao; Lu, Jibao; Ma, Yandong; Huang, Baibiao
2012-10-01
Based on first-principles calculations and effective Hamiltonian analysis, we predict a topological phase transition from normal to topological insulators and the opening of a gap without breaking the time-reversal symmetry in TlBi(S1-xSex)2. The transition can be driven by modulating the Se concentration, and the rescaled spin-orbit coupling and lattice parameters are the key ingredients for the transition. For topological surface states, the Dirac cone evolves differently as the explicit breaking of inversion symmetry and the energy band can be opened under asymmetry surface. Our results present theoretical evidence for experimental observations [Xu et al., Science 332, 560 (2011); Sato et al., Nat. Phys. 7, 840 (2011)].
NASA Astrophysics Data System (ADS)
Li, Dingping; Rosenstein, Baruch; Shapiro, B. Ya.; Shapiro, I.
2015-06-01
New two-dimensional systems such as the surfaces of topological insulators (TIs) and graphene offer the possibility of experimentally investigating situations considered exotic just a decade ago. These situations include the quantum phase transition of the chiral type in electronic systems with a relativistic spectrum. Phonon-mediated (conventional) pairing in the Dirac semimetal appearing on the surface of a TI causes a transition into a chiral superconducting state, and exciton condensation in these gapless systems has long been envisioned in the physics of narrow-band semiconductors. Starting from the microscopic Dirac Hamiltonian with local attraction or repulsion, the Bardeen-Cooper-Schrieffer type of Gaussian approximation is developed in the framework of functional integrals. It is shown that owing to an ultrarelativistic dispersion relation, there is a quantum critical point governing the zero-temperature transition to a superconducting state or the exciton condensed state. Quantum transitions having critical exponents differ greatly from conventional ones and belong to the chiral universality class. We discuss the application of these results to recent experiments in which surface superconductivity was found in TIs and estimate the feasibility of phonon pairing.
Geometrical requirements for transition-metal-centered aromatic boron wheels: the case of VB10(-).
Li, Wei-Li; Romanescu, Constantin; Piazza, Zachary A; Wang, Lai-Sheng
2012-10-21
A class of transition-metal-centered aromatic boron wheels (D(nh)-M©B(n)(q-)) have been recently produced and characterized according to an electronic design principle. Here we investigate the interplay between electronic and geometric requirements for the molecular wheels using the case of VB(10)(-), which is isoelectronic to the decacoordinated molecular wheels, Ta©B(10)(-) and Nb©B(10)(-). Photoelectron spectra of VB(10)(-) are observed to be broad and complicated with relatively low electron binding energies, in contrast to the simple and high electron binding energies observed for the molecular wheels of its heavier congeners. An unbiased global minimum search found the most stable isomer of VB(10)(-) to be a singlet "boat"-like structure (C(2)), in which the V atom is coordinated to a quasi-planar B(10) unit. A similar triplet C(2v) boat-like isomer is found to be almost degenerate to the C(2) structure, whereas the beautiful molecular wheel structure, D(10h)-V©B(10)(-), is significantly higher in energy on the potential energy surface. Therefore, even though the VB(10)(-) system fulfills the electronic requirement to form a D(10h)-M©B(10)(-) aromatic molecular wheel, the V atom is too small to stabilize the ten-membered boron ring. PMID:22968622
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.
Nagel, Sidney
2007-01-17
The exhilarating spray from waves crashing into the shore, the distressing sound of a faucet leaking in the night, and the indispensable role of bubbles dissolving gas into the oceans are but a few examples of the ubiquitous presence and profound importance of drop formation and splashing in our lives. During fission, a fluid forms a neck that becomes vanishingly thin at the point of breakup. This topological transition is accompanied by a dynamic singularity in which physical properties such as pressure diverge. Singularities of this sort often organize the overall dynamical evolution of nonlinear systems. I will first discuss the role of singularities in the breakup of droplets. I will then present a second experiment, selective withdrawal, in which we study the steady-state shape of a liquid as it is withdrawn by a nozzle through a surrounding fluid. Here, a change in topology may again be accompanied by a singularity. Applications of this geometry that rely on singular dynamical behavior are relevant for the coating of biological particles that may be of particular use in medical transplantation technologies.
NASA Astrophysics Data System (ADS)
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 triangle lattice symmetry and $C_{6v}$ rotation symmetry leads to rich physics in the study of accidental degeneracy's in photonic bands. We systematically evaluate different types of accidental nodal points, depending on the dispersions around them and their topological properties, when the geometry and permittivity are continuously changed. These accidental nodal points can be the critical states lying between a topological phase and a normal phase and are thus important for the study of topological photonic states. In time-reversal systems, this leads to the photonic quantum spin Hall insulator where the spin is defined upon the orbital angular momentum for transverse-magnetic polarization. We study the topological phase transition as well as the properties of the edge and bulk states and their application potentials in optics.
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)
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.
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).