Topological and geometrical aspects of phase transitions
NASA Astrophysics Data System (ADS)
Santos, F. A. N.; Rehn, J. A.; Coutinho-Filho, M. D.
2014-03-01
In the first part of this review, we use a topological approach to describe the frustration- and field-induced phase transitions exhibited by the infinite-range XY model on the AB2 chain, including noncollinear spin structures. For this purpose, we have computed the Euler characteristic, χ, as well as other topological invariants, which are found to behave similarly as a function of the energy level in the context of Morse theory. Our findings and those available in the literature suggest that the cusp-like singularity exhibited by χ at the critical energy, Ec, put together with the divergence of the density of Jacobian's critical points emerge as necessary and sufficient conditions for the occurrence of finite-temperature topology-induced phase transitions. In the second part, we present an alternative solution of the Ising chain in a field under free and periodic boundary conditions, in the microcanonical, canonical, and grand canonical ensembles, from a unified combinatorial and topological perspective. In particular, the computation of the per-site entropy as a function of the energy unveils a residual value for critical values of the magnetic field, a phenomenon for which we provide a topological interpretation and a connection with the Fibonacci sequence. We also show that, in the thermodynamic limit, the per-site microcanonical entropy is equal to the logarithm of the per-site Euler characteristic. Finally, we emphasize that our combinatorial approach to the canonical ensemble allows exact computation of the thermally averaged value <χ>(T) of the Euler characteristic; our results show that the conjecture <χ>(Tc)= 0, where Tc is the critical temperature, is valid for the Ising chain.
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 transitions, topological strings, and generalized complex geometry
NASA Astrophysics Data System (ADS)
Chuang, Wu-Yen
Mirror symmetry is one of the most beautiful symmetries in string theory. It helps us very effectively gain insight 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-Kahlerity." In this thesis we demonstrate how to construct a new class of symplectic non-Kahler and complex non-Kahler string theory vacua via geometric transitions. The class admits a mirror pairing by construction. From a variety of sources, including supergravity and KK reduction on SU(3) structure manifolds, we conclude that string theory connects Calabi-Yau spaces to both complex non-Kahler and symplectic non-Kahler 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) worldsheet theory with non-trivial H flux turned on. We show that the usual Kahler 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.
Scaling of geometric quantum discord close to a topological phase transition.
Shan, Chuan-Jia; Cheng, Wei-Wen; Liu, Ji-Bing; Cheng, Yong-Shan; Liu, Tang-Kun
2014-03-26
Quantum phase transition is one of the most interesting aspects in quantum many-body systems. Recently, geometric quantum discord has been introduced to signature the critical behavior of various quantum systems. However, it is well-known that topological quantum phase transition can not be described by the conventional Landau's symmetry breaking theory, and thus it is unknown that whether previous study can be applicable in this case. Here, we study the topological quantum phase transition in Kitaev's 1D p-wave spinless quantum wire model in terms of its ground state geometric quantum discord. The derivative of geometric quantum discord is nonanalytic at the critical point, in both zero temperature and finite temperature cases. The scaling behavior and the universality are verified numerically. Therefore, our results clearly show that all the key ingredients of the topological phase transition can be captured by the nearest neighbor and long-range geometric quantum discord.
Topological Lifshitz transitions
NASA Astrophysics Data System (ADS)
Volovik, G. E.
2017-01-01
Different types of Lifshitz transitions are governed by topology in momentum space. They involve the topological transitions with the change of topology of Fermi surfaces, Weyl and Dirac points, nodal lines, and also the transitions between the fully gapped states.
Topological minimally entangled states via geometric measure
NASA Astrophysics Data System (ADS)
Buerschaper, Oliver; García-Saez, Artur; Orús, Román; Wei, Tzu-Chieh
2014-11-01
Here we show how the Minimally Entangled States (MES) of a 2d system with topological order can be identified using the geometric measure of entanglement. We show this by minimizing this measure for the doubled semion, doubled Fibonacci and toric code models on a torus with non-trivial topological partitions. Our calculations are done either quasi-exactly for small system sizes, or using the tensor network approach in Orús et al (arXiv:1406.0585) for large sizes. As a byproduct of our methods, we see that the minimisation of the geometric entanglement can also determine the number of Abelian quasiparticle excitations in a given model. The results in this paper provide a very efficient and accurate way of extracting the full topological information of a 2d quantum lattice model from the multipartite entanglement structure of its ground states.
Frustrated topological symmetry breaking: Geometrical frustration and anyon condensation
NASA Astrophysics Data System (ADS)
Schulz, Marc D.; Burnell, Fiona J.
2016-10-01
We study the phase diagram of a topological string-net-type lattice model in the presence of geometrically frustrated interactions. These interactions drive several phase transitions that reduce the topological order, leading to a rich phase diagram including both Abelian (Z2) and non-Abelian (Ising×Ising¯ ) topologically ordered phases, as well as phases with broken translational symmetry. Interestingly, one of these phases simultaneously exhibits (Abelian) topological order and long-ranged order due to translational symmetry breaking, with nontrivial interactions between excitations in the topological order and defects in the long-ranged order. We introduce a variety of effective models, valid along certain lines in the phase diagram, which can be used to characterize both topological and symmetry-breaking order in these phases and in many cases allow us to characterize the phase transitions that separate them. We use exact diagonalization and high-order series expansion to study areas of the phase diagram where these models break down and to approximate the location of the phase boundaries.
Geometric stability of topological lattice phases
Jackson, T. S.; Möller, Gunnar; Roy, Rahul
2015-01-01
The fractional quantum Hall (FQH) effect illustrates the range of novel phenomena which can arise in a topologically ordered state in the presence of strong interactions. The possibility of realizing FQH-like phases in models with strong lattice effects has attracted intense interest as a more experimentally accessible venue for FQH phenomena which calls for more theoretical attention. Here we investigate the physical relevance of previously derived geometric conditions which quantify deviations from the Landau level physics of the FQHE. We conduct extensive numerical many-body simulations on several lattice models, obtaining new theoretical results in the process, and find remarkable correlation between these conditions and the many-body gap. These results indicate which physical factors are most relevant for the stability of FQH-like phases, a paradigm we refer to as the geometric stability hypothesis, and provide easily implementable guidelines for obtaining robust FQH-like phases in numerical or real-world experiments. PMID:26530311
Chromatin Topological Transitions
NASA Astrophysics Data System (ADS)
Lavelle, C.; Bancaud, A.; Recouvreux, P.; Barbi, M.; Victor, J.; Viovy, J.
DNA transaction events occurring during a cell cycle (transcription,repair, replication) are always associated with severe topological constraints on the double helix. However, since nuclear DNA is bound to various proteins (including histones) that control its accessibility and 3D organization, these topological constraints propagate or accumulate on a chromatin substrate. This paper focuses on chromatin fiber response to physiological mechanical constraints expected to occur during transcription elongation. We will show in particular how recent single molecule techniques help us to understand how chromatin conformational dynamics could manage harsh DNA supercoiling changes.
Topology-driven magnetic quantum phase transition in topological insulators.
Zhang, Jinsong; Chang, Cui-Zu; Tang, Peizhe; Zhang, Zuocheng; Feng, Xiao; Li, Kang; Wang, Li-Li; Chen, Xi; Liu, Chaoxing; Duan, Wenhui; He, Ke; Xue, Qi-Kun; Ma, Xucun; Wang, Yayu
2013-03-29
The breaking of time reversal symmetry in topological insulators may create previously unknown quantum effects. We observed a magnetic quantum phase transition in Cr-doped Bi2(SexTe1-x)3 topological insulator films grown by means of molecular beam epitaxy. Across the critical point, a topological quantum phase transition is revealed through both angle-resolved photoemission measurements and density functional theory calculations. We present strong evidence that the bulk band topology is the fundamental driving force for the magnetic quantum phase transition. The tunable topological and magnetic properties in this system are well suited for realizing the exotic topological quantum phenomena in magnetic topological insulators.
Geometric Potential and Transport in Photonic Topological Crystals
Szameit, Alexander; Dreisow, Felix; Heinrich, Matthias; Keil, Robert; Nolte, Stefan; Tuennermann, Andreas; Longhi, Stefano
2010-04-16
We report on the experimental realization of an optical analogue of a quantum geometric potential for light wave packets constrained on thin dielectric guiding layers fabricated in silica by the femtosecond laser writing technology. We further demonstrate the optical version of a topological crystal, with the observation of Bloch oscillations and Zener tunneling of a purely geometric nature.
Finite octree meshing through topologically driven geometric operators
NASA Technical Reports Server (NTRS)
Grice, Kurt R.
1987-01-01
The octree technique is developed into the finite octree, and an overview is given. Modeler requirements are given. The octree discretization is discussed along with geometric communication operators. Geometric communication operators returning topological associativity and geometric communication operators returning spatial data are also discussed and illustrated. The advantages are given of the boundary representation and of geometric communication operators. The implementation plays an important role in the integration with a variety of geometric modelers. The capabilities of closed loop processes within a complete finite element system are presented.
Exploiting geometric degrees of freedom in topological quantum computing
Xu Haitan; Wan Xin
2009-07-15
In a topological quantum computer, braids of non-Abelian anyons in a (2+1)-dimensional space time form quantum gates, whose fault tolerance relies on the topological, rather than geometric, properties of the braids. Here we propose to create and exploit redundant geometric degrees of freedom to improve the theoretical accuracy of topological single- and two-qubit quantum gates. We demonstrate the power of the idea using explicit constructions in the Fibonacci model. We compare its efficiency with that of the Solovay-Kitaev algorithm and explain its connection to the leakage errors reduction in an earlier construction [H. Xu and X. Wan, Phys. Rev. A 78, 042325 (2008)].
Geometric quantum phase in the spacetime of topological defects
NASA Astrophysics Data System (ADS)
Bakke, K.; Furtado, C.; Nascimento, J. R.
2011-07-01
In this contribution, 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 background. We also study the influence of noninertial effects of a rotating frame and and obtain several contributions to the relativistic geometric phase due to the noninertial effects and the topology of spacetime. The analogous Aharonov-Casher and He-Mckellar-Wilkens effects are investigated in the nonrelativistic dynamics with the presence of a topological defect and under the influence of noninertial effects. We also obtain effects analogous to the Sagnac effect and Mashhoon effect due to the presence of the topological defect.
Quantum algorithm for topological and geometric analysis of data
NASA Astrophysics Data System (ADS)
Lloyd, Seth; Zanardi, Paolo; Garnerone, Silvano
2015-03-01
Topological methods for analyzing data sets provide a powerful technique for extracting useful information from data. Data that represents geometric features of the world typically gives a distorted picture of those features, if only because the devices and systems that sense the world and that generate the data by their very nature induce distortions. By definition, topological features are those that persist under continuous distortions of the data. Topological methods can therefore identify features of the real system from which the data was collected, but that have been distorted by the data collection process. Persistent homology is a sophisticated tool for identifying such topological features -connected components, holes, or voids - and for determining how such features persist as the data is viewed at different scales. This talk presents quantum machine learning algorithms for calculating Betti numbers in persistent homology, and for finding eigenvectors and eigenvalues of the combinatorial Laplacian (the quantities that famously allow one to ``hear the shape of a drum''). The algorithms provide an exponential speedup over classical algorithms for topological and geometrical data analysis.
Hagedorn transition and topological entanglement entropy
NASA Astrophysics Data System (ADS)
Zuo, Fen; Gao, Yi-Hong
2016-06-01
Induced by the Hagedorn instability, weakly-coupled U (N) gauge theories on a compact manifold exhibit a confinement/deconfinement phase transition in the large-N limit. Recently we discover that the thermal entropy of a free theory on S3 gets reduced by a universal constant term, -N2 / 4, compared to that from completely deconfined colored states. This entropy deficit is due to the persistence of Gauss's law, and actually independent of the shape of the manifold. In this paper we show that this universal term can be identified as the topological entangle entropy both in the corresponding 4 + 1 D bulk theory and the dimensionally reduced theory. First, entanglement entropy in the bulk theory contains the so-called "particle" contribution on the entangling surface, which naturally gives rise to an area-law term. The topological term results from the Gauss's constraint of these surface states. Secondly, the high-temperature limit also defines a dimensionally reduced theory. We calculate the geometric entropy in the reduced theory explicitly, and find that it is given by the same constant term after subtracting the leading term of O (β-1). The two procedures are then applied to the confining phase, by extending the temperature to the complex plane. Generalizing the recently proposed 2D modular description to an arbitrary matter content, we show the leading local term is missing and no topological term could be definitely isolated. For the special case of N = 4 super Yang-Mills theory, the results obtained here are compared with that at strong coupling from the holographic derivation.
Clique topology reveals intrinsic geometric structure in neural correlations.
Giusti, Chad; Pastalkova, Eva; Curto, Carina; Itskov, Vladimir
2015-11-03
Detecting meaningful structure in neural activity and connectivity data is challenging in the presence of hidden nonlinearities, where traditional eigenvalue-based methods may be misleading. We introduce a novel approach to matrix analysis, called clique topology, that extracts features of the data invariant under nonlinear monotone transformations. These features can be used to detect both random and geometric structure, and depend only on the relative ordering of matrix entries. We then analyzed the activity of pyramidal neurons in rat hippocampus, recorded while the animal was exploring a 2D environment, and confirmed that our method is able to detect geometric organization using only the intrinsic pattern of neural correlations. Remarkably, we found similar results during nonspatial behaviors such as wheel running and rapid eye movement (REM) sleep. This suggests that the geometric structure of correlations is shaped by the underlying hippocampal circuits and is not merely a consequence of position coding. We propose that clique topology is a powerful new tool for matrix analysis in biological settings, where the relationship of observed quantities to more meaningful variables is often nonlinear and unknown.
Topological phase transitions in frustrated magnets
NASA Astrophysics Data System (ADS)
Southern, B. W.; Peles, A.
2006-06-01
The role of topological excitations in frustrated Heisenberg antiferromagnets between two and three spatial dimensions is considered. In particular, the antiferromagnetic Heisenberg model on a stacked triangular geometry with a finite number of layers is studied using Monte Carlo methods. A phase transition that is purely topological in nature occurs at a finite temperature for all film thicknesses. The results indicate that topological excitations are important for a complete understanding of the critical properties of the model between two and three dimensions.
Observation of topological transitions in interacting quantum circuits.
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.
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.
In the Realm of Geometric Transitions
Alexander, S
2004-09-09
We complete the duality cycle by constructing the geometric transition duals in the type IIB, type I and heterotic theories. We show that in the type IIB theory the background on the closed string side is a Kahler deformed conifold, as expected, even though the mirror type IIA backgrounds are non-Kahler (both before and after the transition). On the other hand, the Type I and heterotic backgrounds are non-Kahler. Therefore, on the heterotic side these backgrounds give rise to new torsional manifolds that have not been studied before. We show the consistency of these backgrounds by verifying the torsional equation.
Lassoing saddle splay and the geometrical control of topological defects
NASA Astrophysics Data System (ADS)
Tran, Lisa; Lavrentovich, Maxim O.; Beller, Daniel A.; Li, Ningwei; Stebe, Kathleen J.; Kamien, Randall D.
2016-06-01
Systems with holes, such as colloidal handlebodies and toroidal droplets, have been studied in the nematic liquid crystal (NLC) 4-cyano-4'-pentylbiphenyl (5CB): Both point and ring topological defects can occur within each hole and around the system while conserving the system's overall topological charge. However, what has not been fully appreciated is the ability to manipulate the hole geometry with homeotropic (perpendicular) anchoring conditions to induce complex, saddle-like deformations. We exploit this by creating an array of holes suspended in an NLC cell with oriented planar (parallel) anchoring at the cell boundaries. We study both 5CB and a binary mixture of bicyclohexane derivatives (CCN-47 and CCN-55). Through simulations and experiments, we study how the bulk saddle deformations of each hole interact to create defect structures, including an array of disclination lines, reminiscent of those found in liquid-crystal blue phases. The line locations are tunable via the NLC elastic constants, the cell geometry, and the size and spacing of holes in the array. This research lays the groundwork for the control of complex elastic deformations of varying length scales via geometrical cues in materials that are renowned in the display industry for their stability and easy manipulability.
Topological and geometric measurements of force-chain structure
NASA Astrophysics Data System (ADS)
Giusti, Chad; Papadopoulos, Lia; Owens, Eli T.; Daniels, Karen E.; Bassett, Danielle S.
2016-09-01
Developing quantitative methods for characterizing structural properties of force chains in densely packed granular media is an important step toward understanding or predicting large-scale physical properties of a packing. A promising framework in which to develop such methods is network science, which can be used to translate particle locations and force contacts into a graph in which particles are represented by nodes and forces between particles are represented by weighted edges. Recent work applying network-based community-detection techniques to extract force chains opens the door to developing statistics of force-chain structure, with the goal of identifying geometric and topological differences across packings, and providing a foundation on which to build predictions of bulk material properties from mesoscale network features. Here we discuss a trio of related but fundamentally distinct measurements of the mesoscale structure of force chains in two-dimensional (2D) packings, including a statistic derived using tools from algebraic topology, which together provide a tool set for the analysis of force chain architecture. We demonstrate the utility of this tool set by detecting variations in force-chain architecture with pressure. Collectively, these techniques can be generalized to 3D packings, and to the assessment of continuous deformations of packings under stress or strain.
Topological and geometric measurements of force-chain structure.
Giusti, Chad; Papadopoulos, Lia; Owens, Eli T; Daniels, Karen E; Bassett, Danielle S
2016-09-01
Developing quantitative methods for characterizing structural properties of force chains in densely packed granular media is an important step toward understanding or predicting large-scale physical properties of a packing. A promising framework in which to develop such methods is network science, which can be used to translate particle locations and force contacts into a graph in which particles are represented by nodes and forces between particles are represented by weighted edges. Recent work applying network-based community-detection techniques to extract force chains opens the door to developing statistics of force-chain structure, with the goal of identifying geometric and topological differences across packings, and providing a foundation on which to build predictions of bulk material properties from mesoscale network features. Here we discuss a trio of related but fundamentally distinct measurements of the mesoscale structure of force chains in two-dimensional (2D) packings, including a statistic derived using tools from algebraic topology, which together provide a tool set for the analysis of force chain architecture. We demonstrate the utility of this tool set by detecting variations in force-chain architecture with pressure. Collectively, these techniques can be generalized to 3D packings, and to the assessment of continuous deformations of packings under stress or strain.
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.
2016-01-01
Systems with holes, such as colloidal handlebodies and toroidal droplets, have been studied in the nematic liquid crystal (NLC) 4-cyano-4′-pentylbiphenyl (5CB): Both point and ring topological defects can occur within each hole and around the system while conserving the system’s overall topological charge. However, what has not been fully appreciated is the ability to manipulate the hole geometry with homeotropic (perpendicular) anchoring conditions to induce complex, saddle-like deformations. We exploit this by creating an array of holes suspended in an NLC cell with oriented planar (parallel) anchoring at the cell boundaries. We study both 5CB and a binary mixture of bicyclohexane derivatives (CCN-47 and CCN-55). Through simulations and experiments, we study how the bulk saddle deformations of each hole interact to create defect structures, including an array of disclination lines, reminiscent of those found in liquid-crystal blue phases. The line locations are tunable via the NLC elastic constants, the cell geometry, and the size and spacing of holes in the array. This research lays the groundwork for the control of complex elastic deformations of varying length scales via geometrical cues in materials that are renowned in the display industry for their stability and easy manipulability. PMID:27222582
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.
Topological Quantum Field Theory and the Geometric Langlands Correspondence
NASA Astrophysics Data System (ADS)
Setter, Kevin
In the pioneering work of A. Kapustin and E. Witten, the geometric Langlands program of number theory was shown to be intimately related to duality of GL-twisted N = 4 super Yang-Mills theory compactified on a Riemann surface. In this thesis, we generalize Kapustin-Witten by investigating compactification of the GL-twisted theory to three dimensions on a circle (for various values of the twisting parameter t). By considering boundary conditions in the three-dimensional description, we classify codimension-two surface operators of the GL-twisted theory, generalizing those surface operators studied by S. Gukov and E. Witten. For t = i, we propose a complete description of the 2-category of surface operators in terms of module categories, and, in addition, we determine the monoidal category of line operators which includes Wilson lines as special objects. For t = 1 and t = 0, we discuss surface and line operators in the abelian case. We generalize Kapustin-Witten also by analyzing a separate twisted version of N = 4, the Vafa-Witten theory. After introducing a new four-dimensional topological gauge theory, the gauged 4d A-model, we locate the Vafa-Witten theory as a special case. Compactification of the Vafa-Witten theory on a circle and on a Riemann surface is discussed. Several novel two- and three-dimensional topological gauge theories are studied throughout the thesis and in the appendices. In work unrelated to the main thread of the thesis, we conclude by classifying codimension-one topological defects in two-dimensional sigma models with various amounts of supersymmetry.
Superconductivity Bordering Rashba Type Topological Transition
Jin, M. L.; Sun, F.; Xing, L. Y.; Zhang, S. J.; Feng, S. M.; Kong, P. P.; Li, W. M.; Wang, X. C.; Zhu, J. L.; Long, Y. W.; Bai, H. Y.; Gu, C. Z.; Yu, R. C.; Yang, W. G.; Shen, G. Y.; Zhao, Y. S.; Mao, H. K.; Jin, C. Q.
2017-01-01
Strong spin orbital interaction (SOI) can induce unique quantum phenomena such as topological insulators, the Rashba effect, or p-wave superconductivity. Combining these three quantum phenomena into a single compound has important scientific implications. Here we report experimental observations of consecutive quantum phase transitions from a Rashba type topological trivial phase to topological insulator state then further proceeding to superconductivity in a SOI compound BiTeI tuned via pressures. The electrical resistivity measurement with V shape change signals the transition from a Rashba type topological trivial to a topological insulator phase at 2 GPa, which is caused by an energy gap close then reopen with band inverse. Superconducting transition appears at 8 GPa with a critical temperature TC of 5.3 K. Structure refinements indicate that the consecutive phase transitions are correlated to the changes in the Bi–Te bond and bond angle as function of pressures. The Hall Effect measurements reveal an intimate relationship between superconductivity and the unusual change in carrier density that points to possible unconventional superconductivity. PMID:28051188
Superconductivity Bordering Rashba Type Topological Transition.
Jin, M L; Sun, F; Xing, L Y; Zhang, S J; Feng, S M; Kong, P P; Li, W M; Wang, X C; Zhu, J L; Long, Y W; Bai, H Y; Gu, C Z; Yu, R C; Yang, W G; Shen, G Y; Zhao, Y S; Mao, H K; Jin, C Q
2017-01-04
Strong spin orbital interaction (SOI) can induce unique quantum phenomena such as topological insulators, the Rashba effect, or p-wave superconductivity. Combining these three quantum phenomena into a single compound has important scientific implications. Here we report experimental observations of consecutive quantum phase transitions from a Rashba type topological trivial phase to topological insulator state then further proceeding to superconductivity in a SOI compound BiTeI tuned via pressures. The electrical resistivity measurement with V shape change signals the transition from a Rashba type topological trivial to a topological insulator phase at 2 GPa, which is caused by an energy gap close then reopen with band inverse. Superconducting transition appears at 8 GPa with a critical temperature TC of 5.3 K. Structure refinements indicate that the consecutive phase transitions are correlated to the changes in the Bi-Te bond and bond angle as function of pressures. The Hall Effect measurements reveal an intimate relationship between superconductivity and the unusual change in carrier density that points to possible unconventional superconductivity.
Superconductivity Bordering Rashba Type Topological Transition
NASA Astrophysics Data System (ADS)
Jin, M. L.; Sun, F.; Xing, L. Y.; Zhang, S. J.; Feng, S. M.; Kong, P. P.; Li, W. M.; Wang, X. C.; Zhu, J. L.; Long, Y. W.; Bai, H. Y.; Gu, C. Z.; Yu, R. C.; Yang, W. G.; Shen, G. Y.; Zhao, Y. S.; Mao, H. K.; Jin, C. Q.
2017-01-01
Strong spin orbital interaction (SOI) can induce unique quantum phenomena such as topological insulators, the Rashba effect, or p-wave superconductivity. Combining these three quantum phenomena into a single compound has important scientific implications. Here we report experimental observations of consecutive quantum phase transitions from a Rashba type topological trivial phase to topological insulator state then further proceeding to superconductivity in a SOI compound BiTeI tuned via pressures. The electrical resistivity measurement with V shape change signals the transition from a Rashba type topological trivial to a topological insulator phase at 2 GPa, which is caused by an energy gap close then reopen with band inverse. Superconducting transition appears at 8 GPa with a critical temperature TC of 5.3 K. Structure refinements indicate that the consecutive phase transitions are correlated to the changes in the Bi–Te bond and bond angle as function of pressures. The Hall Effect measurements reveal an intimate relationship between superconductivity and the unusual change in carrier density that points to possible unconventional superconductivity.
Superconductivity bordering Rashba type topological transition
Jin, M. L.; Sun, F.; Xing, L. Y.; ...
2017-01-04
Strong spin orbital interaction (SOI) can induce unique quantum phenomena such as topological insulators, the Rashba effect, or p-wave superconductivity. Combining these three quantum phenomena into a single compound has important scientific implications. Here we report experimental observations of consecutive quantum phase transitions from a Rashba type topological trivial phase to topological insulator state then further proceeding to superconductivity in a SOI compound BiTeI tuned via pressures. The electrical resistivity measurement with V shape change signals the transition from a Rashba type topological trivial to a topological insulator phase at 2 GPa, which is caused by an energy gap closemore » then reopen with band inverse. Superconducting transition appears at 8 GPa with a critical temperature TC of 5.3 K. Structure refinements indicate that the consecutive phase transitions are correlated to the changes in the Bi–Te bond and bond angle as function of pressures. As a result, the Hall Effect measurements reveal an intimate relationship between superconductivity and the unusual change in carrier density that points to possible unconventional superconductivity.« less
Scaling theory of topological phase transitions
NASA Astrophysics Data System (ADS)
Chen, Wei
2016-02-01
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.
Strain-induced topological quantum phase transition in phosphorene oxide
NASA Astrophysics Data System (ADS)
Kang, Seoung-Hun; Park, Jejune; Woo, Sungjong; Kwon, Young-Kyun
Using ab initio density functional theory, we investigate the structural stability and electronic properties of phosphorene oxides (POx) with different oxygen compositions x. A variety of configurations are modeled and optimized geometrically to search for the equilibrium structure for each x value. Our electronic structure calculations on the equilibrium configuration obtained for each x reveal that the band gap tends to increase with the oxygen composition of x < 0.5, and then to decrease with x > 0.5. We further explore the strain effect on the electronic structure of the fully oxidized phosphorene, PO, with x = 1. At a particular strain without spin-orbit coupling (SOC) is observed a band gap closure near the Γ point in the k space. We further find the strain in tandem with SOC induces an interesting band inversion with a reopened very small band gap (5 meV), and thus gives rise to a topological quantum phase transition from a normal insulator to a topological insulator. Such a topological phase transition is confirmed by the wave function analysis and the band topology identified by the Z2 invariant calculation.
Geometrical clusterization and deconfinement phase transition in SU(2) gluodynamics
NASA Astrophysics Data System (ADS)
Ivanytskyi, A.; Bugaev, K.; Nikonov, E.; Ilgenfritz, E.-M.; Oliinychenko, D.; Sagun, V.; Mishustin, I.; Zinovjev, G.; Petrov, V.
2017-03-01
A novel approach to identify the geometrical (anti)clusters formed by the Polyakov loops of the same sign and to study their properties in the lattice SU(2) gluodynamics is developed. The (anti)cluster size distributions are analyzed for the lattice coupling constant β ∈ 2 [2:3115; 3]. The found distributions are similar to the ones existing in 2- and 3-dimensional Ising systems. Using the suggested approach, we explain the phase transition in SU(2) gluodynamics at β = 2.52 as a transition between two liquids during which one of the liquid droplets (the largest cluster of a certain Polyakov loop sign) experiences a condensation, while another droplet (the next to the largest cluster of opposite Polyakov loop sign) evaporates. The clusters of smaller sizes form two accompanying gases, which behave oppositely to their liquids. The liquid drop formula is used to analyze the distributions of the gas (anti)clusters and to determine their bulk, surface and topological parts of free energy. Surprisingly, even the monomer multiplicities are reproduced with high quality within such an approach. The behavior of surface tension of gaseous (anti)clusters is studied. It is shown that this quantity can serve as an order parameter of the deconfinement phase transition in SU(2) gluodynamics. Moreover, the critical exponent β of surface tension coefficient of gaseous clusters is found in the upper vicinity of critical temperature. Its value coincides with the one found for 3-dimensional Ising model within error bars. The Fisher topological exponent τ of (anti)clusters is found to have the same value 1:806±0:008, which agrees with an exactly solvable model of the nuclear liquid-gas phase transition and disagrees with the Fisher droplet model, which may evidence for the fact that the SU(2) gluodynamics and the model are in the same universality class.
Quantum Monte Carlo simulation of topological phase transitions
NASA Astrophysics Data System (ADS)
Yamamoto, Arata; Kimura, Taro
2016-12-01
We study the electron-electron interaction effects on topological phase transitions by the ab initio quantum Monte Carlo simulation. We analyze two-dimensional class A topological insulators and three-dimensional Weyl semimetals with the long-range Coulomb interaction. The direct computation of the Chern number shows the electron-electron interaction modifies or extinguishes topological phase transitions.
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.
Lloyd, Seth; Garnerone, Silvano; Zanardi, Paolo
2016-01-25
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
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.
Qin, Wei; Zhang, Zhenyu
2014-12-31
At the interface of an s-wave superconductor and a three-dimensional topological insulator, Majorana zero modes and Majorana helical states have been proposed to exist respectively around magnetic vortices and geometrical edges. Here we first show that randomly distributed magnetic impurities at such an interface will induce bound states that broaden into impurity bands inside (but near the edges of) the superconducting gap, which remains open unless the impurity concentration is too high. Next we find that an increase in the superconducting gap suppresses both the oscillation magnitude and the period of the Ruderman-Kittel-Kasuya-Yosida interaction between two magnetic impurities. Within a mean-field approximation, the ferromagnetic Curie temperature is found to be essentially independent of the superconducting gap, an intriguing phenomenon due to a compensation effect between the short-range ferromagnetic and long-range antiferromagnetic interactions. The existence of robust superconductivity and persistent ferromagnetism at the interface allows realization of a novel topological phase transition from a nonchiral to a chiral superconducting state at sufficiently low temperatures, providing a new platform for topological quantum computation.
Geometrical and Topological Methods in Time Domain Antenna Synthesis
1994-04-30
observable are necessarily topological invariants. 2. To most mathematicians, Witten’s use of Feynmann path integrals is tantamount to witchcraft, and so an...quantum field theory and Vassiliev’s invariants. The recent work of Baez[6] and Kontsevich[47], appear to be the first successes at making the Feynmann
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.
Park, Byung Cheol; Kim, Tae-Hyeon; Sim, Kyung Ik; Kang, Boyoun; Kim, Jeong Won; Cho, Beongki; Jeong, Kwang-Ho; Cho, Mann-Ho; Kim, Jae Hoon
2015-03-16
Strong spin-orbit interaction and time-reversal symmetry in topological insulators generate novel quantum states called topological surface states. Their study provides unique opportunities to explore exotic phenomena such as spin Hall effects and topological phase transitions, relevant to the development of quantum devices for spintronics and quantum computation. Although ultrahigh-vacuum surface probes can identify individual topological surface states, standard electrical and optical experiments have so far been hampered by the interference of bulk and quantum well states. Here, with terahertz time-domain spectroscopy of ultrathin Bi₂Se₃ films, we give evidence for topological phase transitions, a single conductance quantum per topological surface state, and a quantized terahertz absorbance of 2.9% (four times the fine structure constant). Our experiment demonstrates the feasibility to isolate, detect and manipulate topological surface states in the ambient at room temperature for future fundamental research on the novel physics of topological insulators and their practical applications.
Disorder-induced topological transitions in multichannel Majorana wires
NASA Astrophysics Data System (ADS)
Pekerten, B.; Teker, A.; Bozat, Ö.; Wimmer, M.; Adagideli, I.
2017-02-01
In this work, we investigate the effect of disorder on the topological properties of multichannel superconductor nanowires. While the standard expectation is that the spectral gap is closed and opened at transitions that change the topological index of the wire, we show that the closing and opening of a transport gap can also cause topological transitions, even in the presence of nonzero density of states across the transition. Such transport gaps induced by disorder can change the topological index, driving a topologically trivial wire into a nontrivial state or vice versa. We focus on the Rashba spin-orbit coupled semiconductor nanowires in proximity to a conventional superconductor, which is an experimentally relevant system, and we obtain analytical formulas for topological transitions in these wires, valid for generic realizations of disorder. Full tight-binding simulations show excellent agreement with our analytical results without any fitting parameters.
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.
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.
NASA Astrophysics Data System (ADS)
Deymier, P. A.; Runge, K.; Vasseur, J. O.
2016-12-01
We illustrate the concept of geometric phase in the case of two prototypical elastic systems, namely the one-dimensional harmonic oscillator and a one-dimensional binary superlattice. We demonstrate formally the relationship between the variation of the geometric phase in the spectral and wave number domains and the parallel transport of a vector field along paths on curved manifolds possessing helicoidal twists which exhibit non-conventional topology.
Geometric constraints for shape and topology optimization in architectural design
NASA Astrophysics Data System (ADS)
Dapogny, Charles; Faure, Alexis; Michailidis, Georgios; Allaire, Grégoire; Couvelas, Agnes; Estevez, Rafael
2017-02-01
This work proposes a shape and topology optimization framework oriented towards conceptual architectural design. A particular emphasis is put on the possibility for the user to interfere on the optimization process by supplying information about his personal taste. More precisely, we formulate three novel constraints on the geometry of shapes; while the first two are mainly related to aesthetics, the third one may also be used to handle several fabrication issues that are of special interest in the device of civil structures. The common mathematical ingredient to all three models is the signed distance function to a domain, and its sensitivity analysis with respect to perturbations of this domain; in the present work, this material is extended to the case where the ambient space is equipped with an anisotropic metric tensor. Numerical examples are discussed in two and three space dimensions.
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.
Sinai Diffusion at Quasi-1D Topological Phase Transitions
NASA Astrophysics Data System (ADS)
Bagrets, Dmitry; Altland, Alexander; Kamenev, Alex
2016-11-01
We consider critical quantum transport in disordered topological quantum wires at the transition between phases with different topological indices. Focusing on the example of thermal transport in class D ("Majorana") quantum wires, we identify a transport universality class distinguished for anomalous retardation in the propagation of excitations—a quantum generalization of Sinai diffusion. We discuss the expected manifestations of this transport mechanism for heat propagation in topological superconductors near criticality and provide a microscopic theory explaining the phenomenon.
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.
Geometrically induced reversion of Hall current in a topological insulator cavity
NASA Astrophysics Data System (ADS)
Campos, W. H.; Moura-Melo, W. A.; Fonseca, J. M.
2017-02-01
An electric charge near the surface of a topological insulator induces an image magnetic monopole. Here, we show that if the topological insulator surface has a negative curvature, namely in the case of a semispherical cavity, the induced Hall current reverses its rotation as the electric charge crosses the semisphere geometric focus. Such a reversion is shown to be equivalent of inverting the charge of the image magnetic monopole. We also discuss upon the case of a semicylindrical cavity, where Hall current reversion appears to be feasible of probing in realistic experiments.
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.
NASA Astrophysics Data System (ADS)
Wang, Yingjun; Benson, David J.
2016-12-01
In this paper, an approach based on the fast point-in-polygon (PIP) algorithm and trimmed elements is proposed for isogeometric topology optimization (TO) with arbitrary geometric constraints. The isogeometric parameterized level-set-based TO method, which directly uses the non-uniform rational basis splines (NURBS) for both level set function (LSF) parameterization and objective function calculation, provides higher accuracy and efficiency than previous methods. The integration of trimmed elements is completed by the efficient quadrature rule that can design the quadrature points and weights for arbitrary geometric shape. Numerical examples demonstrate the efficiency and flexibility of the method.
Topological phase transitions in line-nodal superconductors
NASA Astrophysics Data System (ADS)
Han, SangEun; Cho, Gil Young; Moon, Eun-Gook
2017-03-01
Fathoming interplay between symmetry and topology of many-electron wave functions has deepened our understanding of quantum many-body systems, particularly after the discovery of topological insulators. Topology of electron wave functions often enforces and protects emergent gapless excitation, and symmetry is intrinsically tied to the topological protection of the excitations. Namely, unless the symmetry is broken, the topological nature of the excitations is intact. We show intriguing phenomena of interplay between symmetry and topology in three-dimensional topological phase transitions associated with line-nodal superconductors. More specifically, we discover an exotic universality class out of topological line-nodal superconductors. The order parameter of broken symmetries is strongly correlated with underlying line-nodal fermions, and this gives rise to a large anomalous dimension in sharp contrast to that of the Landau-Ginzburg theory. Remarkably, hyperscaling violation and emergent relativistic scaling appear in spite of the presence of nonrelativistic fermionic excitation. We also propose characteristic experimental signatures around the phase transitions, for example, a linear phase boundary in a temperature-tuning parameter phase diagram, and discuss the implication of recent experiments in pnictides and heavy-fermion systems.
Specific features of magnetostriction at electron topological transitions in metals
NASA Astrophysics Data System (ADS)
Mikitik, G. P.; Sharlai, Yu. V.
2017-01-01
The properties of magnetostriction in metals are studied in cases when the chemical potential of electrons is close to the critical energy of the electron energy spectrum, at which there is an electron topological transition of 2½ or 3½ kind. It is shown that the experimental study of magnetostriction can be an effective method for detecting these transitions in metals.
NASA Astrophysics Data System (ADS)
Wakatsuki, Ryohei; Ezawa, Motohiko; Nagaosa, Naoto
2014-05-01
Motivated by the InSb nanowire superconductor system, we investigate a system where one-dimensional topological superconductors are placed in parallel. It would be simulated well by a ladder of the Kitaev chains. The system undergoes multiple topological phase transitions, where the number of Majorana fermions changes as a function of the interchain superconducting pairings. We analytically determine the topological phase diagram by explicitly calculating the topological number and the band structure. They show even-odd effects with respect to the number of legs of the ladder. When the relative phase between the inter- and intrachain superconducting pairings is 0 or π, the system belongs to the class BDI characterized by the Z index, and otherwise it belongs to the class D characterized by the Z2 index. This topological class change would be caused by applying the Josephson current or an external magnetic field, and could be observed by measuring the zero-bias differential conductance.
Topologically insulating states in ternary transition metal dichalcogenides
NASA Astrophysics Data System (ADS)
Lin, Xianqing; Ni, Jun
2017-01-01
The topological and electronic properties of monolayered monoclinic transition metal dichalcogenide (TMD) alloys (1T '-M1-xNxX2 with M, N = Cr, Mo, W and X = S, Se) have been studied through calculations based on the projected Wannier functions obtained from first-principles calculations. We predict that the ternary compounds 1T '-Mo1-xCrxS2 with x up to 7/12 and all 1T '-Mo1-xWxSe2 host topologically insulating states with band gaps comparable to the pure systems. For Cr contained alloys, the mechanism of sign changing of Berry curvature is proposed to explain the trivial band topology of some configurations. The predicted topologically insulating ternary TMDs may be promising candidates for future realization of topological devices.
Chiral topological excitons in the monolayer transition metal dichalcogenides.
Gong, Z R; Luo, W Z; Jiang, Z F; Fu, H C
2017-02-10
We theoretically investigate the chiral topological excitons emerging in the monolayer transition metal dichalcogenides, where a bulk energy gap of valley excitons is opened up by a position dependent external magnetic field. We find two emerging chiral topological nontrivial excitons states, which exactly connects to the bulk topological properties, i.e., Chern number = 2. The dependence of the spectrum of the chiral topological excitons on the width of the magnetic field domain wall as well as the magnetic filed strength is numerically revealed. The chiral topological valley excitons are not only important to the excitonic transport due to prevention of the backscattering, but also give rise to the quantum coherent control in the optoelectronic applications.
Chiral topological excitons in the monolayer transition metal dichalcogenides
NASA Astrophysics Data System (ADS)
Gong, Z. R.; Luo, W. Z.; Jiang, Z. F.; Fu, H. C.
2017-02-01
We theoretically investigate the chiral topological excitons emerging in the monolayer transition metal dichalcogenides, where a bulk energy gap of valley excitons is opened up by a position dependent external magnetic field. We find two emerging chiral topological nontrivial excitons states, which exactly connects to the bulk topological properties, i.e., Chern number = 2. The dependence of the spectrum of the chiral topological excitons on the width of the magnetic field domain wall as well as the magnetic filed strength is numerically revealed. The chiral topological valley excitons are not only important to the excitonic transport due to prevention of the backscattering, but also give rise to the quantum coherent control in the optoelectronic applications.
Chiral topological excitons in the monolayer transition metal dichalcogenides
Gong, Z. R.; Luo, W. Z.; Jiang, Z. F.; Fu, H. C.
2017-01-01
We theoretically investigate the chiral topological excitons emerging in the monolayer transition metal dichalcogenides, where a bulk energy gap of valley excitons is opened up by a position dependent external magnetic field. We find two emerging chiral topological nontrivial excitons states, which exactly connects to the bulk topological properties, i.e., Chern number = 2. The dependence of the spectrum of the chiral topological excitons on the width of the magnetic field domain wall as well as the magnetic filed strength is numerically revealed. The chiral topological valley excitons are not only important to the excitonic transport due to prevention of the backscattering, but also give rise to the quantum coherent control in the optoelectronic applications. PMID:28186154
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.
Quantum phase transition induced by real-space topology
NASA Astrophysics Data System (ADS)
Li, C.; Zhang, G.; Lin, S.; Song, Z.
2016-12-01
A quantum phase transition (QPT), including both topological and symmetry breaking types, is usually induced by the change of global parameters, such as external fields or global coupling constants. In this work, we demonstrate the existence of QPT induced by the real-space topology of the system. We investigate the groundstate properties of the tight-binding model on a honeycomb lattice with the torus geometry based on exact results. It is shown that the ground state experiences a second-order QPT, exhibiting the scaling behavior, when the torus switches to a tube, which reveals the connection between quantum phase and the real-space topology of the system.
Quantum phase transition induced by real-space topology
Li, C.; Zhang, G.; Lin, S.; Song, Z.
2016-01-01
A quantum phase transition (QPT), including both topological and symmetry breaking types, is usually induced by the change of global parameters, such as external fields or global coupling constants. In this work, we demonstrate the existence of QPT induced by the real-space topology of the system. We investigate the groundstate properties of the tight-binding model on a honeycomb lattice with the torus geometry based on exact results. It is shown that the ground state experiences a second-order QPT, exhibiting the scaling behavior, when the torus switches to a tube, which reveals the connection between quantum phase and the real-space topology of the system. PMID:28004736
Interaction effects and quantum phase transitions in topological insulators
Varney, Christopher N.; Sun Kai; Galitski, Victor; Rigol, Marcos
2010-09-15
We study strong correlation effects in topological insulators via the Lanczos algorithm, which we utilize to calculate the exact many-particle ground-state wave function and its topological properties. We analyze the simple, noninteracting Haldane model on a honeycomb lattice with known topological properties and demonstrate that these properties are already evident in small clusters. Next, we consider interacting fermions by introducing repulsive nearest-neighbor interactions. A first-order quantum phase transition was discovered at finite interaction strength between the topological band insulator and a topologically trivial Mott insulating phase by use of the fidelity metric and the charge-density-wave structure factor. We construct the phase diagram at T=0 as a function of the interaction strength and the complex phase for the next-nearest-neighbor hoppings. Finally, we consider the Haldane model with interacting hard-core bosons, where no evidence for a topological phase is observed. An important general conclusion of our work is that despite the intrinsic nonlocality of topological phases their key topological properties manifest themselves already in small systems and therefore can be studied numerically via exact diagonalization and observed experimentally, e.g., with trapped ions and cold atoms in optical lattices.
Exotic quantum phase transitions of strongly interacting topological insulators
NASA Astrophysics Data System (ADS)
Slagle, Kevin; You, Yi-Zhuang; Xu, Cenke
2015-03-01
Using determinant quantum Monte Carlo simulations, we demonstrate that an extended Hubbard model on a bilayer honeycomb lattice has two novel quantum phase transitions. The first is a quantum phase transition between the weakly interacting gapless Dirac fermion phase and a strongly interacting fully gapped and symmetric trivial phase, which cannot be described by the standard Gross-Neveu model. The second is a quantum critical point between a quantum spin Hall insulator with spin Sz conservation and the previously mentioned strongly interacting fully gapped phase. At the latter quantum critical point the single-particle excitations remain gapped, while spin and charge gaps both close. We argue that the first quantum phase transition is related to the Z16 classification of the topological superconductor 3He-B phase with interactions, while the second quantum phase transition is a topological phase transition described by a bosonic O (4 ) nonlinear sigma model field theory with a Θ term.
Temperature-Induced Topological Phase Transitions: Promoted versus Suppressed Nontrivial Topology
NASA Astrophysics Data System (ADS)
Antonius, Gabriel; Louie, Steven G.
2016-12-01
Contrary to previous two-band model studies which find increasing temperature would induce a topological phase transition, we show here through first-principles calculations that the opposite is also realizable, depending on the material's full band structure and symmetry of the electron-phonon coupling potential. This finding explains recent experimental results by Wojek et al. [Nat. Commun. 6, 8463 (2015), 10.1038/ncomms9463]. We show that the topological phase diagram of BiTl(S1 -δSeδ)2 as a function of doping and temperature contains two distinct regions with nontrivial topology. In BiTlS2 , the phonons promote the topological phase at high temperature, while in BiTlSe2, the system is driven back into the trivial phase.
Topological quantum phase transitions and topological flat bands on the kagomé lattice.
Liu, Ru; Chen, Wen-Chao; Wang, Yi-Fei; Gong, Chang-De
2012-08-01
We investigate the topological properties of the tight-binding electrons on the two-dimensional kagomé lattice with two kinds of short-range hopping integral and two kinds of staggered magnetic flux. Considering the nearest-neighbor hopping (t(1)) with the staggered flux parameter φ(1) and the next nearest-neighbor hopping (t(2)) with the staggered flux parameter φ(2), we demonstrate a series of topological quantum phase transitions and find some topological bands with high Chern numbers, when tuning one parameter (t(2) or φ(2)) while the others are fixed. We have also found that, in some parameter regions, the system exhibits interesting topological flat bands with Chern number C =± 1 and a large gap above them, and the flatness ratio can reach a high value of about 170.
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.
Multifarious topological quantum phase transitions in two-dimensional topological superconductors.
Liu, Xiao-Ping; Zhou, Yuan; Wang, Yi-Fei; Gong, Chang-De
2016-06-22
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.
Statistical Mechanics of the Geometric Control of Flow Topology in Two-Dimensional Turbulence
NASA Astrophysics Data System (ADS)
Nadiga, Balasubramanya; Loxley, Peter
2013-04-01
We apply the principle of maximum entropy to two dimensional turbulence in a new fashion to predict the effect of geometry on flow topology. We consider two prototypical regimes of turbulence that lead to frequently observed self-organized coherent structures. Our theory predicts bistable behavior that exhibits hysteresis and large abrupt changes in flow topology in one regime; the other regime is predicted to exhibit monstable behavior with a continuous change of flow topology. The predictions are confirmed in fully nonlinear numerical simulations of the two-dimensional Navier-Stokes equation. These results suggest an explanation of the low frequency regime transitions that have been observed in the non-equilibrium setting of this problem. Following further development in the non-equilibrium context, we expect that insights developed in this problem should be useful in developing a better understanding of the phenomenon of low frequency regime transitions that is a pervasive feature of the weather and climate systems. Familiar occurrences of this phenomenon---wherein extreme and abrupt qualitative changes occur, seemingly randomly, after very long periods of apparent stability---include blocking in the extra-tropical winter atmosphere, the bimodality of the Kuroshio extension system, the Dansgaard-Oeschger events, and the glacial-interglacial transitions.
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.
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.
NASA Astrophysics Data System (ADS)
Chen, M. N.; Su, W.; Deng, M. X.; Ruan, Jiawei; Luo, W.; Shao, D. X.; Sheng, L.; Xing, D. Y.
2016-11-01
A great deal of attention has been paid to the topological phases engineered by photonics over the past few years. Here, we propose a topological quantum phase transition to a quantum anomalous Hall (QAH) phase induced by off-resonant circularly polarized light in a two-dimensional system that is initially in a quantum spin Hall phase or a trivial insulator phase. This provides an alternative method to realize the QAH effect, other than magnetic doping. The circularly polarized light effectively creates a Zeeman exchange field and a renormalized Dirac mass, which are tunable by varying the intensity of the light and drive the quantum phase transition. Both the transverse and longitudinal Hall conductivities are studied, and the former is consistent with the topological phase transition when the Fermi level lies in the band gap. A highly controllable spin-polarized longitudinal electrical current can be generated when the Fermi level is in the conduction band, which may be useful for designing topological spintronics.
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.
Understanding the physical systems from their underlying geometrical and topological properties
NASA Astrophysics Data System (ADS)
Cirilo-Lombardo, Diego Julio
2016-01-01
As it is well known, a certain lack of theoretical understanding of the mechanisms governing the various phenomena exists in several areas of physics. In particular, it concerns those which involve transport of charged particles in low dimensions. In this work the physics of the 2-dimensional charge transport with parallel (in plane) magnetic field is analyzed from the geometrical and algebraic viewpoint making emphasis of how the physical interpretation arises from a consistent mathematical formulation of the problem. As a new result of this investigation with respect to the current literature we explicitly show that: (i) the specific form of the low dimensional Dirac equation enforces the field solution to fulfil the Majorana condition, (ii) the quantum Hall effect is successfully explained, (iii) a new topological effect (as the described by the Aharonov-Casher theorems) is presented and (iv) the link with supersymmetrical models is briefly commented.
Geometric Effect on Quantum Anomalous Hall State in Magnetic Topological Insulator
NASA Astrophysics Data System (ADS)
Xing, Yanxia
An intriguing observation on the quantum anomalous Hall (QAH) effect in a magnetic topological insulator (MTI) is the dissipative edge states. With the aid of non-equilibrium Green's functions,the QAH effect in an MTI with a three dimensional effective tight-binding model is studied.We predict that due to geometric structure in the third dimension z,the unideal contact between terminal leads and central scattering region induces the backscattering in the central Hall bar,as the function of split gates. Such backscattering leads to a nonzero longitudinal resistance and quantized Hall resistance, which would explain the dissipative edge states in experiments.A further numerical simulation prove above prediction as well.These results are rewarding on future experimental observations and transport calculations based on first principe.
Metal-Insulator Transition and Topological Properties of Pyrochlore Iridates
NASA Astrophysics Data System (ADS)
Zhang, Hongbin; Haule, Kristjan; Vanderbilt, David
2017-01-01
Combining density functional theory (DFT) and embedded dynamical mean-field theory (DMFT) methods, we study the metal-insulator transition in R2Ir2 O7 (R =Y , Eu, Sm, Nd, Pr, and Bi) and the topological nature of the insulating compounds. Accurate free energies evaluated using the charge self-consistent DFT +DMFT method reveal that the metal-insulator transition occurs for an A -cation radius between that of Nd and Pr, in agreement with experiments. The all-in-all-out magnetic phase, which is stable in the Nd compound but not the Pr one, gives rise to a small Ir4 + magnetic moment of ≈0.4 μB and opens a sizable correlated gap. We demonstrate that within this state-of-the-art theoretical method, the insulating bulk pyrochlore iridates are topologically trivial.
Soap-film dynamics and topological transitions under continuous deformation*
NASA Astrophysics Data System (ADS)
Moffatt, H. K.; Goldstein, Raymond E.; Pesci, Adriana I.
2016-10-01
The response of a soap film to the continuous deformation of its wire boundary is considered, with particular attention to the topological transitions that can occur at critical stages of the deformation process. Two well-known examples that have been studied by both theory and experiment are the catenoid suspended between circular wires in parallel planes, and the Möbius-strip soap film spanning a wire that is twisted and folded back on itself. In this latter case, we have shown in previous publications that, when the wire is unfolded, the soap film undergoes a topological transition through a boundary singularity to a two-sided film, with a corresponding jump in the linking number between the axis of the wire and the Plateau boundary on its surface. Here, we review this particular aspect of the problem, and propose a simplified model experiment through which the slipping adjustment of a Plateau border on a solid surface may be investigated.
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 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. Finally, 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.
Thermally Driven Electronic Topological Transition in FeTi
Yang, F. C.; Muñoz, J. A.; Hellman, O.; ...
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
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
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
2015-09-08
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.
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.
Cho, Gil Young; Moon, Eun-Gook
2016-01-21
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 phase transition and electrically tunable diamagnetism in silicene
NASA Astrophysics Data System (ADS)
Ezawa, M.
2012-11-01
Silicene is a monolayer of silicon atoms forming a honeycomb lattice. The lattice is actually made of two sublattices with a tiny separation. Silicene is a topological insulator, which is characterized by a full insulating gap in the bulk and helical gapless edges. It undergoes a phase transition from a topological insulator to a band insulator by applying external electric field. Analyzing the spin Chern number based on the effective Dirac theory, we find the origin to be a pseudospin meron in the momentum space. The peudospin degree of freedom arises from the two-sublattice structure. Our analysis makes clear the mechanism how a phase transition occurs from a topological insulator to a band insulator under increasing electric field. We propose a method to determine the critical electric field with the aid of diamagnetism of silicene. Diamagnetism is tunable by the external electric field, and exhibits a singular behaviour at the critical electric field. Our result is important also from the viewpoint of cross correlation between electric field and magnetism. Furthermore, nano-electromechanic devices transforming electric force to mechanical force may be feasible. Our finding will be important for future electro-magnetic correlated devices.
Topological Phase Transition in Metallic Single-Wall Carbon Nanotube
NASA Astrophysics Data System (ADS)
Okuyama, Rin; Izumida, Wataru; Eto, Mikio
2017-01-01
The topological phase transition is theoretically studied in a metallic single-wall carbon nanotube (SWNT) by applying a magnetic field B parallel to the tube. The Z topological invariant, winding number, is changed discontinuously when a small band gap is closed at a critical value of B, which can be observed as a change in the number of edge states owing to the bulk-edge correspondence. This is confirmed by numerical calculations for finite SWNTs of ˜1 µm length, using a one-dimensional lattice model to effectively describe the mixing between σ and π orbitals and spin-orbit interaction, which are relevant to the formation of the band gap in metallic SWNTs.
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.
Dirac point movement and topological phase transition in patterned graphene.
Dvorak, Marc; Wu, Zhigang
2015-02-28
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.
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.
Topology Optimisation of Wideband Coaxial-to-Waveguide Transitions.
Hassan, Emadeldeen; Noreland, Daniel; Wadbro, Eddie; Berggren, Martin
2017-03-23
To maximize the matching between a coaxial cable and rectangular waveguides, we present a computational topology optimisation approach that decides for each point in a given domain whether to hold a good conductor or a good dielectric. The conductivity is determined by a gradient-based optimisation method that relies on finite-difference time-domain solutions to the 3D Maxwell's equations. Unlike previously reported results in the literature for this kind of problems, our design algorithm can efficiently handle tens of thousands of design variables that can allow novel conceptual waveguide designs. We demonstrate the effectiveness of the approach by presenting optimised transitions with reflection coefficients lower than -15 dB over more than a 60% bandwidth, both for right-angle and end-launcher configurations. The performance of the proposed transitions is cross-verified with a commercial software, and one design case is validated experimentally.
Topology Optimisation of Wideband Coaxial-to-Waveguide Transitions
Hassan, Emadeldeen; Noreland, Daniel; Wadbro, Eddie; Berggren, Martin
2017-01-01
To maximize the matching between a coaxial cable and rectangular waveguides, we present a computational topology optimisation approach that decides for each point in a given domain whether to hold a good conductor or a good dielectric. The conductivity is determined by a gradient-based optimisation method that relies on finite-difference time-domain solutions to the 3D Maxwell’s equations. Unlike previously reported results in the literature for this kind of problems, our design algorithm can efficiently handle tens of thousands of design variables that can allow novel conceptual waveguide designs. We demonstrate the effectiveness of the approach by presenting optimised transitions with reflection coefficients lower than −15 dB over more than a 60% bandwidth, both for right-angle and end-launcher configurations. The performance of the proposed transitions is cross-verified with a commercial software, and one design case is validated experimentally. PMID:28332585
Topology Optimisation of Wideband Coaxial-to-Waveguide Transitions
NASA Astrophysics Data System (ADS)
Hassan, Emadeldeen; Noreland, Daniel; Wadbro, Eddie; Berggren, Martin
2017-03-01
To maximize the matching between a coaxial cable and rectangular waveguides, we present a computational topology optimisation approach that decides for each point in a given domain whether to hold a good conductor or a good dielectric. The conductivity is determined by a gradient-based optimisation method that relies on finite-difference time-domain solutions to the 3D Maxwell’s equations. Unlike previously reported results in the literature for this kind of problems, our design algorithm can efficiently handle tens of thousands of design variables that can allow novel conceptual waveguide designs. We demonstrate the effectiveness of the approach by presenting optimised transitions with reflection coefficients lower than ‑15 dB over more than a 60% bandwidth, both for right-angle and end-launcher configurations. The performance of the proposed transitions is cross-verified with a commercial software, and one design case is validated experimentally.
Disorder-induced topological phase transitions in two-dimensional spin-orbit coupled superconductors
NASA Astrophysics Data System (ADS)
Qin, Wei; Xiao, Di; Chang, Kai; Shen, Shun-Qing; Zhang, Zhenyu
2016-12-01
Normal superconductors with Rashba spin-orbit coupling have been explored as candidate systems of topological superconductors. Here we present a comparative theoretical study of the effects of different types of disorder on the topological phases of two-dimensional Rashba spin-orbit coupled superconductors. First, we show that a topologically trivial superconductor can be driven into a chiral topological superconductor upon diluted doping of isolated magnetic disorder, which close and reopen the quasiparticle gap of the paired electrons in a nontrivial manner. Secondly, the superconducting nature of a topological superconductor is found to be robust against Anderson disorder, but the topological nature is not, converting the system into a topologically trivial state even in the weak scattering limit. These topological phase transitions are distinctly characterized by variations in the topological invariant. We discuss the central findings in connection with existing experiments, and provide new schemes towards eventual realization of topological superconductors.
Disorder-induced topological phase transitions in two-dimensional spin-orbit coupled superconductors
Qin, Wei; Xiao, Di; Chang, Kai; Shen, Shun-Qing; Zhang, Zhenyu
2016-01-01
Normal superconductors with Rashba spin-orbit coupling have been explored as candidate systems of topological superconductors. Here we present a comparative theoretical study of the effects of different types of disorder on the topological phases of two-dimensional Rashba spin-orbit coupled superconductors. First, we show that a topologically trivial superconductor can be driven into a chiral topological superconductor upon diluted doping of isolated magnetic disorder, which close and reopen the quasiparticle gap of the paired electrons in a nontrivial manner. Secondly, the superconducting nature of a topological superconductor is found to be robust against Anderson disorder, but the topological nature is not, converting the system into a topologically trivial state even in the weak scattering limit. These topological phase transitions are distinctly characterized by variations in the topological invariant. We discuss the central findings in connection with existing experiments, and provide new schemes towards eventual realization of topological superconductors. PMID:27991541
Exact result on topology and phase transitions at any finite N.
Casetti, Lapo; Cohen, E G D; Pettini, Marco
2002-03-01
We study analytically the topology of a family of submanifolds of the configuration space of the mean-field XY model, computing also a topological invariant (the Euler characteristic). We prove that a particular topological change of these submanifolds is connected to the phase transition of this system, and exists also at finite N. The present result is the first analytic proof that a phase transition has a topological origin and provides a key to a possible better understanding of the origin of phase transitions at their deepest level, as well as to a possible definition of phase transitions at finite N.
NASA Astrophysics Data System (ADS)
Li, Linhu; Castro, Eduardo V.; Sacramento, Pedro D.
2016-11-01
The effect of strain in zigzag ribbons of monolayer transition-metal dichalcogenides with induced superconductivity is studied using a minimal three-band tight-binding model. The unstrained system shows a topological phase with Majorana zero modes localized at the boundaries of the one-dimensional (1D) zigzag edges. By direct inspection of the spectrum and wave functions we examine the evolution of the topological phase as an in-plane, uniaxial deformation is imposed. It is found that strain shifts the energy of 1D edge states, thus causing a topological phase transition which eliminates the Majorana modes. For realistic parameter values, we show that the effect of strain can be changed from completely destructive—in which case a small built-in strain is enough to destroy the topological phase—to a situation where strain becomes an effective tuning parameter which can be used to manipulate Majorana zero modes. These two regimes are accessible by increasing the value of the applied Zeeman field within realistic values. We also study how strain effects are affected by the chemical potential, showing, in particular, how unwanted effects can be minimized. Finally, as a cross-check of the obtained results, we reveal the connection between 1D Majorana zero modes in the zigzag edge and the multiband Berry phase, which serves as a topological invariant of this system.
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.
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.
Zhang, Qianfan; Zhang, Zhiyong; Zhu, Zhiyong; Schwingenschlögl, Udo; Cui, Yi
2012-03-27
Topological insulator is a new state of matter attracting tremendous interest due to its gapless linear dispersion and spin momentum locking topological states located near the surface. Heterostructures, which have traditionally been powerful in controlling the electronic properties of semiconductor devices, are interesting for topological insulators. Here, we studied the spatial distribution of the topological state in Sb(2)Se(3)-Bi(2)Se(3) heterostructures by first-principle simulation and discovered that an exotic topological state exists. Surprisingly, the state migrates from the nontrivial Bi(2)Se(3) into the trivial Sb(2)Se(3) region and spreads across the entire Sb(2)Se(3) slab, extending beyond the concept of "surface" state while preserving all of the topological surface state characteristics. This unusual topological state arises from the coupling between different materials and the modification of electronic structure near Fermi energy. Our study demonstrates that heterostructures can open up opportunities for controlling the real-space distribution of the topological state and inducing quantum phase transitions between topologically trivial and nontrivial states.
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.
Quantum phase transitions and topological proximity effects in graphene nanoribbon heterostructures.
Zhang, Gufeng; Li, Xiaoguang; Wu, Guangfen; Wang, Jie; Culcer, Dimitrie; Kaxiras, Efthimios; Zhang, Zhenyu
2014-03-21
Topological insulators are bulk insulators that possess robust chiral conducting states along their interfaces with normal insulators. A tremendous research effort has recently been devoted to topological insulator-based heterostructures, in which conventional proximity effects give rise to a series of exotic physical phenomena. Here we establish the potential existence of topological proximity effects at the interface between a topological insulator and a normal insulator, using graphene-based heterostructures as prototypical systems. Unlike conventional proximity effects in topological insulator based heterostructures, which refer to various phase transitions associated with the symmetry breaking of specific local order parameters, topological proximity effects describe the rich variety of quantum phase transitions associated with the global properties of the system measured by the location of the topological edge states. Specifically, we show that the location of the topological edge states exhibits a versatile tunability as a function of the interface orientation, the strength of the interface tunnel coupling between a topological graphene nanoribbon and a normal graphene nanoribbon, the spin-orbit coupling strength in the normal graphene nanoribbon, and the width of the system. For zigzag and bearded graphene nanoribbons, the topological edge states can be tuned to be either at the interface or outer edge of the normal ribbon. For armchair graphene nanoribbons, the potential location of the topological edge state can be further shifted to the edge of or within the normal ribbon, to the interface, or diving into the topological graphene nanoribbon. We further show that the topological phase diagram established for the prototypical graphene heterostructures can also explain the intriguing quantum phase transition reported recently in other topological-insulator heterostructures. We also discuss potential experimental realizations of the predicted topological
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.
Topological phase transition induced by atomic displacements in PbS and PbTe
NASA Astrophysics Data System (ADS)
Kim, Jinwoong; Jhi, Seung-Hoon
2013-03-01
Discovery of 3D topological insulator initiates exploration of finding new materials having topological insulating phase or mechanisms for topological phase transitions. Introducing interactions or strains into non-interacting electron systems, for example, can produce non-trivial topological phases in them otherwise having trivial band insulating phase at equilibrium conditions. Using first-principles methods, we study emerging topological phases in band insulating PbS and PbTe, which are induced by selective atomic displacements. Phonon modes corresponding to the displacements are identified and conditions of inducing the topological phase transition are suggested. We show that surface states develop flickering Dirac cones at band-inversion k-points upon dynamic atomic displacements with sufficient amplitude. Our results demonstrate that elementary excitation modes like phonon can induce topological phases in trivial band insulators.
Topological phase transitions in group IV-VI semiconductors by phonons
NASA Astrophysics Data System (ADS)
Kim, Jinwoong; Jhi, Seung-Hoon
2015-09-01
The topological insulator has an intriguing electronic structure in that it has nontrivial topology enforcing the helical Dirac fermionic states at interfaces to the band insulators. Protected by the time-reversal symmetry and finite band gaps in the bulk, the topology is immune to external nonmagnetic perturbations. One essential question is whether elementary excitations in solids like phonons can trigger a transition in the topological property of the electronic structures. Here we investigate the development of topological insulating phases in IV-VI compounds under dynamic lattice deformations using first-principles calculations. Unlike the static state of topological phases at equilibrium conditions, we show that nontrivial topological phases are induced in the compounds by the dynamic lattice deformations from selective phonon modes. Calculations of the time-reversal polarization show that the Z2 invariant of the compounds is flipped by the selective phonon modes and that the compounds exhibit oscillating topological phases upon dynamic lattice deformations.
First-order character and observable signatures of topological quantum phase transitions.
Amaricci, A; Budich, J C; Capone, M; Trauzettel, B; Sangiovanni, G
2015-05-08
Topological quantum phase transitions are characterized by changes in global topological invariants. These invariants classify many-body systems beyond the conventional paradigm of local order parameters describing spontaneous symmetry breaking. For noninteracting electrons, it is well understood that such transitions are continuous and always accompanied by a gap closing in the energy spectrum, given that the symmetries protecting the topological phase are maintained. Here, we demonstrate that a sufficiently strong electron-electron interaction can fundamentally change the situation: we discover a topological quantum phase transition of first-order character in the genuine thermodynamic sense that occurs without a gap closing. Our theoretical study reveals the existence of a quantum critical endpoint associated with an orbital instability on the transition line between a 2D topological insulator and a trivial band insulator. Remarkably, this phenomenon entails unambiguous signatures related to the orbital occupations that can be detected experimentally.
Topological quantum phase transitions and edge states in spin-orbital coupled Fermi gases.
Zhou, Tao; Gao, Yi; Wang, Z D
2014-06-11
We study superconducting states in the presence of spin-orbital coupling and Zeeman field. It is found that a phase transition from a Fulde-Ferrell-Larkin-Ovchinnikov state to the topological superconducting state occurs upon increasing the spin-orbital coupling. The nature of this topological phase transition and its critical property are investigated numerically. Physical properties of the topological superconducting phase are also explored. Moreover, the local density of states is calculated, through which the topological feature may be tested experimentally.
Unconventional transformation of spin Dirac phase across a topological quantum phase transition
Xu, Su -Yang; Neupane, Madhab; Belopolski, Ilya; Liu, Chang; Alidoust, Nasser; Bian, Guang; Jia, Shuang; Landolt, Gabriel; Slomski, Batosz; Dil, J. Hugo; Shibayev, Pavel P.; Basak, Susmita; Chang, Tay -Rong; Jeng, Horng -Tay; Cava, Robert J.; Lin, Hsin; Bansil, Arun; Hasan, M. Zahid
2015-04-17
The topology of a topological material can be encoded in its surface states. These surface states can only be removed by a bulk topological quantum phase transition into a trivial phase. Here we use photoemission spectroscopy to image the formation of protected surface states in a topological insulator as we chemically tune the system through a topological transition. Surprisingly, we discover an exotic spin-momentum locked, gapped surface state in the trivial phase that shares many important properties with the actual topological surface state in anticipation of the change of topology. Using a spin-resolved measurement, we show that apart from a surface bandgap these states develop spin textures similar to the topological surface states well before the transition. Our results provide a general paradigm for understanding how surface states in topological phases arise from a quantum phase transition and are suggestive for the future realization of Weyl arcs, condensed matter supersymmetry and other fascinating phenomena in the vicinity of a quantum criticality.
Unconventional transformation of spin Dirac phase across a topological quantum phase transition
Xu, Su -Yang; Neupane, Madhab; Belopolski, Ilya; ...
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 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.
Nagarajan, Mahesh B.; Coan, Paola; Huber, Markus B.; Diemoz, Paul C.; Wismüller, Axel
2015-01-01
Phase contrast X-ray computed tomography (PCI-CT) has attracted significant interest in recent years for its ability to provide significantly improved image contrast in low absorbing materials such as soft biological tissue. In the research context of cartilage imaging, previous studies have demonstrated the ability of PCI-CT to visualize structural details of human patellar cartilage matrix and capture changes to chondrocyte organization induced by osteoarthritis. This study evaluates the use of geometrical and topological features for volumetric characterization of such chondrocyte patterns in the presence (or absence) of osteoarthritic damage. Geometrical features derived from the scaling index method (SIM) and topological features derived from Minkowski Functionals were extracted from 1392 volumes of interest (VOI) annotated on PCI-CT images of ex vivo human patellar cartilage specimens. These features were subsequently used in a machine learning task with support vector regression to classify VOIs as healthy or osteoarthritic; classification performance was evaluated using the area under the receiver-operating characteristic (ROC) curve (AUC). Our results show that the classification performance of SIM-derived geometrical features (AUC: 0.90 ± 0.09) significantly outperform Minkowski Functionals volume (AUC: 0.54 ± 0.02), surface (AUC: 0.72 ± 0.06), mean breadth (AUC: 0.74 ± 0.06) and Euler characteristic (AUC: 0.78 ± 0.04) (p < 10−4). These results suggest that such geometrical features can provide a detailed characterization of the chondrocyte organization in the cartilage matrix in an automated manner, while also enabling classification of cartilage as healthy or osteoarthritic with high accuracy. Such features could potentially serve as diagnostic imaging markers for evaluating osteoarthritis progression and its response to different therapeutic intervention strategies. PMID:26142112
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.
Zhang, G; Stillinger, F H; Torquato, S
2016-12-28
Disordered hyperuniform many-particle systems have attracted considerable recent attention, since they behave like crystals in the manner in which they suppress large-scale density fluctuations, and yet also resemble statistically isotropic liquids and glasses with no Bragg peaks. One important class of such systems is the classical ground states of "stealthy potentials." The degree of order of such ground states depends on a tuning parameter χ. Previous studies have shown that these ground-state point configurations can be counterintuitively disordered, infinitely degenerate, and endowed with novel physical properties (e.g., negative thermal expansion behavior). In this paper, we focus on the disordered regime (0 < χ < 1/2) in which there is no long-range order and control the degree of short-range order. We map these stealthy disordered hyperuniform point configurations to two-phase media by circumscribing each point with a possibly overlapping sphere of a common radius a: the "particle" and "void" phases are taken to be the space interior and exterior to the spheres, respectively. The hyperuniformity of such two-phase media depends on the sphere sizes: While it was previously analytically proven that the resulting two-phase media maintain hyperuniformity if spheres do not overlap, here we show numerically that they lose hyperuniformity whenever the spheres overlap. We study certain transport properties of these systems, including the effective diffusion coefficient of point particles diffusing in the void phase as well as static and time-dependent characteristics associated with diffusion-controlled reactions. Besides these effective transport properties, we also investigate several related structural properties, including pore-size functions, quantizer error, an order metric, and percolation thresholds. We show that these transport, geometrical, and topological properties of our two-phase media derived from decorated stealthy ground states are distinctly
Existence of topological nontrivial surface states in strained transition metals: W, Ta, Mo, and Nb
NASA Astrophysics Data System (ADS)
Thonig, Danny; Rauch, Tomáš; Mirhosseini, Hossein; Henk, Jürgen; Mertig, Ingrid; Wortelen, Henry; Engelkamp, Bernd; Schmidt, Anke B.; Donath, Markus
2016-10-01
We show that a series of transition metals with strained body-centered cubic lattice—W, Ta, Nb, and Mo—hosts surface states that are topologically protected by mirror symmetry and, thus, exhibits nonzero topological invariants. These findings extend the class of topologically nontrivial systems by topological crystalline transition metals. The investigation is based on calculations of the electronic structures and of topological invariants. The signatures of a Dirac-type surface state in W(110), e.g., the linear dispersion and the spin texture, are verified. To further support our prediction, we investigate Ta(110) both theoretically and experimentally by spin-resolved inverse photoemission: unoccupied topologically nontrivial surface states are observed.
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
2016-04-22
Many phenomena in solid-state physics can be understood in terms of their topological properties. Recently, controlled protocols of quantum walk (QW) are proving to be effective simulators of such phenomena. Here we report the realization of a photonic QW showing both the trivial and the non-trivial topologies associated with chiral symmetry in one-dimensional (1D) periodic systems. We find that the probability distribution moments of the walker position after many steps can be used as direct indicators of the topological quantum transition: while varying a control parameter that defines the system phase, these moments exhibit a slope discontinuity at the transition point. Numerical simulations strongly support the conjecture that these features are general of 1D topological systems. Extending this approach to higher dimensions, different topological classes, and other typologies of quantum phases may offer general instruments for investigating and experimentally detecting quantum transitions in such complex systems.
Topological quantum phase transitions on the kagomé and square-octagon lattices.
Liu, Xiao-Ping; Chen, Wen-Chao; Wang, Yi-Fei; Gong, Chang-De
2013-07-31
We study the topological quantum phase transitions of tight-binding electrons on two representative multi-band lattice models with superimposed staggered fluxes: the kagomé lattice and the square-octagon lattice. By considering the nearest-neighbor and next-nearest-neighbor hopping parameters (t1 and t2) and the staggered flux parameter φ, we obtain rich topological quantum phase transitions for both the lattices. The whole phase diagram for the kagomé lattice in the t2-φ parameter space is obtained. We also illustrate a series of topological quantum phase transitions as well as topological bands of high Chern numbers for the square-octagon lattice. Furthermore, interesting topological flat bands with high flatness ratios (e.g. of about 43) are found in the square-octagon lattice, especially when the next-next-nearest-neighbor hopping (t3) is included.
Exploration of Geometric Noise Suppression in Transition Edge Sensors
NASA Technical Reports Server (NTRS)
Chervenak, J. A.; Allen, C. A.; Abrahams, J. A.; Miller, T. M.; Talley, D. J.; Staguhn, J. G.; Benford, D. J.; Mosely, S. H.; Finkbeiner, F. M.; Brekosky, R. G.
2004-01-01
We present noise data on Mo/Au superconducting transition edge sensors featuring the noise suppression geometry using normal metal bars transverse to the bias current. The effectiveness of the bars in far-infrared bolometers and x-ray microcalorimeters is evaluated. We have examined the effect of the resistivity of the superconducting bilayer on excess noise in bolometer devices. We have also studied the effect of bar density on energy resolution in x-ray devices. We address the question of whether the reduction is noise is necessarily coupled to a reduction in the effective transition sharpness. We propose a fabrication technique experiment to examine the dependence of alpha and noise suppression in similar transverse bar densities.
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.
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 Technical Reports Server (NTRS)
Checlair, Jade; McKay, Christopher P.; Imanaka, Hiroshi
2016-01-01
Extensive studies characterizing Titan present an opportunity to study the atmospheric properties of Titan-like exoplanets. Using an existing model of Titan's atmospheric haze, we computed geometric albedo spectra and effective transit height spectra for six values of the haze production rate (zero haze to twice present) over a wide range of wavelengths (0.2-2 microns). In the geometric albedo spectra, the slope in the UV-visible changes from blue to red when varying the haze production rate values from zero to twice the current Titan value. This spectral feature is the most effective way to characterize the haze production rates. Methane absorption bands in the visible-NIR compete with the absorbing haze, being more prominent for smaller haze production rates. The effective transit heights probe a region of the atmosphere where the haze and gas are optically thin and that is thus not effectively probed by the geometric albedo. The effective transit height decreases smoothly with increasing wavelength, from 376 km to 123 km at 0.2 and 2 microns, respectively. When decreasing the haze production rate, the methane absorption bands become more prominent, and the effective transit height decreases with a steeper slope with increasing wavelength. The slope of the geometric albedo in the UV-visible increases smoothly with increasing haze production rate, while the slope of the effective transit height spectra is not sensitive to the haze production rate other than showing a sharp rise when the haze production rate increases from zero. We conclude that geometric albedo spectra provide the most sensitive indicator of the haze production rate and the background Rayleigh gas. Our results suggest that important and complementary information can be obtained from the geometric albedo and motivates improvements in the technology for direct imaging of nearby exoplanets.
NASA Astrophysics Data System (ADS)
Chen, Wei; Legner, Markus; Rüegg, Andreas; Sigrist, Manfred
2017-02-01
The correlation functions related to topological phase transitions in inversion-symmetric lattice models described by 2 ×2 Dirac Hamiltonians are discussed. In one dimension, the correlation function measures the charge-polarization correlation between Wannier states at different positions, while in two dimensions it measures the itinerant-circulation correlation between Wannier states. The correlation function is nonzero in both the topologically trivial and nontrivial states, and allows us to extract a correlation length that diverges at topological phase transitions. The correlation length and the curvature function that defines the topological invariants are shown to have universal critical exponents, allowing the notion of universality classes to be introduced. Particularly in two dimensions, the universality class is determined by the orbital symmetry of the Dirac model. The scaling laws that constrain the critical exponents are revealed, and are predicted to be satisfied even in interacting systems, as demonstrated in an interacting topological Kondo insulator.
Fermi points and topological quantum phase transitions in a multi-band superconductor.
Puel, T O; Sacramento, P D; Continentino, M A
2015-10-28
The importance of models with an exact solution for the study of materials with non-trivial topological properties has been extensively demonstrated. The Kitaev model plays a guiding role in the search for Majorana modes in condensed matter systems. Also, the sp-chain with an anti-symmetric mixing among the s and p bands is a paradigmatic example of a topological insulator with well understood properties. Interestingly, these models share the same universality class for their topological quantum phase transitions. In this work we study a two-band model of spinless fermions with attractive inter-band interactions. We obtain its zero temperature phase diagram, which presents a rich variety of phases including a Weyl superconductor and a topological insulator. The transition from the topological to the trivial superconducting phase has critical exponents different from those of Kitaev's model.
Zeeman-Field-Tuned Topological Phase Transitions in a Two-Dimensional Class-DIII Superconductor
Deng, W. Y.; Geng, H.; Luo, W.; Sheng, L.; Xing, D. Y.
2016-01-01
We investigate the topological phase transitions in a two-dimensional time-reversal invariant topological superconductor in the presence of a Zeeman field. Based on the spin Chern number theory, we find that the system exhibits a number of topologically distinct phases with changing the out-of-plane component of the Zeeman field, including a quantum spin Hall-like phase, quantum anomalous Hall-like phases with total Chern number C = −2, −1, 1 and 2, and a topologically trivial superconductor phase. The BdG band gap closes at each boundary of the phase transitions. Furthermore, we demonstrate that the zero bias conductance provides clear transport signatures of the different topological phases, which are robust against symmetry-breaking perturbations. PMID:27148675
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
Efficient Geometric Probabilities of Multi-Transiting Exoplanetary Systems from CORBITS
NASA Astrophysics Data System (ADS)
Brakensiek, Joshua; Ragozzine, Darin
2016-04-01
NASA’s Kepler Space Telescope has successfully discovered thousands of exoplanet candidates using the transit method, including hundreds of stars with multiple transiting planets. In order to estimate the frequency of these valuable systems, it is essential to account for the unique geometric probabilities of detecting multiple transiting extrasolar planets around the same parent star. In order to improve on previous studies that used numerical methods, we have constructed an efficient, semi-analytical algorithm called the Computed Occurrence of Revolving Bodies for the Investigation of Transiting Systems (CORBITS), which, given a collection of conjectured exoplanets orbiting a star, computes the probability that any particular group of exoplanets can be observed to transit. The algorithm applies theorems of elementary differential geometry to compute the areas bounded by circular curves on the surface of a sphere. The implemented algorithm is more accurate and orders of magnitude faster than previous algorithms, based on comparisons with Monte Carlo simulations. We use CORBITS to show that the present solar system would only show a maximum of three transiting planets, but that this varies over time due to dynamical evolution. We also used CORBITS to geometrically debias the period ratio and mutual Hill sphere distributions of Kepler's multi-transiting planet candidates, which results in shifting these distributions toward slightly larger values. In an Appendix, we present additional semi-analytical methods for determining the frequency of exoplanet mutual events, i.e., the geometric probability that two planets will transit each other (planet-planet occultation, relevant to transiting circumbinary planets) and the probability that this transit occurs simultaneously as they transit their star. The CORBITS algorithms and several worked examples are publicly available.
NASA Astrophysics Data System (ADS)
Goswami, Pallab; Chakravarty, Sudip
2017-02-01
The quantum phase transition between two clean, noninteracting topologically distinct gapped states in three dimensions is governed by a massless Dirac fermion fixed point, irrespective of the underlying symmetry class, and this constitutes a remarkably simple example of superuniversality. For a sufficiently weak disorder strength, we show that the massless Dirac fixed point is at the heart of the robustness of superuniversality. We establish this by considering both perturbative and nonperturbative effects of disorder. The superuniversality breaks down at a critical strength of disorder, beyond which the topologically distinct localized phases become separated by a delocalized diffusive phase. In the global phase diagram, the disorder controlled fixed point where superuniversality is lost, serves as a multicritical point, where the delocalized diffusive and two topologically distinct localized phases meet and the nature of the localization-delocalization transition depends on the underlying symmetry class. Based on these features, we construct the global phase diagrams of noninteracting, dirty topological systems in three dimensions. We also establish a similar structure of the phase diagram and the superuniversality for weak disorder in higher spatial dimensions. By noting that 1 /r2 power-law correlated disorder acts as a marginal perturbation for massless Dirac fermions in any spatial dimension d , we have established a general renormalization group framework for addressing disorder driven critical phenomena for fixed spatial dimension d >2 .
Electronic and geometric structure of transition-metal nanoclusters
Jennison, D.R.; Schultz, P.A.; Sears, M.P.; Klitsner, T.
1996-08-01
A massively-parallel ab initio computer code, which uses Gaussian bases, pseudopotentials, and the local density approximation, permits the study of transition-metal systems with literally hundreds of atoms. We present total energies and relaxed geometries for Ru, Pd, and Ag clusters with N = 55, 135, and 140 atoms; we also used the DMOL code to study 13-atom Pd and Cu clusters, with and without hydrogen. The N = 55 and 135 clusters were chosen because of simultaneous cubo-octahedral (fcc) and icosahedral (icos) sub-shell closings, and we find icos geometries are preferred. Remarkably large compressions of the central atoms are observed for the icos structures (up to 6% compared with bulk interatomic spacings), while small core compressions ({approx} 1 %) are found for the fcc geometry. In contrast, large surface compressive relaxations are found for the fcc clusters ({approx} 2-3% in average nearest neighbor spacing), while the icos surface displays small compressions ({approx} 1%). Energy differences between icos and fcc are smallest for Pd, and for all systems the single-particle densities of states closely resembles bulk results. Calculations with N = 134 suggest slow changes in relative energy with N. Noting that the 135-atom fcc has a much more open surface than the icos, we also compare N = 140 icos and fcc, the latter forming an octahedron with close packed facets. These icos and fcc clusters have identical average coordinations and the octahedron is found to be preferred for Ru and Pd but not for Ag. Finally, we compare Harris functional and LDA energy differences on the N = 140 clusters, and find fair agreement only for Ag.
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.
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.
Interacting weak topological insulators and their transition to Dirac semimetal phases
NASA Astrophysics Data System (ADS)
Sangiovanni, Giorgio; Hanke, Werner; Li, Gang; Trauzettel, Bjoern
Topological insulators in the presence of strong Coulomb interaction constitute novel phases of matter. Transitions between these phases can be driven by single-particle or many-body effects. On the basis of ab-initio calculations, we identify a concrete material, i.e. Ca2PtO4, that turns out to be a hole-doped weak topological insulator. Interestingly, the Pt- d orbitals in this material are relevant for the band inversion that gives rise to the topological phase. Therefore, Coulomb interaction should be of importance in Ca2PtO4. To study the influence of interactions on the weak topological insulating phase, we look at a toy model corresponding to a layer-stacked 3D version of the Bernevig-Hughes-Zhang model with local interactions. For small to intermediate interaction strength, we discover novel interaction-driven topological phase transitions between the weak topological insulator and two Dirac semimetal phases. The latter correspond to gapless topological phases. For strong interactions, the system eventually becomes a Mott insulator. DFG Grant No. Ha 1537/23-1 within the Forschergruppe FOR 1162, SPP Grant Ha 1537/24-2, SFB 1170 ``ToCoTronics'', SPP 1666, the Helmholtz Foundation (VITI), the ``Elitenetzwerk Bayern'' (ENB graduate school on ``Topological insulators'').
Topological phase transition in a ladder of the dimerized Kitaev superconductor chains
NASA Astrophysics Data System (ADS)
Zhou, Bo-Zhen; Zhou, Bin
2016-10-01
We investigate the topological properties of a ladder model of the dimerized Kitaev superconductor chains. The topological class of the system is determined by the relative phase θ between the inter- and intra-chain superconducting pairing. One topological class is the class BDI characterized by the ℤ index, and the other is the class D characterized by the ℤ2 index. For the two different topological classes, the topological phase diagrams of the system are presented by calculating two different topological numbers, i.e., the ℤ index winding number W and the ℤ2 index Majorana number ℳ, respectively. In the case of θ =0, the topological class belongs to the class BDI, multiple topological phase transitions accompanying the variation of the number of Majorana zero modes are observed. In the case of θ =π/2 it belongs to the class D. Our results show that for the given value of dimerization, the topologically nontrivial and trivial phases alternate with the variation of chemical potential. Project supported by the National Natural Science Foundation of China (Grant No. 11274102), the Program for New Century Excellent Talents in University of Ministry of Education of China (Grant No. NCET-11-0960), and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20134208110001).
Topological phase transitions with SO(4) symmetry in (2+1)D interacting Dirac fermions
NASA Astrophysics Data System (ADS)
Xu, Xiao Yan; Beach, K. S. D.; Sun, Kai; Assaad, F. F.; Meng, Zi Yang
2017-02-01
Interaction-driven topological phase transitions in Dirac semimetals are investigated by means of large-scale quantum Monte Carlo simulations. The interaction among Dirac fermions is introduced by coupling them to Ising spins that realize the quantum dynamics of the two-dimensional transverse field Ising model. The ground-state phase diagram, in which the tuning parameters are the transverse field and the coupling between fermion and Ising spins, is determined. At weak and intermediate coupling, a second-order Ising quantum phase transition and a first-order topological phase transition between two topologically distinct Dirac semimetals are observed. Interestingly, at the latter, the Dirac points smear out to form nodal lines in the Brillouin zone, and collective bosonic fluctuations with SO(4) symmetry are strongly enhanced. At strong coupling, these two phase boundaries merge into a first-order transition.
Effect of the type-I to type-II Weyl semimetal topological transition on superconductivity
NASA Astrophysics Data System (ADS)
Li, Dingping; Rosenstein, Baruch; Shapiro, B. Ya.; Shapiro, I.
2017-03-01
The influence of recently discovered topological transition between type-I and type-II Weyl semimetals on superconductivity is considered. A set of Gorkov equations for weak superconductivity in Weyl semimetal under topological phase transition is derived and solved. The critical temperature and superconducting gap both have spikes in the transition point as functions of the tilt parameter of the Dirac cone determined, in turn, by the material parameters like pressure. The spectrum of superconducting excitations is different in two phases: The sharp cone pinnacle is characteristic for type I, while two parallel almost flat bands, are formed in type II. Spectral density is calculated on both sides of transition to demonstrate the different weights of the bands. The superconductivity thus can be used as a clear indicator for the topological transformation. Results are discussed in the light of recent experiments.
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.
NASA Astrophysics Data System (ADS)
Najarbashi, G.; Seifi, B.
2017-02-01
In this paper, we generalize the results of Oh (Phys Lett A 373:644-647, 2009) to Dzyaloshinskii-Moriya model under non-uniform external magnetic field to investigate the relation between entanglement, geometric phase (or Berry phase) and quantum phase transition. We use quaternionic representation to relate the geometric phase to the quantum phase transition. For small values of DM parameter, the Berry phase is more appropriate than the concurrence measure, while for large values, the concurrence is a good indicator to show the phase transition. On the other hand, by increasing the DM interaction the phase transition occurs for large values of anisotropy parameter. In addition, for small values of magnetic field the concurrence measure is appropriate indicator for quantum phase transition, but for large values of magnetic field the Berry phase shows a sharp changes in the phase transition points. The results show that the Berry phase and concurrence form a complementary system from phase transition point of view.
Interacting weak topological insulators and their transition to Dirac semimetal phases
NASA Astrophysics Data System (ADS)
Li, Gang; Hanke, Werner; Sangiovanni, Giorgio; Trauzettel, Björn
2015-12-01
Topological insulators in the presence of a strong Coulomb interaction constitute novel phases of matter. Transitions between these phases can be driven by single-particle or many-body effects. On the basis of ab initio calculations, we identify a concrete material, i.e., Ca2PtO4 , that turns out to be a hole-doped weak topological insulator. Interestingly, the Pt d orbitals in this material are relevant for the band inversion that gives rise to the topological phase. Therefore, Coulomb interactions should be of importance in Ca2PtO4 . To study the influence of interactions on the weak topological insulating phase, we look at a toy model corresponding to a layer-stacked three-dimensional version of the Bernevig-Hughes-Zhang model with local interactions. For a low to intermediate interaction strength, we discover novel interaction-driven topological phase transitions between the weak topological insulator and two Dirac semimetal phases. The latter correspond to gapless topological phases. For strong interactions, the system eventually becomes a Mott insulator.
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.
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.
Geometric entanglement and quantum phase transitions in two-dimensional quantum lattice models
NASA Astrophysics Data System (ADS)
Shi, Qian-Qian; Wang, Hong-Lei; Li, Sheng-Hao; Cho, Sam Young; Batchelor, Murray T.; Zhou, Huan-Qiang
2016-06-01
Geometric entanglement (GE), as a measure of multipartite entanglement, has been investigated as a universal tool to detect phase transitions in quantum many-body lattice models. In this paper we outline a systematic method to compute GE for two-dimensional (2D) quantum many-body lattice models based on the translational invariant structure of infinite projected entangled pair state (iPEPS) representations. By employing this method, the q -state quantum Potts model on the square lattice with q ∈{2 ,3 ,4 ,5 } is investigated as a prototypical example. Further, we have explored three 2D Heisenberg models: the antiferromagnetic spin-1/2 X X X and anisotropic X Y X models in an external magnetic field, and the antiferromagnetic spin-1 X X Z model. We find that continuous GE does not guarantee a continuous phase transition across a phase transition point. We observe and thus classify three different types of continuous GE across a phase transition point: (i) GE is continuous with maximum value at the transition point and the phase transition is continuous, (ii) GE is continuous with maximum value at the transition point but the phase transition is discontinuous, and (iii) GE is continuous with nonmaximum value at the transition point and the phase transition is continuous. For the models under consideration, we find that the second and the third types are related to a point of dual symmetry and a fully polarized phase, respectively.
Quantum topological transition in hyperbolic metamaterials based on high Tc superconductors.
Smolyaninov, Igor I
2014-07-30
Hyperbolic metamaterials are known to exhibit a transition in the topology of the photon iso-frequency surface from a closed ellipsoid to an open hyperboloid, resulting in a considerable increase of the photonic density of states. This topological transition may also be described as a change of metric signature of the effective optical space. Here we demonstrate that high Tc superconductors exhibit hyperbolic metamaterial behavior in the far infrared and THz frequency ranges. In the THz range the hyperbolic behavior occurs only in the normal state, while no propagating photon modes exist in the superconducting state. Thus, a quantum topological transition may be observed for THz photons at zero temperature as a function of the external magnetic field, in which the effective Minkowski spacetime arises in the mixed state of the superconductor at some critical value of the external magnetic field. Nucleation of effective Minkowski spacetime occurs via the formation of quantized Abrikosov vortices.
Criticality of the metal-topological insulator transition driven by disorder
NASA Astrophysics Data System (ADS)
Yamakage, Ai; Nomura, Kentaro; Imura, Ken-Ichiro; Kuramoto, Yoshio
2013-05-01
Employing scaling analysis of the localization length, we deduce the critical exponent of the metal-topological insulator transitions induced by disorder. The obtained exponent ν˜2.7 shows no conspicuous deviation from the value established for metal-ordinary insulator transitions in systems of the symplectic class. We investigate the topological phase diagram upon carrier doping to reveal the nature of the so-called topological Anderson insulator (TAI) region. The critical exponent of the metal-TAI transition is also first estimated, shown to be undistinguishable from the above value within the numerical error. By symmetry considerations we determine the explicit form of Rashba spin-orbit coupling in systems of C4v point group symmetry.
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.
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
NASA Astrophysics Data System (ADS)
den Hollander, Richard J. M.; Bouma, Henri; Baan, Jan; Eendebak, Pieter T.; van Rest, Jeroen H. C.
2015-10-01
Person tracking across non-overlapping cameras and other types of video analytics benefit from spatial calibration information that allows an estimation of the distance between cameras and a relation between pixel coordinates and world coordinates within a camera. In a large environment with many cameras, or for frequent ad-hoc deployments of cameras, the cost of this calibration is high. This creates a barrier for the use of video analytics. Automating the calibration allows for a short configuration time, and the use of video analytics in a wider range of scenarios, including ad-hoc crisis situations and large scale surveillance systems. We show an autocalibration method entirely based on pedestrian detections in surveillance video in multiple non-overlapping cameras. In this paper, we show the two main components of automatic calibration. The first shows the intra-camera geometry estimation that leads to an estimate of the tilt angle, focal length and camera height, which is important for the conversion from pixels to meters and vice versa. The second component shows the inter-camera topology inference that leads to an estimate of the distance between cameras, which is important for spatio-temporal analysis of multi-camera tracking. This paper describes each of these methods and provides results on realistic video data.
NASA Astrophysics Data System (ADS)
Brakensiek, Joshua; Ragozzine, D.
2012-10-01
The transit method for discovering extra-solar planets relies on detecting regular diminutions of light from stars due to the shadows of planets passing in between the star and the observer. NASA's Kepler Mission has successfully discovered thousands of exoplanet candidates using this technique, including hundreds of stars with multiple transiting planets. In order to estimate the frequency of these valuable systems, our research concerns the efficient calculation of geometric probabilities for detecting multiple transiting extrasolar planets around the same parent star. In order to improve on previous studies that used numerical methods (e.g., Ragozzine & Holman 2010, Tremaine & Dong 2011), we have constructed an efficient, analytical algorithm which, given a collection of conjectured exoplanets orbiting a star, computes the probability that any particular group of exoplanets are transiting. The algorithm applies theorems of elementary differential geometry to compute the areas bounded by circular curves on the surface of a sphere (see Ragozzine & Holman 2010). The implemented algorithm is more accurate and orders of magnitude faster than previous algorithms, based on comparison with Monte Carlo simulations. Expanding this work, we have also developed semi-analytical methods for determining the frequency of exoplanet mutual events, i.e., the geometric probability two planets will transit each other (Planet-Planet Occultation) and the probability that this transit occurs simultaneously as they transit their star (Overlapping Double Transits; see Ragozzine & Holman 2010). The latter algorithm can also be applied to calculating the probability of observing transiting circumbinary planets (Doyle et al. 2011, Welsh et al. 2012). All of these algorithms have been coded in C and will be made publicly available. We will present and advertise these codes and illustrate their value for studying exoplanetary systems.
Transition from nonresonant to resonant random lasers by the geometrical confinement of disorder.
Ghofraniha, N; Viola, I; Zacheo, A; Arima, V; Gigli, G; Conti, C
2013-12-01
We report on a transition in random lasers that is induced by the geometrical confinement of the emitting material. Different dye doped paper devices with controlled geometry are fabricated by soft lithography and show two distinguished behaviors in the stimulated emission: in the absence of boundary constraints, the energy threshold decreases for larger laser volumes showing the typical trend of diffusive nonresonant random lasers, while when the same material is lithographed into channels, the walls act as cavity and the resonant behavior typical of standard lasers is observed. The experimental results are consistent with the general theories of random and standard lasers and a clear phase diagram of the transition is reported.
Harvey, Miguel Angel; Suarez, Sebastián; Baggio, Ricardo
2016-11-01
The structures of three related complexes of general formula M(pds)(nab)2 [pds is the peroxodi-sulfate anion and nab is an nitro-gen-containing aromatic base], viz. bis(2,9-dimethyl-1,10-phenanthroline-κ(2)N,N')(peroxodi-sulfato-κ(2)O,O')cadmium, [Cd(S2O8)(C14H12N2)2], (V), bis-(3,4,7,8-tetra-methy-1,10-phenanthroline-κ(2)N,N')(peroxodi-sulfato-κ(2)O,O')zinc, [Zn(S2O8)(C16H16N2)2], (VI), and bis-(3,4,7,8-tetra-methy-1,10-phenanthroline-κ(2)N,N')(peroxodi-sulfato-κ(2)O,O')cadmium, [Cd(S2O8)(C16H16N2)2], (VII), present the same topological coordination, with three chelating ligands in an MN4O2 polyhedron. The main difference resides in the fact that the first two complexes are bis-ected by a crystallographic twofold axis, thus providing a symmetrical environment to the cation, while in the third one this symmetry is disrupted into a clearly unsymmetrical disposition, probably by way of an unusually strong intra-molecular C-H⋯O hydrogen bond. The situation is compared with similar inter-actions in the literature. The structure of (V) is based on a redetermination in the correct space group C2/c of the structure originally described in the Cc space group [Harvey et al. (2001). Aust. J. Chem.54, 307-311; Marsh (2004 ▸). Acta Cryst. B60, 252-253].
Harvey, Miguel Angel; Suarez, Sebastián; Baggio, Ricardo
2016-01-01
The structures of three related complexes of general formula M(pds)(nab)2 [pds is the peroxodisulfate anion and nab is an nitrogen-containing aromatic base], viz. bis(2,9-dimethyl-1,10-phenanthroline-κ2 N,N′)(peroxodisulfato-κ2 O,O′)cadmium, [Cd(S2O8)(C14H12N2)2], (V), bis(3,4,7,8-tetramethy-1,10-phenanthroline-κ2 N,N′)(peroxodisulfato-κ2 O,O′)zinc, [Zn(S2O8)(C16H16N2)2], (VI), and bis(3,4,7,8-tetramethy-1,10-phenanthroline-κ2 N,N′)(peroxodisulfato-κ2 O,O′)cadmium, [Cd(S2O8)(C16H16N2)2], (VII), present the same topological coordination, with three chelating ligands in an MN4O2 polyhedron. The main difference resides in the fact that the first two complexes are bisected by a crystallographic twofold axis, thus providing a symmetrical environment to the cation, while in the third one this symmetry is disrupted into a clearly unsymmetrical disposition, probably by way of an unusually strong intramolecular C—H⋯O hydrogen bond. The situation is compared with similar interactions in the literature. The structure of (V) is based on a redetermination in the correct space group C2/c of the structure originally described in the Cc space group [Harvey et al. (2001). Aust. J. Chem. 54, 307–311; Marsh (2004 ▸). Acta Cryst. B60, 252–253]. PMID:27840713
Glazyrin, K; Pourovskii, L V; Dubrovinsky, L; Narygina, O; McCammon, C; Hewener, B; Schünemann, V; Wolny, J; Muffler, K; Chumakov, A I; Crichton, W; Hanfland, M; Prakapenka, V B; Tasnádi, F; Ekholm, M; Aichhorn, M; Vildosola, V; Ruban, A V; Katsnelson, M I; Abrikosov, I A
2013-03-15
We discover that hcp phases of Fe and Fe(0.9)Ni(0.1) undergo an electronic topological transition at pressures of about 40 GPa. This topological change of the Fermi surface manifests itself through anomalous behavior of the Debye sound velocity, c/a lattice parameter ratio, and Mössbauer center shift observed in our experiments. First-principles simulations within the dynamic mean field approach demonstrate that the transition is induced by many-electron effects. It is absent in one-electron calculations and represents a clear signature of correlation effects in hcp Fe.
First-order transition induced by topological defects in the O (3 ) principal chiral model
NASA Astrophysics Data System (ADS)
Sorokin, A. O.
2017-03-01
Using Monte Carlo simulations, we study thermal and critical properties of two systems, in which domain walls and so-called Z2 vortices as topological defects are presented. The main model is a lattice version of the O (3 ) principal chiral model. We find a first-order transition and give qualitative arguments that the first order is induced by topological defects. We also consider the model of frustrated antiferromagnet on a square lattice with the additional exchange interaction between spins of the third range order. This model belongs to the same symmetry class. In this model, a transition is of first order too.
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
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
Disorder-driven topological phase transition in Bi2Se3 films
Brahlek, Matthew; Koirala, Nikesh; Salehi, Maryam; ...
2016-10-03
Topological insulators (TI) are a phase of matter that host unusual metallic states on their surfaces. Unlike the states that exist on the surface of conventional materials, these so-called topological surfaces states (TSS) are protected against disorder-related localization effects by time reversal symmetry through strong spin-orbit coupling. By combining transport measurements, angle-resolved photo-emission spectroscopy and scanning tunneling microscopy, we show that there exists a critical level of disorder beyond which the TI Bi2Se3 loses its ability to protect the metallic TSS and transitions to a fully insulating state. The absence of the metallic surface channels dictates that there is amore » change in material’s topological character, implying that disorder can lead to a topological phase transition even without breaking the time reversal symmetry. This observation challenges the conventional notion of topologically-protected surface states, and will provoke new studies as to the fundamental nature of topological phase of matter in the presence of disorder.« less
Disorder-driven topological phase transition in B i2S e3 films
NASA Astrophysics Data System (ADS)
Brahlek, Matthew; Koirala, Nikesh; Salehi, Maryam; Moon, Jisoo; Zhang, Wenhan; Li, Haoxiang; Zhou, Xiaoqing; Han, Myung-Geun; Wu, Liang; Emge, Thomas; Lee, Hang-Dong; Xu, Can; Rhee, Seuk Joo; Gustafsson, Torgny; Armitage, N. Peter; Zhu, Yimei; Dessau, Daniel S.; Wu, Weida; Oh, Seongshik
2016-10-01
Topological insulators (TI) are a phase of matter that host unusual metallic surface states. Unlike the states that exist on the surface of conventional materials, these so-called topological surfaces states (TSS) are protected against disorder-related localization effects by time reversal symmetry through strong spin-orbit coupling. By combining transport measurements, angle-resolved photoemission spectroscopy, and scanning tunneling microscopy, we show that there exists a critical level of disorder beyond which the TI B i2S e3 loses its ability to protect the metallic TSS and transitions to a fully insulating state. The absence of the metallic surface channels dictates that there is a change in the material's topological character, implying that disorder can lead to a topological phase transition even without breaking the time reversal symmetry. This observation challenges the conventional notion of topologically protected surface states and should prompt new studies as to the fundamental nature of topological phase of matter in the presence of disorder.
Bona fide interaction-driven topological phase transition in correlated SPT states
NASA Astrophysics Data System (ADS)
Meng, Zi Yang; He, Yuan-Yao; Wu, Han-Qing; You, Yi-Zhuang; Xu, Cenke; Lu, Zhong-Yi
It is expected the interplay between non-trivial band topology and strong electron correlation will lead to very rich physics. Thus a controlled study of the competition between topology and correlation is of great interest. Here, employing large-scale quantum Monte Carlo simulations, we provide a concrete example of the Kane-Mele-Hubbard model on an AA stacking bilayer honeycomb lattice with inter-layer antiferromagnetic interaction. Our simulation identified several different phases: a quantum spin-Hall insulator (QSH), a xy-plane antiferromagnetic Mott insulator (xy-AFM) and an inter-layer dimer-singlet insulator (dimer-singlet). Most importantly, a bona fide topological phase transition between the QSH and the dimer-singlet insulators, purely driven by the inter-layer antiferromagnetic interaction is found. At the transition, the spin and charge gap of the system close while the single-particle excitations remain gapped, which means that this transition has no mean field analogue and it can be viewed as a transition between bosonic SPT states. At one special point, this transition is described by a (2+1)d O(4) nonlinear sigma model with exact SO(4) symmetry, and a topological term at theta=p. Relevance of this work towards more general interacting SPT states is discussed.
Dynamical Quantum Phase Transitions: Role of Topological Nodes in Wave Function Overlaps
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.
Locating topological phase transitions using nonequilibrium signatures in local bulk observables
NASA Astrophysics Data System (ADS)
Roy, Sthitadhi; Moessner, Roderich; Das, Arnab
2017-01-01
Topological quantum phases cannot be characterized by local order parameters in the bulk. In this work, however, we show that nonanalytic signatures of a topological quantum critical point do remain in local observables in the bulk, and manifest themselves as nonanalyticities in their expectation values taken over a family of nonequilibrium states generated using a quantum quench protocol. The signature can be used for precisely locating the critical points in parameter space. A large class of initial states can be chosen for the quench, including finite temperature states. We demonstrate these results in tractable models of noninteracting fermions exhibiting topological phase transitions in one and two spatial dimensions. We also show that the nonanalyticities can be absent if the gap closing is nontopological, i.e., when it corresponds to no phase transition.
Spin Chern number and topological phase transition on the Lieb lattice with spin-orbit coupling
NASA Astrophysics Data System (ADS)
Chen, Rui; Zhou, Bin
2017-03-01
We propose that quantum anomalous Hall effect may occur in the Lieb lattice, when Rashba spin-orbit coupling, spin-independent and spin-dependent staggered potentials are introduced into the lattice. It is found that spin Chern numbers of two degenerate flat bands change from 0 to ±2 due to Rashba spin-orbit coupling effect. The inclusion of Rashba spin-orbit coupling and two kinds of staggered potentials opens a gap between the two flat bands. The topological property of the gap is determined by the amplitudes of Rashba spin-orbit coupling and staggered potentials, and thus the topological phase transition from quantum anomalous Hall effect to normal insulator can occur. Finally, the topological phase transition from quantum spin Hall state to normal insulator is discussed when Rashba spin-orbit coupling and intrinsic spin-orbit coupling coexist in the Lieb lattice.
Theory of topological quantum phase transitions in 3D noncentrosymmetric systems.
Yang, Bohm-Jung; Bahramy, Mohammad Saeed; Arita, Ryotaro; Isobe, Hiroki; Moon, Eun-Gook; Nagaosa, Naoto
2013-02-22
We construct a general theory describing the topological quantum phase transitions in 3D systems with broken inversion symmetry. While the consideration of the system's codimension generally predicts the appearance of a stable metallic phase between the normal and topological insulators, it is shown that a direct topological phase transition between two insulators is also possible when an accidental band crossing occurs along directions with high crystalline symmetry. At the quantum critical point, the energy dispersion becomes quadratic along one direction while the dispersions along the other two orthogonal directions are linear, which manifests the zero chirality of the band touching point. Because of the anisotropic dispersion at quantum critical point, various thermodynamic and transport properties show unusual temperature dependence and anisotropic behaviors.
Quantum anomalous Hall effect and tunable topological states in 3d transition metals doped silicene.
Zhang, Xiao-Long; Liu, Lan-Feng; Liu, Wu-Ming
2013-10-09
Silicene is an intriguing 2D topological material which is closely analogous to graphene but with stronger spin orbit coupling effect and natural compatibility with current silicon-based electronics industry. Here we demonstrate that silicene decorated with certain 3d transition metals (Vanadium) can sustain a stable quantum anomalous Hall effect using both analytical model and first-principles Wannier interpolation. We also predict the quantum valley Hall effect and electrically tunable topological states could be realized in certain transition metal doped silicene where the energy band inversion occurs. Our findings provide new scheme for the realization of quantum anomalous Hall effect and platform for electrically controllable topological states which are highly desirable for future nanoelectronics and spintronics application.
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.
Turbulence Nonlinearities Shed Light on Geometric Asymmetry in Tokamak Confinement Transitions
NASA Astrophysics Data System (ADS)
Cziegler, I.; Hubbard, A. E.; Hughes, J. W.; Terry, J. L.; Tynan, G. R.
2017-03-01
A comprehensive study of fully frequency-resolved nonlinear kinetic energy transfer has been performed for the first time in a diverted tokamak, providing new insight into the parametric dependences of edge turbulence transitions. Measurements using gas puff imaging in the turbulent L -mode state illuminate the source of the long known but as yet unexplained "favorable-unfavorable" geometric asymmetry of the power threshold for transition to the turbulence-suppressed H mode. Results from the recently discovered I mode point to a competition between zonal flow (ZF) and geodesic-acoustic modes (GAM) for turbulent energy, while showing new evidence that the I -to-H transition is still dominated by ZFs. The availability of nonlinear drive for the GAM against net heat flux through the edge corresponds very well to empirical scalings found experimentally for accessing the I mode.
Self-consistent Purcell factor and spontaneous topological transition in hyperbolic metamaterials
NASA Astrophysics Data System (ADS)
Krasikov, Sergey; Iorsh, Ivan V.
2016-10-01
In this work we develop a self-consistent approach for calculation of the Purcell factor and Lamb shift in highly dispersive hyperbolic metamaterial accounting for the effective dipole frequency shift. Also we theoretically predict the possibility of spontaneous topological transition, which occurs not due to the external change of the system parameters but only due to the Lamb shift.
NASA Astrophysics Data System (ADS)
Tuchin, Kirill
2016-12-01
Metastable C P -odd domains of the hot QCD matter are coupled to QED via the chiral anomaly. The topology of electromagnetic field in these domains is characterized by magnetic helicity. It is argued, using the Maxwell-Chern-Simons model, that spatial inhomogeneity of the domains induces spontaneous transitions of electromagnetic field between the opposite magnetic helicity states.
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.
Signatures of topological quantum phase transitions in driven and dissipative qubit arrays
NASA Astrophysics Data System (ADS)
Dong, Y. L.; Neupert, Titus; Chitra, R.; Schmidt, Sebastian
2016-07-01
We study photonic signatures of symmetry broken and topological phases in a driven, dissipative circuit QED realization of spin-1/2 chains. Specifically, we consider the transverse-field XY model and a dual model with three-spin interactions. The former has a ferromagnetic and a paramagnetic phase, while the latter features, in addition, a symmetry protected topological phase. Using the method of third quantization, we calculate the nonequilibrium steady state of the open spin chains for arbitrary system sizes and temperatures. We find that the bilocal correlation function of the spins at both ends of the chain provides a sensitive measure for both symmetry-breaking and topological phase transitions of the systems, but no universal means to distinguish between the two types of transitions. Both models have equivalent representations in terms of free Majorana fermions, which host zero, one and two topological Majorana end modes in the paramagnetic, ferromagnetic, and symmetry protected topological phases, respectively. The correlation function we study retains its bilocal character in the fermionic representation, so that our results are equally applicable to the fermionic models in their own right. We propose a photonic realization of the dissipative transverse-field XY model in a tunable setup, where an array of superconducting transmon qubits is coupled at both ends to a photonic microwave circuit.
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.
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.
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 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).
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.
Electric control of topological phase transitions in Dirac semimetal thin films
NASA Astrophysics Data System (ADS)
Pan, Hui; Wu, Meimei; Liu, Ying; Yang, Shengyuan A.
2015-09-01
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.
NASA Astrophysics Data System (ADS)
Hung, Hsiang-Hsuan; Chua, Victor; Wang, Lei; Fiete, Gregory A.
2014-06-01
We theoretically study topological phase transitions in four generalized versions of the Kane-Mele-Hubbard model with up to 2×182 sites. All models are free of the fermion-sign problem allowing numerically exact quantum Monte Carlo (QMC) calculations to be performed to extremely low temperatures. We numerically compute the Z2 invariant and spin Chern number Cσ directly from the zero-frequency single-particle Green's functions, and study the topological phase transitions driven by the tight-binding parameters at different on-site interaction strengths. The Z2 invariant and spin Chern number, which are complementary to each another, characterize the topological phases and identify the critical points of topological phase transitions. Although the numerically determined phase boundaries are nearly identical for different system sizes, we find strong system-size dependence of the spin Chern number, where quantized values are only expected upon approaching the thermodynamic limit. For the Hubbard models we considered, the QMC results show that correlation effects lead to shifts in the phase boundaries relative to those in the noninteracting limit, without any spontaneously symmetry breaking. The interaction-induced shift is nonperturbative in the interactions and cannot be captured within a "simple" self-consistent calculation either, such as Hartree-Fock. Furthermore, our QMC calculations suggest that quantum fluctuations from interactions stabilize topological phases in systems where the one-body terms preserve the D3 symmetry of the lattice, and destabilize topological phases when the one-body terms break the D3 symmetry.
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.
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.
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.
Electronic topological transition in zinc under pressure: An x-ray absorption spectroscopy study
Aquilanti, G.; Trapananti, A.; Pascarelli, S.; Minicucci, M.; Principi, E.; Liscio, F.; Twarog, A.
2007-10-01
Zinc metal has been studied at high pressure using x-ray absorption spectroscopy. In order to investigate the role of the different degrees of hydrostaticity on the occurrence of structural anomalies following the electronic topological transition, two pressure transmitting media have been used. Results show that the electronic topological transition, if it exists, does not induce an anomaly in the local environment of compressed Zn as a function of hydrostatic pressure and any anomaly must be related to a loss of hydrostaticity of the pressure transmitting medium. The near-edge structures of the spectra, sensitive to variations in the electronic density of states above the Fermi level, do not show any evidence of electronic transition whatever pressure transmitting medium is used.
NASA Astrophysics Data System (ADS)
Li, Chun-Hong; Long, Yu-Jia; Zhao, Ling-Xiao; Shan, Lei; Ren, Zhi-An; Zhao, Jian-Zhou; Weng, Hong-Ming; Dai, Xi; Fang, Zhong; Ren, Cong; Chen, Gen-Fu
2017-03-01
We report the anisotropic magnetotransport measurement on a noncompound band semiconductor black phosphorus (BP) with magnetic field B up to 16 Tesla applied in both perpendicular and parallel to electric current I under hydrostatic pressures. The BP undergoes a topological Lifshitz transition from band semiconductor to a zero-gap Dirac semimetal state at a critical pressure Pc, characterized by a weak localization-weak antilocalization transition at low magnetic fields and the emergence of a nontrivial Berry phase of π detected by SdH magneto-oscillations in magnetoresistance curves. In the transition region, we observe a pressure-dependent negative MR only in the B ∥I configuration. This negative longitudinal MR is attributed to the Adler-Bell-Jackiw anomaly (topological E .B term) in the presence of weak antilocalization corrections.
A topological investigation of phase transitions of cascading failures in power grids
NASA Astrophysics Data System (ADS)
Koç, Yakup; Warnier, Martijn; Van Mieghem, Piet; Kooij, Robert E.; Brazier, Frances M. T.
2014-12-01
Cascading failures are one of the main reasons for blackouts in electric power transmission grids. The economic cost of such failures is in the order of tens of billion dollars annually. The loading level of power system is a key aspect to determine the amount of the damage caused by cascading failures. Existing studies show that the blackout size exhibits phase transitions as the loading level increases. This paper investigates the impact of the topology of a power grid on phase transitions in its robustness. Three spectral graph metrics are considered: spectral radius, effective graph resistance and algebraic connectivity. Experimental results from a model of cascading failures in power grids on the IEEE power systems demonstrate the applicability of these metrics to design/optimise a power grid topology for an enhanced phase transition behaviour of the system.
Signatures of a pressure-induced topological quantum phase transition in BiTeI.
Xi, Xiaoxiang; Ma, Chunli; Liu, Zhenxian; Chen, Zhiqiang; Ku, Wei; Berger, H; Martin, C; Tanner, D B; Carr, G L
2013-10-11
We report the observation of two signatures of a pressure-induced topological quantum phase transition in the polar semiconductor BiTeI using x-ray powder diffraction and infrared spectroscopy. The x-ray data confirm that BiTeI remains in its ambient-pressure structure up to 8 GPa. The lattice parameter ratio c/a shows a minimum between 2.0-2.9 GPa, indicating an enhanced c-axis bonding through p(z) band crossing as expected during the transition. Over the same pressure range, the infrared spectra reveal a maximum in the optical spectral weight of the charge carriers, reflecting the closing and reopening of the semiconducting band gap. Both of these features are characteristics of a topological quantum phase transition and are consistent with a recent theoretical proposal.
Topological phase transition and quantum spin Hall edge states of antimony few layers
Kim, Sung Hwan; Jin, Kyung-Hwan; Park, Joonbum; Kim, Jun Sung; Jhi, Seung-Hoon; Yeom, Han Woong
2016-01-01
While two-dimensional (2D) topological insulators (TI’s) initiated the field of topological materials, only very few materials were discovered to date and the direct access to their quantum spin Hall edge states has been challenging due to material issues. Here, we introduce a new 2D TI material, Sb few layer films. Electronic structures of ultrathin Sb islands grown on Bi2Te2Se are investigated by scanning tunneling microscopy. The maps of local density of states clearly identify robust edge electronic states over the thickness of three bilayers in clear contrast to thinner islands. This indicates that topological edge states emerge through a 2D topological phase transition predicted between three and four bilayer films in recent theory. The non-trivial phase transition and edge states are confirmed for epitaxial films by extensive density-functional-theory calculations. This work provides an important material platform to exploit microscopic aspects of the quantum spin Hall phase and its quantum phase transition. PMID:27624972
Topological phase transition and quantum spin Hall edge states of antimony few layers.
Kim, Sung Hwan; Jin, Kyung-Hwan; Park, Joonbum; Kim, Jun Sung; Jhi, Seung-Hoon; Yeom, Han Woong
2016-09-14
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.
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.
Phase transition of geometrically frustrated TbNiAl in a magnetic field
Ehlers, Georg
2007-01-01
The phase transitions of the geometrically frustrated antiferromagnet TbNiAl in a magnetic field are studied by means of neutron powder diffraction, ac susceptibility, and muon spin relaxation ({mu}SR) measurements. Neutron powder diffraction reveals that, in addition to antiferromagnetic order, ferromagnetic order is induced in a field as low as B{approx}0.02T . At higher fields, ferromagnetic and antiferromagnetic order coexist in different domains in the sample, and the domain balance depends on both magnetic field and temperature. Antiferromagnetic Bragg reflections are observed below a Neel temperature of T{sub N}=47K which is independent of the field. Ferromagnetic Bragg peaks are observed below a field-dependent Curie temperature which increases from {Tc}=52K at B=0.2T to {Tc}=70K at B=5T . Both phase transitions are concurrently observed in ac susceptibility and {mu}SR measurements.
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.
García-Jacas, C R; Marrero-Ponce, Y; Barigye, S J; Hernández-Ortega, T; Cabrera-Leyva, L; Fernández-Castillo, A
2016-12-01
Novel N-tuple topological/geometric cutoffs to consider specific inter-atomic relations in the QuBiLS-MIDAS framework are introduced in this manuscript. These molecular cutoffs permit the taking into account of relations between more than two atoms by using (dis-)similarity multi-metrics and the concepts related with topological and Euclidean-geometric distances. To this end, the kth two-, three- and four-tuple topological and geometric neighbourhood quotient (NQ) total (or local-fragment) spatial-(dis)similarity matrices are defined, to represent 3D information corresponding to the relations between two, three and four atoms of the molecular structures that satisfy certain cutoff criteria. First, an analysis of a diverse chemical space for the most common values of topological/Euclidean-geometric distances, bond/dihedral angles, triangle/quadrilateral perimeters, triangle area and volume was performed in order to determine the intervals to take into account in the cutoff procedures. A variability analysis based on Shannon's entropy reveals that better distribution patterns are attained with the descriptors based on the cutoffs proposed (QuBiLS-MIDAS NQ-MDs) with regard to the results obtained when all inter-atomic relations are considered (QuBiLS-MIDAS KA-MDs - 'Keep All'). A principal component analysis shows that the novel molecular cutoffs codify chemical information captured by the respective QuBiLS-MIDAS KA-MDs, as well as information not captured by the latter. Lastly, a QSAR study to obtain deeper knowledge of the contribution of the proposed methods was carried out, using four molecular datasets (steroids (STER), angiotensin converting enzyme (ACE), thermolysin inhibitors (THER) and thrombin inhibitors (THR)) widely used as benchmarks in the evaluation of several methodologies. One to four variable QSAR models based on multiple linear regression were developed for each compound dataset following the original division into training and test sets. The
Flux-driven quantum phase transitions in two-leg Kitaev ladder topological superconductor systems
NASA Astrophysics Data System (ADS)
Wang, H. Q.; Shao, L. B.; Pan, Y. M.; Shen, R.; Sheng, L.; Xing, D. Y.
2016-12-01
We investigate a two-leg ladder topological superconductor system consisting of two parallel Kitaev chains with interchain coupling. It is found that either uniform or staggered fluxes threading through the ladder holes may change the ladder system from the BDI class in the Altland-Zirnbauer (AZ) classification to the D class. After explicitly calculating the topological Z and/or Z2 indices and from the evolution of Majorana zero energy states (MZES), we obtain the flux-dependent phase diagrams, and find that quantum phase transitions between topologically distinct phases characterized by different number of MZES may happen by simply tuning the flux, which could be realized experimentally in ultracold systems.
Topological phase transitions and universality in the Haldane-Hubbard model
NASA Astrophysics Data System (ADS)
Giuliani, Alessandro; Jauslin, Ian; Mastropietro, Vieri; Porta, Marcello
2016-11-01
We study the Haldane-Hubbard model by exact renormalization group techniques. We analytically construct the topological phase diagram, for weak interactions. We predict that many-body interactions induce a shift of the transition line: in particular, repulsive interactions enlarge the topologically nontrivial region. The presence of new intermediate phases, absent in the noninteracting case, is rigorously excluded at weak coupling. Despite the nontrivial renormalization of the wave function and of the Fermi velocity, the conductivity is universal: at the renormalized critical line, both the discontinuity of the transverse conductivity and the longitudinal conductivity are independent of the interaction, thanks to remarkable cancellations due to lattice Ward identities. In contrast to the quantization of the transverse conductivity, the universality of the longitudinal conductivity cannot be explained via topological arguments.
Zhou, Tong; Zhang, Jiayong; Zhao, Bao; Zhang, Huisheng; Yang, Zhongqin
2015-08-12
Electronic and topological behaviors of Sb(111) monolayers decorated with H and certain magnetic atoms are investigated by using ab initio methods. The drastic exchange field induced by the magnetic atoms, together with strong spin-orbit coupling (SOC) of Sb atoms, generates one new category of valley polarized topological insulators, called quantum spin-quantum anomalous Hall (QSQAH) insulators in the monolayer, with a band gap up to 53 meV. The strong SOC is closely related to Sb px and py orbitals, instead of pz orbitals in usual two-dimensional (2D) materials. Topological transitions from quantum anomalous Hall states to QSQAH states and then to time-reversal-symmetry-broken quantum spin Hall states are achieved by tuning the SOC strength. The behind mechanism is revealed. Our work is helpful for future valleytronic and spintronic applications in 2D materials.
Topological 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.
Aspects of Floquet bands and topological phase transitions in a continuously driven superlattice
NASA Astrophysics Data System (ADS)
Zhou, Longwen; Wang, Hailong; Ho, Derek Y. H.; Gong, Jiangbin
2014-09-01
The recent creation of novel topological states of matter via periodic driving fields has attracted much attention. To contribute to the growing knowledge on this subject, we study the well-known Harper-Aubry-André model modified by a continuous time-periodic modulation and report on its topological properties along with several other interesting features. The Floquet bands are found to have non-zero Chern numbers which are generally different from those in the original static model. Topological phase transitions (discontinuous change of Chern numbers) take place as we tune the amplitude or period of the driving field. We demonstrate that the non-trivial Floquet band topology manifests via the quantized transport of Wannier states in the lattice space. For certain parameter choices, very flat yet topologically non-trivial Floquet bands emerge, a feature potentially useful for simulating the physics of strongly correlated systems. In some cases with an even number of Floquet bands, the spectrum features linearly dispersing Dirac cones which hold potential for the simulation of high energy physics or Klein tunnelling. Taking open boundary conditions, we observe anomalous counter-propagating chiral edge modes and degenerate zero modes. We end by discussing how these theoretical predictions may be verified experimentally.
Topological phase transition of single-crystal Bi based on empirical tight-binding calculations
NASA Astrophysics Data System (ADS)
Ohtsubo, Yoshiyuki; Kimura, Shin-ichi
2016-12-01
The topological order of single-crystal Bi and its surface states on the (111) surface are studied in detail based on empirical tight-binding (TB) calculations. New TB parameters are presented that are used to calculate the surface states of semi-infinite single-crystal Bi(111), which agree with the experimental angle-resolved photoelectron spectroscopy results. The influence of the crystal lattice distortion is surveyed and it is revealed that a topological phase transition is driven by in-plane expansion with topologically non-trivial bulk bands. In contrast with the semi-infinite system, the surface-state dispersions on finite-thickness slabs are non-trivial irrespective of the bulk topological order. The role of the interaction between the top and bottom surfaces in the slab is systematically studied, and it is revealed that a very thick slab is required to properly obtain the bulk topological order of Bi from the (111) surface state: above 150 biatomic layers in this case.
NASA Astrophysics Data System (ADS)
Sato, T.; Segawa, Kouji; Kosaka, K.; Souma, S.; Nakayama, K.; Eto, K.; Minami, T.; Ando, Yoichi; Takahashi, T.
2011-11-01
The three-dimensional (3D) topological insulator is a novel quantum state of matter where an insulating bulk hosts a linearly dispersing surface state, which can be viewed as a sea of massless Dirac fermions protected by the time-reversal symmetry (TRS). Breaking the TRS by a magnetic order leads to the opening of a gap in the surface state, and consequently the Dirac fermions become massive. It has been proposed theoretically that such a mass acquisition is necessary to realize novel topological phenomena, but achieving a sufficiently large mass is an experimental challenge. Here we report an unexpected discovery that the surface Dirac fermions in a solid-solution system TlBi(S1-xSex)2 acquire a mass without explicitly breaking the TRS. We found that this system goes through a quantum phase transition from the topological to the non-topological phase, and, by tracing the evolution of the electronic states using the angle-resolved photoemission, we observed that the massless Dirac state in TlBiSe2 switches to a massive state before it disappears in the non-topological phase. This result suggests the existence of a condensed-matter version of the `Higgs mechanism' where particles acquire a mass through spontaneous symmetry breaking.
Geometrical and Anderson transitions in harmonic chains with constrained long-range couplings.
Morais, P A; Andrade, J S; Nascimento, E M; Lyra, M L
2011-10-01
Low-dimensional systems with long-range couplings usually present phase transitions which are absent in the short-ranged counterpart model. In this work, we show that a harmonic chain with long-range couplings restricted by a cost function proportional to the chain length N exhibits two distinct phase transitions. In the present model, two sites at a distance r>1 are connected by a spring with probability 1/r(α) with the constraint that the total length of the non-nearest-neighbor couplings is limited to λN, where λ is a cost parameter. A geometrical phase transition is found at α=1.5 between a phase with a finite number of long-range couplings and a phase on which the number of long-range couplings is proportional to the system size. Further, the normal vibrational modes of this chain display a phase transition from delocalized to localized modes at a smaller value of α. Maximum effective disorder is reached at α=2 for which the frequency of the lowest vibrational mode exhibits a pronounced peak.
Quasi-one Dimensional Topological Insulator: Möbius Molecular Devices in Peierls Transition
NASA Astrophysics Data System (ADS)
Gong, Zhi-Rui; Song, Zhi; Sun, Chang-Pu
2016-10-01
We show that, assisted by the Peierls transition of lattice, as a quasi-one dimensional (Q1D) tight binding system, a Möbius molecular device can behave as a simple topological insulator. With the Peierls phase transition to form a domain wall, the solitonary zero modes exist as the ground state of this electron-phonon hybrid system, which is protected by the Z2 topology of the Möbius strip. The robustness of the ground state prevents these degenerate zero modes from their energy spectrum splitting caused by any perturbation. Supported by the National Natural Science Foundation of China under Grant No. 11504241 and the Natural Science Foundation of Shenzhen University under Grant No. 201551
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.
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
2015-11-02
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.
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
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.
Topologically induced swarming phase transition on a 2D percolated lattice
NASA Astrophysics Data System (ADS)
Quint, David A.; Gopinathan, Ajay
2015-07-01
The emergence of collective motion, or swarming, in groups of moving individuals who orient themselves using only information from their neighbors is a very general phenomenon that occurs at multiple spatio-temporal scales. Swarms that occur in natural environments typically have to contend with spatial disorder such as obstacles that can hinder an individual’s motion or can disrupt communication with neighbors. We study swarming agents, possessing both aligning and mutually avoiding repulsive interactions, in a 2D percolated network representing a topologically disordered environment. We numerically find a phase transition from a collectively moving swarm to a disordered gas-like state above a critical value of the topological or environmental disorder. For agents that utilize only alignment interactions, we find that the swarming transition does not exist in the large system size limit, while the addition of a mutually repulsive interaction can restore the existence of the transition at a finite critical value of disorder. We find there is a finite range of topological disorder where swarming can occur and that this range can be maximized by an optimal amount of mutual repulsion.
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
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.
Surface-state spin textures in strained bulk HgTe: Strain-induced topological phase transitions
NASA Astrophysics Data System (ADS)
Kirtschig, Frank; van den Brink, Jeroen; Ortix, Carmine
2016-12-01
The opening of a band gap due to compressive uniaxial strain renders bulk HgTe a strong three-dimensional topological insulator with protected gapless surface states at any surface. By employing a six-band k .p model, we determine the spin textures of the topological surface states of bulk HgTe uniaxially strained along the (100 ) direction. We show that at the (010 ) and (001 ) surfaces, an increase in the strain magnitude triggers a topological phase transition where the winding number of the surface-state spin texture is flipped while the four topological invariants characterizing the bulk band structure of the material are unchanged.
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.
Quantum phase transitions between a class of symmetry protected topological states
Tsui, Lokman; Jiang, Hong-Chen; Lu, Yuan-Ming; Lee, Dung-Hai
2015-07-01
The subject of this paper is the phase transition between symmetry protected topological states (SPTs). We consider spatial dimension d and symmetry group G so that the cohomology group, Hd+1(G,U(1)), contains at least one Z2n or Z factor. We show that the phase transition between the trivial SPT and the root states that generate the Z2n or Z groups can be induced on the boundary of a (d+1)-dimensional View the MathML source-symmetric SPT by a View the MathML source symmetry breaking field. Moreover we show these boundary phase transitions can be “transplanted” to d dimensions and realized in lattice models as a function of a tuning parameter. The price one pays is for the critical value of the tuning parameter there is an extra non-local (duality-like) symmetry. In the case where the phase transition is continuous, our theory predicts the presence of unusual (sometimes fractionalized) excitations corresponding to delocalized boundary excitations of the non-trivial SPT on one side of the transition. This theory also predicts other phase transition scenarios including first order transition and transition via an intermediate symmetry breaking phase.
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.
Simultaneous transitions in cuprate momentum-space topology and electronic symmetry breaking.
Fujita, K; Kim, Chung Koo; Lee, Inhee; Lee, Jinho; Hamidian, M H; Firmo, I A; Mukhopadhyay, S; Eisaki, H; Uchida, S; Lawler, M J; Kim, E-A; Davis, J C
2014-05-09
The existence of electronic symmetry breaking in the underdoped cuprates and its disappearance with increased hole density p are now widely reported. However, the relation between this transition and the momentum-space (k-space) electronic structure underpinning the superconductivity has not yet been established. Here, we visualize the Q = 0 (intra-unit-cell) and Q ≠ 0 (density-wave) broken-symmetry states, simultaneously with the coherent k-space topology, for Bi₂Sr₂CaCu₂O(8+δ) samples spanning the phase diagram 0.06 ≤ p ≤ 0.23. We show that the electronic symmetry-breaking tendencies weaken with increasing p and disappear close to a critical doping p(c) = 0.19. Concomitantly, the coherent k-space topology undergoes an abrupt transition, from arcs to closed contours, at the same p(c). These data reveal that the k-space topology transformation in cuprates is linked intimately with the disappearance of the electronic symmetry breaking at a concealed critical point.
NASA Astrophysics Data System (ADS)
Zhou, Jian; Jena, Puru
2017-02-01
While most of the two-dimensional (2D) topological crystalline insulators (TCIs) belong to group IV-VI narrow-band-gap semiconductors in a square lattice, in the present work we predict a TCI family based on transition metal intercalated compounds in a hexagonal lattice. First-principles calculations combined with a substrate-fixed globally optimal structural search technique show that a layer of Os prefers a uniform distribution between two graphene sheets. Band dispersion calculations reveal a Dirac point and a Dirac nodal ring near the Fermi level. The Dirac point is ascribed to the hybridization of e2 and e2* orbitals, and the Dirac ring is formed due to dispersion of s and e1* orbitals. Upon inclusion of spin-orbit coupling, these Dirac states open topologically nontrivial local band gaps, which are characterized by nonzero mirror Chern numbers. The quantum spin Hall effect is also observed by integrating the spin Berry curvature in the Brillouin zone. In contrast to the 2D group IV-VI TCIs whose band inversions at X and Y points are "locked" by C4 rotation symmetry, here the relative energy of two local band gaps can be manipulated by in-plane biaxial strains. Some other similar intercalation compounds are also shown to be topologically nontrivial. Our work extends the 2D TCI family into a hexagonal lattice composed of transition metals.
Combined fast reversible liquidlike elastic deformation with topological phase transition in Na3Bi
NASA Astrophysics Data System (ADS)
Cheng, Xiyue; Li, Ronghan; Li, Dianzhong; Li, Yiyi; Chen, Xing-Qiu
2015-10-01
By means of first-principles calculations, we identified the structural phase transition of Na3Bi from the hexagonal ground state to the cubic c F 16 phase above 0.8 GPa, in agreement with the experimental findings. Upon the releasing of pressure, the cF 16 phase of Na3Bi is mechanically stable at ambient condition. The calculations revealed that the c F 16 phase is topological semimetal (TS), similar to well-known HgTe, and it even exhibits an unusually low C' modulus (only about 1.9 GPa) and a huge anisotropy Au of as high as 11, which is the third-highest value among all known cubic crystals in their elastic behaviors. These facts render cF 16 -type Na3Bi very soft with a liquidlike elastic deformation in the (110)<1 1 ¯0 > slip system. Importantly, accompanying this deformation, Na3Bi shows a topological phase transition from a TS state at its strain-free cubic phase to a topological insulator (TI) at its distorted phase. Because the C' elastic deformation has almost no energy cost in a reversible and liquidlike soft manner, cF 16 -type Na3Bi would potentially provide a fast on/off switching method between TS and TI, which would be beneficial to quantum electronic devices for practical applications.
Pressure-induced topological phase transition in the polar semiconductor BiTeBr
NASA Astrophysics Data System (ADS)
Ohmura, Ayako; Higuchi, Yuichiro; Ochiai, Takayuki; Kanou, Manabu; Ishikawa, Fumihiro; Nakano, Satoshi; Nakayama, Atsuko; Yamada, Yuh; Sasagawa, Takao
2017-03-01
We performed x-ray diffraction and electrical resistivity measurement up to pressures of 5 GPa and the first-principles calculations utilizing experimental structural parameters to investigate the pressure-induced topological phase transition in BiTeBr having a noncentrosymmetric layered structure (space group P 3 m 1 ). The P 3 m 1 structure remains stable up to pressures of 5 GPa; the ratio of lattice constants c /a has a minimum at pressures of 2.5-3 GPa. In the same range, the temperature dependence of resistivity changes from metallic to semiconducting at 3 GPa and has a plateau region between 50 and 150 K in the semiconducting state. Meanwhile, the pressure variation of band structure shows that the bulk band-gap energy closes at 2.9 GPa and re-opens at higher pressures. Furthermore, according to the Wilson loop analysis, the topological nature of electronic states in noncentrosymmetric BiTeBr at 0 and 5 GPa are explicitly revealed to be trivial and nontrivial, respectively. These results strongly suggest that pressure-induced topological phase transition in BiTeBr occurs at the pressures of 2.9 GPa.
Nagarajan, Mahesh B; Coan, Paola; Huber, Markus B; Diemoz, Paul C; Wismüller, Axel
2015-11-01
Phase-contrast X-ray computed tomography (PCI-CT) has attracted significant interest in recent years for its ability to provide significantly improved image contrast in low absorbing materials such as soft biological tissue. In the research context of cartilage imaging, previous studies have demonstrated the ability of PCI-CT to visualize structural details of human patellar cartilage matrix and capture changes to chondrocyte organization induced by osteoarthritis. This study evaluates the use of geometrical and topological features for volumetric characterization of such chondrocyte patterns in the presence (or absence) of osteoarthritic damage. Geometrical features derived from the scaling index method (SIM) and topological features derived from Minkowski Functionals were extracted from 1392 volumes of interest (VOI) annotated on PCI-CT images of ex vivo human patellar cartilage specimens. These features were subsequently used in a machine learning task with support vector regression to classify VOIs as healthy or osteoarthritic; classification performance was evaluated using the area under the receiver operating characteristic curve (AUC). Our results show that the classification performance of SIM-derived geometrical features (AUC: 0.90 ± 0.09) is significantly better than Minkowski Functionals volume (AUC: 0.54 ± 0.02), surface (AUC: 0.72 ± 0.06), mean breadth (AUC: 0.74 ± 0.06) and Euler characteristic (AUC: 0.78 ± 0.04) (p < 10(-4)). These results suggest that such geometrical features can provide a detailed characterization of the chondrocyte organization in the cartilage matrix in an automated manner, while also enabling classification of cartilage as healthy or osteoarthritic with high accuracy. Such features could potentially serve as diagnostic imaging markers for evaluating osteoarthritis progression and its response to different therapeutic intervention strategies.
NASA Astrophysics Data System (ADS)
Torrents, Genís; Illa, Xavier; Vives, Eduard; Planes, Antoni
2017-01-01
A simple model for the growth of elongated domains (needle-like) during a martensitic phase transition is presented. The model is purely geometric and the only interactions are due to the sequentiality of the kinetic problem and to the excluded volume, since domains cannot retransform back to the original phase. Despite this very simple interaction, numerical simulations show that the final observed microstructure can be described as being a consequence of dipolar-like interactions. The model is analytically solved in 2D for the case in which two symmetry related domains can grow in the horizontal and vertical directions. It is remarkable that the solution is analytic both for a finite system of size L ×L and in the thermodynamic limit L →∞ , where the elongated domains become lines. Results prove the existence of criticality, i.e., that the domain sizes observed in the final microstructure show a power-law distribution characterized by a critical exponent. The exponent, nevertheless, depends on the relative probabilities of the different equivalent variants. The results provide a plausible explanation of the weak universality of the critical exponents measured during martensitic transformations in metallic alloys. Experimental exponents show a monotonous dependence with the number of equivalent variants that grow during the transition.
NASA Astrophysics Data System (ADS)
Yamauchi, Kunihiko; Barone, Paolo; Picozzi, Silvia
2017-01-01
The possibility to engineer the coupling of spin and valley physics is explored in ferroelectric oxide heterostructures with eg2 electronic configuration. We show that the polar structural distortion induces the appearance of spin-valley coupled properties, at the same time as being responsible for a topological transition from a quantum spin-Hall insulating phase to a trivial band insulator. The coupled spin-valley physics is affected by the topological band inversion in a nontrivial way; while the valley-dependent spin polarization of both conduction and valence bands is preserved, a change of the Berry curvature and of spin-valley selection rules is predicted, leading to different circular dichroic response as well as valley and spin Hall effects.
Pressure induced Ag2Te polymorphs in conjunction with topological non trivial to metal transition
NASA Astrophysics Data System (ADS)
Zhu, J.; Oganov, A. R.; Feng, W. X.; Yao, Y. G.; Zhang, S. J.; Yu, X. H.; Zhu, J. L.; Yu, R. C.; Jin, C. Q.; Dai, X.; Fang, Z.; Zhao, Y. S.
2016-08-01
Silver telluride (Ag2Te) is well known as superionic conductor and topological insulator with polymorphs. Pressure induced three phase transitions in Ag2Te have been reported in previous. Here, we experimentally identified high pressure phase above 13 GPa of Ag2Te by using high pressure synchrotron x ray diffraction method in combination with evolutionary crystal structure prediction, showing it crystallizes into a monoclinic structure of space group C2/m with lattice parameters a = 6.081Å, b = 5.744Å, c = 6.797 Å, β = 105.53°. The electronic properties measurements of Ag2Te reveal that the topologically non-trivial semiconducting phase I and semimetallic phase II previously predicated by theory transformed into bulk metals for high pressure phases in consistent with the first principles calculations.
Skyrmion crystal and topological Hall effect in B20-type transition-metal compounds
NASA Astrophysics Data System (ADS)
Onose, Yoshinori
2011-03-01
Topological objects in solids such as domain walls and vortices have been attracting much attention for long. Among them the spin texture called skyrmion is an unusual topological object, in which the spins point in all the directions wrapping a sphere. The skyrmion hosts finite spin chirality, and therefore is anticipated to induce novel electromagnetic phenomena such as topological Hall effect. In B20-type transition metal compounds MnSi and Fe 1-x Co x Si, the crystallization of skyrmions was observed by the neutron diffraction studies. , . Recently, we have observed the real-space images of skyrmion crystal in thin films of related compounds (Fe 0.5 Co 0.5 Si and FeGe) using Lorentz transmission electron spectroscopy., Nature material, inpress.} We have observed the hexagonal arrangement of skyrmions including the topological defects (chiral domains and dislocations) under the magnetic field normal to the films, and found that the two dimensional skyrmion crystal phase is fairly stabilized by the thin film form of the samples. We have also studied the topological Hall effect caused by the spin chirality of the skyrmion crystal in a related material MnGe. In terms of the Hall measurement, they have shown the real space nature of the fictitious magnetic field caused by the magnetic configuration of the skyrmion crystal, in contrast with the momentum-space fictitious field in another spin chirality system, Nd 2 Mo 2 O7 . This work was done in collaboration with X. Z. Yu, N. Kanazawa, J. H. Park, J. H. Han, K. Kimoto, W. Z. Zhang, S. Ishiwata, Y. Matsui, N. Nagaosa, and Y. Tokura. S. Mühlbauer et al. Science 323, 915 (2009).}
Superconductivity on the verge of electronic topological transition in Fe based superconductors
NASA Astrophysics Data System (ADS)
Ghosh, Haranath; Sen, Smritijit
2017-04-01
A comprehensive first principles study on the electronic topological transition in a number of 122 family of Fe based superconductors is presented. Doping as well as temperature driven Lifshitz transitions are predicted from ab-initio simulations in a variety of Fe based superconductors that are consistent with experimental findings. In all the studied compounds the Lifshitz transitions are consistently found to take place at a doping concentration just around where superconductivity is known to acquire the highest Tc and magnetism disappears. This indicates the intriguing heed to the inter-relationship between superconductivity and Lifshitz transition in Fe-based 122 materials. Systematically, the Lifshitz transition occurs (above certain threshold doping) in some of the electronic Fermi surfaces for hole doped 122 compounds, whereas in hole Fermi surfaces for electron as well as iso-electronic doped 122 compounds. Temperature driven Lifshitz transition is found to occur in the iso-electronic Ru-doped BaFe2As2 compounds. A systematic study of Fermi surface area e.g., variations of (i) areas of each individual Fermi surfaces, (ii) sum total areas of all the electron Fermi Surfaces, (iii) sum total areas of all the hole Fermi Surfaces, (iv) sum total areas of all the five Fermi Surfaces, (v) difference of all hole and all electron Fermi surface areas as a function of doping is a rare wealth of information that can be verified by the de Haas-van Alphen and allied effects (i.e. , Shubnikov-de Haas effect) are presented. Fermi surface area are found to carry sensitivity of topological modifications more acutely than the band structures and can be used as a better experimental tool to identify ETT/LT.
NASA Astrophysics Data System (ADS)
Liu, Y.; Long, Y. J.; Zhao, L. X.; Nie, S. M.; Zhang, S. J.; Weng, Y. X.; Jin, M. L.; Li, W. M.; Liu, Q. Q.; Long, Y. W.; Yu, R. C.; Gu, C. Z.; Sun, F.; Yang, W. G.; Mao, H. K.; Feng, X. L.; Li, Q.; Zheng, W. T.; Weng, H. M.; Dai, X.; Fang, Z.; Chen, G. F.; Jin, C. Q.
2017-03-01
Recently, theoretical studies show that layered HfTe5 is at the boundary of weak & strong topological insulator (TI) and might crossover to a Dirac semimetal state by changing lattice parameters. The topological properties of 3D stacked HfTe5 are expected hence to be sensitive to pressures tuning. Here, we report pressure induced phase evolution in both electronic & crystal structures for HfTe5 with a culmination of pressure induced superconductivity. Our experiments indicated that the temperature for anomaly resistance peak (Tp) due to Lifshitz transition decreases first before climbs up to a maximum with pressure while the Tp minimum corresponds to the transition from a weak TI to strong TI. The HfTe5 crystal becomes superconductive above ~5.5 GPa where the Tp reaches maximum. The highest superconducting transition temperature (Tc) around 5 K was achieved at 20 GPa. Crystal structure studies indicate that HfTe5 transforms from a Cmcm phase across a monoclinic C2/m phase then to a P-1 phase with increasing pressure. Based on transport, structure studies a comprehensive phase diagram of HfTe5 is constructed as function of pressure. The work provides valuable experimental insights into the evolution on how to proceed from a weak TI precursor across a strong TI to superconductors.
Liu, Y.; Long, Y. J.; Zhao, L. X.; Nie, S. M.; Zhang, S. J.; Weng, Y. X.; Jin, M. L.; Li, W. M.; Liu, Q. Q.; Long, Y. W.; Yu, R. C.; Gu, C. Z.; Sun, F.; Yang, W. G.; Mao, H. K.; Feng, X. L.; Li, Q.; Zheng, W. T.; Weng, H. M.; Dai, X.; Fang, Z.; Chen, G. F.; Jin, C. Q.
2017-01-01
Recently, theoretical studies show that layered HfTe5 is at the boundary of weak & strong topological insulator (TI) and might crossover to a Dirac semimetal state by changing lattice parameters. The topological properties of 3D stacked HfTe5 are expected hence to be sensitive to pressures tuning. Here, we report pressure induced phase evolution in both electronic & crystal structures for HfTe5 with a culmination of pressure induced superconductivity. Our experiments indicated that the temperature for anomaly resistance peak (Tp) due to Lifshitz transition decreases first before climbs up to a maximum with pressure while the Tp minimum corresponds to the transition from a weak TI to strong TI. The HfTe5 crystal becomes superconductive above ~5.5 GPa where the Tp reaches maximum. The highest superconducting transition temperature (Tc) around 5 K was achieved at 20 GPa. Crystal structure studies indicate that HfTe5 transforms from a Cmcm phase across a monoclinic C2/m phase then to a P-1 phase with increasing pressure. Based on transport, structure studies a comprehensive phase diagram of HfTe5 is constructed as function of pressure. The work provides valuable experimental insights into the evolution on how to proceed from a weak TI precursor across a strong TI to superconductors. PMID:28300156
Equation of state and topological transitions in amorphous solids under hydrostatic compression
NASA Astrophysics Data System (ADS)
Guo, Yu-zheng; Li, Mo
2010-12-01
Equation of state (EoS) relating volume and pressure or other thermodynamics state variables is well-established in crystalline systems, but remains rather incomplete in structurally disordered materials such as metallic glasses. Recent experiments and calculation show that the EoS in some amorphous metals exhibits constitutive behavior deviating significantly from that predicted from many well-established EoS, suggesting fundamentally different mechanisms in operation. But due to the lack of long-range order, it is difficult to uncover the underlying atomic process directly from experiment. Here we report a systematic investigation of the constitutive response of a model ZrNi metallic glass under hydrostatic compression by using extensive molecular dynamics simulation. We show that at low-pressure, the EoS is dominated by large decrease in the excess volumes, presumably those of the valence electrons; and at high-pressure, hardcore repulsion takes over. The two is bridged by a polymorphic topological transition occurring in close association with Ni, one of the alloy elements with much lower compressibility and rigid neighbor bonds that exhibit the topological transition in both short and medium-range. The complex and detailed topological rearrangement reported here may form the general underlying mechanism for the EoS of many metallic glasses composed predominately of metals with different compressibility, such as early and late transition metals and some rare-earth metals. The necessity of the electronic structural change thought to be responsible for some reported EoS is discussed also in light of this work.
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
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
Internal phase transition induced by external forces in Finsler geometric model for membranes
NASA Astrophysics Data System (ADS)
Koibuchi, Hiroshi; Shobukhov, Andrey
2016-10-01
In this paper, we numerically study an anisotropic shape transformation of membranes under external forces for two-dimensional triangulated surfaces on the basis of Finsler geometry. The Finsler metric is defined by using a vector field, which is the tangential component of a three-dimensional unit vector σ corresponding to the tilt or some external macromolecules on the surface of disk topology. The sigma model Hamiltonian is assumed for the tangential component of σ with the interaction coefficient λ. For large (small) λ, the surface becomes oblong (collapsed) at relatively small bending rigidity. For the intermediate λ, the surface becomes planar. Conversely, fixing the surface with the boundary of area A or with the two-point boundaries of distance L, we find that the variable σ changes from random to aligned state with increasing of A or L for the intermediate region of λ. This implies that an internal phase transition for σ is triggered not only by the thermal fluctuations, but also by external mechanical forces. We also find that the frame (string) tension shows the expected scaling behavior with respect to A/N (L/N) at the intermediate region of A (L) where the σ configuration changes between the disordered and ordered phases. Moreover, we find that the string tension γ at sufficiently large λ is considerably smaller than that at small λ. This phenomenon resembles the so-called soft-elasticity in the liquid crystal elastomer, which is deformed by small external tensile forces.
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.
Wang, Jing; Zhou, Quan; Lian, Biao; ...
2015-08-31
Here, we propose to realize a two-dimensional chiral topological superconducting (TSC) state from the quantum anomalous Hall plateau transition in a magnetic topological insulator thin film through the proximity effect to a conventional s -wave superconductor. This state has a full pairing gap in the bulk and a single chiral Majorana mode at the edge. The optimal condition for realizing such chiral TSC is to have inequivalent superconducting pairing amplitudes on top and bottom surfaces of the doped magnetic topological insulator. We further propose several transport experiments to detect the chiral TSC. One unique signature is that the conductance willmore » be quantized into a half-integer plateau at the coercive field in this hybrid system. In particular, with the point contact formed by a superconducting junction, the conductance oscillates between e2 /2h and e2 /h with the frequency determined by the voltage across the junction. We close by discussing the feasibility of these experimental proposals.« less
Wang, Jing; Zhou, Quan; Lian, Biao; Zhang, Shou -Cheng
2015-08-31
Here, we propose to realize a two-dimensional chiral topological superconducting (TSC) state from the quantum anomalous Hall plateau transition in a magnetic topological insulator thin film through the proximity effect to a conventional s -wave superconductor. This state has a full pairing gap in the bulk and a single chiral Majorana mode at the edge. The optimal condition for realizing such chiral TSC is to have inequivalent superconducting pairing amplitudes on top and bottom surfaces of the doped magnetic topological insulator. We further propose several transport experiments to detect the chiral TSC. One unique signature is that the conductance will be quantized into a half-integer plateau at the coercive field in this hybrid system. In particular, with the point contact formed by a superconducting junction, the conductance oscillates between e^{2} /2h and e2 /h with the frequency determined by the voltage across the junction. We close by discussing the feasibility of these experimental proposals.
NASA Astrophysics Data System (ADS)
Santos, F. A. N.; da Silva, L. C. B.; Coutinho-Filho, M. D.
2017-01-01
We propose a topological approach suitable to establish a connection between thermodynamics and topology in the microcanonical ensemble. Indeed, we report on results that point to the possibility of describing interacting classical spin systems in the thermodynamic limit, including the occurrence of a phase transition, using topological arguments only. Our approach relies on Morse theory, through the determination of the critical points of the potential energy, which is the proper Morse function. Our main finding is that, in the context of the classical models studied, the Euler characteristic χ (E) embeds the necessary features for a correct description of several magnetic thermodynamic quantities of the systems, such as the magnetization, correlation function, susceptibility, and critical temperature. Despite the classical nature of the models, such quantities are those that do not violate the laws of thermodynamics (with the proviso that van der Waals loop states are mean field (MF) artifacts). We also discuss the subtle connection between our approach using the Euler entropy, defined by the logarithm of the modulus of χ (E) per site, and that using the Boltzmann microcanonical entropy. Moreover, the results suggest that the loss of regularity in the Morse function is associated with the occurrence of unstable and metastable thermodynamic solutions in the MF case. The reliability of our approach is tested in two exactly soluble systems: the infinite-range and the one-dimensional short-range XY models in the presence of a magnetic field. In particular, we confirm that the topological hypothesis holds for both the infinite-range ({{T}c}\
Strain-induced topological transition in SrRu2O6 and CaOs2O6
Ochi, Masayuki; Arita, Ryotaro; Trivedi, Nandini; ...
2016-05-24
The topological property of SrRumore » $$_2$$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 way to realize a topological insulating state in a complex oxide, which has not been experimentally demonstrated so far.« less
Topological transitions of the Fermi surface of osmium under pressure: an LDA+DMFT study
NASA Astrophysics Data System (ADS)
Feng, Qingguo; Ekholm, Marcus; Tasnádi, Ferenc; Jönsson, H. Johan M.; Abrikosov, Igor A.
2017-03-01
The influence of pressure on the electronic structure of Os has attracted substantial attention recently due to reports on isostructural electronic transitions in this metal. Here, we theoretically investigate the Fermi surface of Os from ambient to high pressure, using density functional theory combined with dynamical mean field theory. We provide a detailed discussion of the calculated Fermi surface and its dependence on the level of theory used for the treatment of the electron–electron interactions. Although we confirm that Os can be classified as weakly correlated metal, the inclusion of local quantum fluctuations between 5{{d}} electrons beyond the local density approximation explains the most recent experimental reports regarding the occurrence of electronic topological transitions in Os.
Lifshitz topological transitions, induced by doping and deformation in single-crystal bismuth wires
NASA Astrophysics Data System (ADS)
Nikolaeva, A. A.; Konopko, L. A.; Huber, T. E.; Kobylianskaya, A. K.; Para, Gh. I.
2017-02-01
The features associated with the manifestation of Lifshitz electron topological transitions (ETT) in glass-insulated bismuth wires upon qualitative changes to the topology of the Fermi surface are investigated. The variation of the energy spectrum parameters was implemented by doping Bi with an acceptor impurity Sn and using elastic strain of up to 2%, relative to the elongation in the weakly-doped p-type Bi wires. Pure and doped glass-insulated single-crystal bismuth with different diameters and (1011) orientations along the axis were prepared by the Ulitovsky liquid phase casting method. For the first time, ETT-induced anomalies are observed along the temperature dependences of the thermoemf α(T) as triple-changes of the α sign (given heavy doping of Bi wires with an acceptor impurity Sn). The concentration and energy position of the Σ-band given a high degree of bismuth doping with Sn was assessed using the Shubnikov-de Haas effect oscillations, which were detected both from L-electrons and from T-holes in magnetic fields of up to 14 T. It is shown that the Lifshitz electron-topological transitions with elastic deformation of weakly-doped p-type Bi wires are accompanied by anomalies along the deformation dependences of the thermoemf at low temperatures. The effect is interpreted in terms of the formation of a selective scattering channel of L-carriers into the T-band with a high density of states, which is in good agreement with existing theoretical ETT models.
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
NASA Astrophysics Data System (ADS)
Magarill, L. I.; Entin, M. V.
2016-12-01
The electron absorption and the edge photocurrent of a 2D topological insulator are studied for transitions between edge states to 2D states. The circular polarized light is found to produce the edge photocurrent, the direction of which is determined by light polarization and edge orientation. It is shown that the edge-state current is found to exceed the 2D current owing to the topological protection of the edge states.
NASA Astrophysics Data System (ADS)
Sheykhi, A.; Naeimipour, F.; Zebarjad, S. M.
2015-06-01
Considering the Lagrangian of the logarithmic nonlinear electrodynamics in the presence of a scalar dilaton field, we obtain a new class of topological black hole solutions of Einstein-dilaton gravity with two Liouville-type dilaton potentials. Black hole horizons and cosmological horizons, in these spacetimes, can be a two-dimensional positive, zero, or negative constant curvature surface. We find that the behavior of the electric field crucially depends on the dilaton coupling constant α . For small α , the electric field diverges near the origin, although its divergency is weaker than the linear Maxwell field. However, with increasing α , the behavior of the electric field, near the origin, approaches to that of the Maxwell field. We also study casual structure, asymptotic behavior, and physical properties of the solutions. We find that, depending on the model parameters, the topological dilaton black holes may have one or two horizons, and even in some cases we encounter a naked singularity without horizon. We compute the conserved and thermodynamic quantities of the spacetime and investigate that these quantities satisfy the first law of thermodynamics. We also probe thermal stability in the canonical and grand canonical ensembles and disclose the effects of the dilaton field as well as nonlinear parameter on the thermal stability of the solutions. Finally, we investigate thermodynamical geometry of the obtained solutions by introducing a new metric and studying the phase transition points due to the divergency of the Ricci scalar. We find that the dilaton field affects the phase transition points of the system.
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
Phase transitions in charged topological black holes dressed with a scalar hair
NASA Astrophysics Data System (ADS)
Martínez, Cristián; Montecinos, Alejandra
2010-12-01
Phase transitions in charged topological black holes dressed with a scalar field are studied. These black holes are solutions of the Einstein-Maxwell theory with a negative cosmological constant and a conformally coupled real self-interacting scalar field. Comparing, in the grand canonical ensemble, the free energies of the hairy and undressed black holes two different phase transitions are found. The first of them is one of second-order type and it occurs at a temperature defined by the value of the cosmological constant. Below this temperature an undressed black hole spontaneously acquires a scalar hair. The other phase transition is one of first-order type. The corresponding critical temperature, which is bounded from above by the one of the previous case, strongly depends on the coupling constant of the quartic self-interaction potential, and this transition only appears when the coupling constant is less than a certain value. In this case, below the critical temperature the undressed black hole is thermodynamically favored. However, when the temperature exceeds the critical value a hairy black hole is likely to be occur.
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.
Topological phase transitions of (BixSb1-x)2Se3 alloys by density functional theory
NASA Astrophysics Data System (ADS)
Abdalla, L. B.; Padilha José, E.; Schmidt, T. M.; Miwa, R. H.; Fazzio, A.
2015-06-01
We have performed an ab initio total energy investigation of the topological phase transition, and the electronic properties of topologically protected surface states of (BixSb1-x)2Se3 alloys. In order to provide an accurate alloy concentration for the phase transition, we have considered the special quasirandom structures to describe the alloy system. The trivial → topological transition concentration was obtained by (i) the calculation of the band gap closing as a function of Bi concentration (x), and (ii) the calculation of the Z2 topological invariant number. We show that there is a topological phase transition, for x around 0.4, verified for both procedures (i) and (ii). We also show that in the concentration range 0.4 < x < 0.7, the alloy does not present any other band at the Fermi level besides the Dirac cone, where the Dirac point is far from the bulk states. This indicates that a possible suppression of the scattering process due to bulk states will occur.
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.
Fendley, Paul; Moore, Joel E; Xu, Cenke
2007-05-01
We study a constrained statistical-mechanical model in two dimensions that has three useful descriptions. They are (i) the Ising model on the honeycomb lattice, constrained to have three up spins and three down spins on every hexagon, (ii) the three-color and fully packed loop model on the links of the honeycomb lattice, with loops around a single hexagon forbidden, and (iii) three Ising models on interleaved triangular lattices, with domain walls of the different Ising models not allowed to cross. Unlike the three-color model, the configuration space on the sphere or plane is connected under local moves. On higher-genus surfaces there are infinitely many dynamical sectors, labeled by a noncontractible set of nonintersecting loops. We demonstrate that at infinite temperature the transfer matrix admits an unusual structure related to a gauge symmetry for the same model on an anisotropic lattice. This enables us to diagonalize the original transfer matrix for up to 36 sites, finding an entropy per plaquette S/k{B} approximately 0.3661 ... centered and substantial evidence that the model is not critical. We also find the striking property that the eigenvalues of the transfer matrix on an anisotropic lattice are given in terms of Fibonacci numbers. We comment on the possibility of a topological phase, with infinite topological degeneracy, in an associated two-dimensional quantum model.
Hybridization and Field Driven Phase Transitions in Hexagonally Warped Topological Insulators
NASA Astrophysics Data System (ADS)
Menon, Anirudha; Chowdhury, Debashree; Basu, Banasri
2016-09-01
In this paper, we discuss the role of material parameters and external field effects on a thin film topological insulator(TI) in the context of quantum phase transition (QPT). First, we consider an in-plane tilted magnetic field and determine the band structure of the surface states as a function of the tilt angle. We show that the presence of either a hybridization term or hexagonal warping or a combination of both leads to a semi-metal to insulator phase transition which is facilitated by their 𝒫𝒯 symmetry breaking character. We then note that while the introduction of an electric field does not allow for this QPT since it does not break 𝒫𝒯 symmetry, it can be used in conjunction with a tunneling element to reach a phase transition efficiently. The corresponding critical point is then nontrivially dependent on the electric field, which is pointed out here. Then, we demonstrate that including a hexagonal warping term leads to an immediate 𝒫𝒯 symmetry violating QPT.
Campione, Salvatore; Liu, Sheng; Luk, Ting S.; ...
2015-08-05
We employ both the effective medium approximation (EMA) and Bloch theory to compare the dispersion properties of semiconductor hyperbolic metamaterials (SHMs) at mid-infrared frequencies and metallic hyperbolic metamaterials (MHMs) at visible frequencies. This analysis reveals the conditions under which the EMA can be safely applied for both MHMs and SHMs. We find that the combination of precise nanoscale layering and the longer infrared operating wavelengths puts the SHMs well within the effective medium limit and, in contrast to MHMs, allows for the attainment of very high photon momentum states. Additionally, SHMs allow for new phenomena such as ultrafast creation ofmore » the hyperbolic manifold through optical pumping. Furthermore, we examine the possibility of achieving ultrafast topological transitions through optical pumping which can photo-dope appropriately designed quantum wells on the femtosecond time scale.« less
Campione, Salvatore; Liu, Sheng; Luk, Ting S.; Sinclair, Michael B.
2015-08-05
We employ both the effective medium approximation (EMA) and Bloch theory to compare the dispersion properties of semiconductor hyperbolic metamaterials (SHMs) at mid-infrared frequencies and metallic hyperbolic metamaterials (MHMs) at visible frequencies. This analysis reveals the conditions under which the EMA can be safely applied for both MHMs and SHMs. We find that the combination of precise nanoscale layering and the longer infrared operating wavelengths puts the SHMs well within the effective medium limit and, in contrast to MHMs, allows for the attainment of very high photon momentum states. Additionally, SHMs allow for new phenomena such as ultrafast creation of the hyperbolic manifold through optical pumping. Furthermore, we examine the possibility of achieving ultrafast topological transitions through optical pumping which can photo-dope appropriately designed quantum wells on the femtosecond time scale.
A semi-Dirac point and an electromagnetic topological transition in a dielectric photonic crystal.
Wu, Ying
2014-01-27
Accidental degeneracy in a photonic crystal consisting of a square array of elliptical dielectric cylinders leads to both a semi-Dirac point at the center of the Brillouin zone and an electromagnetic topological transition (ETT). A perturbation method is deduced to affirm the peculiar linear-parabolic dispersion near the semi-Dirac point. An effective medium theory is developed to explain the simultaneous semi-Dirac point and ETT and to show that the photonic crystal is either a zero-refractive-index material or an epsilon-near-zero material at the semi-Dirac point. Drastic changes in the wave manipulation properties at the semi-Dirac point, resulting from ETT, are described.
Pressure induced Ag2Te polymorphs in conjunction with topological non trivial to metal transition
Zhu, J.; Oganov, A. R.; Feng, W. X.; ...
2016-08-01
Silver telluride (Ag2Te) is well known as superionic conductor and topologica insulator with polymorphs. Pressure induced three phase transitions in Ag2Te hav been reported in previous. Here, we experimentally identified high pressure phas above 13 GPa of Ag2Te by using high pressure synchrotron x ray diffraction metho in combination with evolutionary crystal structure prediction, showing it crystallize into a monoclinic structure of space group C2/m with lattice parameters a = 6.081Å b = 5.744Å, c = 6.797 Å, β = 105.53°. The electronic properties measurements of Ag2Te reveal that the topologically non-trivial semiconducting phase I and semimetalli phase II previouslymore » predicated by theory transformed into bulk metals fo high pressure phases in consistent with the first principles calculations« less
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).
NASA Astrophysics Data System (ADS)
Gurzhiy, Vladislav V.; Kovrugin, Vadim M.; Tyumentseva, Olga S.; Mikhaylenko, Pavel A.; Krivovichev, Sergey V.; Tananaev, Ivan G.
2015-09-01
Single crystals of seven novel uranyl oxysalts of selenium with protonated methylamine molecules, [C2H8N]2[(UO2)(SeO4)2(H2O)] (I), [C2H8N]2[(UO2)2(SeO4)3(H2O)] (II), [C4H15N3][H3O]0.5[(UO2)2(SeO4)2.93(SeO3)0.07(H2O)](NO3)0.5 (III), [C2H8N]3[H5O2][(UO2)2(SeO4)3(H2O)2]2(H2O)5 (IV), [C2H8N]2[H3O][(UO2)3(SeO4)4(HSeO3)(H2O)](H2SeO3)0.2 (V), [C4H12N]3[H3O][(UO2)3(SeO4)5(H2O)] (VI), and [C2H8N]3(C2H7N)[(UO2)3(SeO4)4(HSeO3)(H2O)] (VII) have been prepared by isothermal evaporation from aqueous solutions. Their crystal structures have been solved by direct methods and their uranyl selenate and selenite-selenate units investigated using black-and-white graphs from the viewpoints of topology of interpolyhedral linkages and isomeric variations. The crystal structure of IV is based upon complex layers with unique topology, which has not been observed previously in uranyl selenates. Investigations of the statistics and local distribution of the U-Obr-Se bond angles demonstrates that shorter angles associate with undulations, whereas larger angles correspond to planar areas of the uranyl selenite layers.
Schoop, Leslie M.; Xie, Lilia S.; Chen, Ru; Gibson, Quinn D.; Lapidus, Saul H.; Kimchi, Itamar; Hirschberger, Max; Haldolaarachchige, Neel; Ali, Mazhar N.; Belvin, Carina A.; Liang, Tian; Neaton, Jeffrey B.; Ong, N P; Vishwanath, Ashvin; Cava, R. J.
2015-06-23
Three-dimensionalDirac semimetals (DSMs) arematerials that have masslessDirac electrons and exhibit exotic physical properties. It has been suggested that structurally distorting a DSM can create a topological insulator but this has not yet been experimentally verified. Furthermore, Majorana fermions have been theoretically proposed to exist inmaterials that exhibit both superconductivity and topological surface states. Herewe showthat the cubic Laves phase Au2Pb has a bulk Dirac cone that is predicted to gap on cooling through a structural phase transition at 100 K. The low temperature phase can be assigned a Z(2) = -1 topological index, and this phase becomes superconducting below 1.2 K. These characteristics make Au2Pb a unique platform for studying the transition between bulk Dirac electrons and topological surface states as well as studying the interaction of superconductivity with topological surface states, combining many different properties of emergent materials-superconductivity, bulk Dirac electrons, and a topologically nontrivial Z(2) invariant.
Pacaud, F.; Micoulaut, M.
2015-08-14
The thermodynamic, dynamic, structural, and rigidity properties of densified liquid germania (GeO{sub 2}) have been investigated using classical molecular dynamics simulation. We construct from a thermodynamic framework an analytical equation of state for the liquid allowing the possible detection of thermodynamic precursors (extrema of the derivatives of the free energy), which usually indicate the possibility of a liquid-liquid transition. It is found that for the present germania system, such precursors and the possible underlying liquid-liquid transition are hidden by the slowing down of the dynamics with decreasing temperature. In this respect, germania behaves quite differently when compared to parent tetrahedral systems such as silica or water. We then detect a diffusivity anomaly (a maximum of diffusion with changing density/volume) that is strongly correlated with changes in coordinated species, and the softening of bond-bending (BB) topological constraints that decrease the liquid rigidity and enhance transport. The diffusivity anomaly is finally substantiated from a Rosenfeld-type scaling law linked to the pair correlation entropy, and to structural relaxation.
Transition between strong and weak topological insulator in ZrTe5 and HfTe5
Fan, Zongjian; Liang, Qi-Feng; Chen, Y. B.; Yao, Shu-Hua; Zhou, Jian
2017-01-01
ZrTe5 and HfTe5 have attracted increasingly attention recently since the theoretical prediction of being topological insulators (TIs). However, subsequent works show many contradictions about their topolog-ical nature. Three possible phases, i.e. strong TI, weak TI, and Dirac semi-metal, have been observed in different experiments until now. Essentially whether ZrTe5 or HfTe5 has a band gap or not is still a question. Here, we present detailed first-principles calculations on the electronic and topological prop-erties of ZrTe5 and HfTe5 on variant volumes and clearly demonstrate the topological phase transition from a strong TI, going through an intermediate Dirac semi-metal state, then to a weak TI when the crystal expands. Our work might give a unified explain about the divergent experimental results and propose the crucial clue to further experiments to elucidate the topological nature of these materials. PMID:28374804
Topological phase transitions and chiral inelastic transport induced by the squeezing of light
Peano, Vittorio; Houde, Martin; Brendel, Christian; Marquardt, Florian; Clerk, Aashish A.
2016-01-01
There is enormous interest in engineering topological photonic systems. Despite intense activity, most works on topological photonic states (and more generally bosonic states) amount in the end to replicating a well-known fermionic single-particle Hamiltonian. Here we show how the squeezing of light can lead to the formation of qualitatively new kinds of topological states. Such states are characterized by non-trivial Chern numbers, and exhibit protected edge modes, which give rise to chiral elastic and inelastic photon transport. These topological bosonic states are not equivalent to their fermionic (topological superconductor) counterparts and, in addition, cannot be mapped by a local transformation onto topological states found in particle-conserving models. They thus represent a new type of topological system. We study this physics in detail in the case of a kagome lattice model, and discuss possible realizations using nonlinear photonic crystals or superconducting circuits. PMID:26931620
Kachalo, Sëma; Naveed, Hammad; Cao, Youfang; Zhao, Jieling; Liang, Jie
2015-01-01
Geometric and mechanical properties of individual cells and interactions among neighboring cells are the basis of formation of tissue patterns. Understanding the complex interplay of cells is essential for gaining insight into embryogenesis, tissue development, and other emerging behavior. Here we describe a cell model and an efficient geometric algorithm for studying the dynamic process of tissue formation in 2D (e.g. epithelial tissues). Our approach improves upon previous methods by incorporating properties of individual cells as well as detailed description of the dynamic growth process, with all topological changes accounted for. Cell size, shape, and division plane orientation are modeled realistically. In addition, cell birth, cell growth, cell shrinkage, cell death, cell division, cell collision, and cell rearrangements are now fully accounted for. Different models of cell-cell interactions, such as lateral inhibition during the process of growth, can be studied in detail. Cellular pattern formation for monolayered tissues from arbitrary initial conditions, including that of a single cell, can also be studied in detail. Computational efficiency is achieved through the employment of a special data structure that ensures access to neighboring cells in constant time, without additional space requirement. We have successfully generated tissues consisting of more than 20,000 cells starting from 2 cells within 1 hour. We show that our model can be used to study embryogenesis, tissue fusion, and cell apoptosis. We give detailed study of the classical developmental process of bristle formation on the epidermis of D. melanogaster and the fundamental problem of homeostatic size control in epithelial tissues. Simulation results reveal significant roles of solubility of secreted factors in both the bristle formation and the homeostatic control of tissue size. Our method can be used to study broad problems in monolayered tissue formation. Our software is publicly
NASA Astrophysics Data System (ADS)
Lyanda-Geller, Yuli; Simion, George
2015-03-01
We investigate a ground state of the two-dimensional (2D) electron liquid in the presence of disorder for Landau level filling factors, for which the re-entrant integer quantum Hall effect is observed. Our particular interest is the range of filling factors, which in a clean 2D system is favorable to formation of the two-electron (2e) bubble crystal. For the smooth random potential due to charged impurities placed far away from the 2D gas, the ground state is a lightly distorted 2e bubble crystal. However, for positively or negatively charged residual impurities located approximately within about three magnetic lengths from the 2D electrons, the ground state contains charged 2e complexes formed either by positively charged impurity and 3e defect bubble, or negatively charged impurity and 2e defect bubble. In the vicinity of 1e and 3e defect bubbles, the 2e bubbles of the crystal change their shape from round to elongated forming hedgehog (for 1e defect) or vortex (for 3e defect) textures. The topological textures due to these complexes interact with vortex and hedgehog excitations, generated as temperature increases that are not bound by residual impurities. The temperature of insulator to metal transition calculated with both bound and unbound defects agrees with experiment. Research was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award DE-SC0010544.
Liu, Minhao; Wang, Wudi; Richardella, Anthony R; Kandala, Abhinav; Li, Jian; Yazdani, Ali; Samarth, Nitin; Ong, N Phuan
2016-07-01
A striking prediction in topological insulators is the appearance of the quantized Hall resistance when the surface states are magnetized. The surface Dirac states become gapped everywhere on the surface, but chiral edge states remain on the edges. In an applied current, the edge states produce a quantized Hall resistance that equals the Chern number C = ±1 (in natural units), even in zero magnetic field. This quantum anomalous Hall effect was observed by Chang et al. With reversal of the magnetic field, the system is trapped in a metastable state because of magnetic anisotropy. We investigate how the system escapes the metastable state at low temperatures (10 to 200 mK). When the dissipation (measured by the longitudinal resistance) is ultralow, we find that the system escapes by making a few very rapid transitions, as detected by large jumps in the Hall and longitudinal resistances. Using the field at which the initial jump occurs to estimate the escape rate, we find that raising the temperature strongly suppresses the rate. From a detailed map of the resistance versus gate voltage and temperature, we show that dissipation strongly affects the escape rate. We compare the observations with dissipative quantum tunneling predictions. In the ultralow dissipation regime, two temperature scales (T 1 ~ 70 mK and T 2 ~ 145 mK) exist, between which jumps can be observed. The jumps display a spatial correlation that extends over a large fraction of the sample.
Liu, Minhao; Wang, Wudi; Richardella, Anthony R.; Kandala, Abhinav; Li, Jian; Yazdani, Ali; Samarth, Nitin; Ong, N. Phuan
2016-01-01
A striking prediction in topological insulators is the appearance of the quantized Hall resistance when the surface states are magnetized. The surface Dirac states become gapped everywhere on the surface, but chiral edge states remain on the edges. In an applied current, the edge states produce a quantized Hall resistance that equals the Chern number C = ±1 (in natural units), even in zero magnetic field. This quantum anomalous Hall effect was observed by Chang et al. With reversal of the magnetic field, the system is trapped in a metastable state because of magnetic anisotropy. We investigate how the system escapes the metastable state at low temperatures (10 to 200 mK). When the dissipation (measured by the longitudinal resistance) is ultralow, we find that the system escapes by making a few very rapid transitions, as detected by large jumps in the Hall and longitudinal resistances. Using the field at which the initial jump occurs to estimate the escape rate, we find that raising the temperature strongly suppresses the rate. From a detailed map of the resistance versus gate voltage and temperature, we show that dissipation strongly affects the escape rate. We compare the observations with dissipative quantum tunneling predictions. In the ultralow dissipation regime, two temperature scales (T1 ~ 70 mK and T2 ~ 145 mK) exist, between which jumps can be observed. The jumps display a spatial correlation that extends over a large fraction of the sample. PMID:27482539
Dyachenko, P. N.; Molesky, S.; Petrov, A. Yu; Störmer, M.; Krekeler, T.; Lang, S.; Ritter, M.; Jacob, Z.; Eich, M.
2016-01-01
Control of thermal radiation at high temperatures is vital for waste heat recovery and for high-efficiency thermophotovoltaic (TPV) conversion. Previously, structural resonances utilizing gratings, thin film resonances, metasurfaces and photonic crystals were used to spectrally control thermal emission, often requiring lithographic structuring of the surface and causing significant angle dependence. In contrast, here, we demonstrate a refractory W-HfO2 metamaterial, which controls thermal emission through an engineered dielectric response function. The epsilon-near-zero frequency of a metamaterial and the connected optical topological transition (OTT) are adjusted to selectively enhance and suppress the thermal emission in the near-infrared spectrum, crucial for improved TPV efficiency. The near-omnidirectional and spectrally selective emitter is obtained as the emission changes due to material properties and not due to resonances or interference effects, marking a paradigm shift in thermal engineering approaches. We experimentally demonstrate the OTT in a thermally stable metamaterial at high temperatures of 1,000 °C. PMID:27263653
NASA Astrophysics Data System (ADS)
Dyachenko, P. N.; Molesky, S.; Petrov, A. Yu; Störmer, M.; Krekeler, T.; Lang, S.; Ritter, M.; Jacob, Z.; Eich, M.
2016-06-01
Control of thermal radiation at high temperatures is vital for waste heat recovery and for high-efficiency thermophotovoltaic (TPV) conversion. Previously, structural resonances utilizing gratings, thin film resonances, metasurfaces and photonic crystals were used to spectrally control thermal emission, often requiring lithographic structuring of the surface and causing significant angle dependence. In contrast, here, we demonstrate a refractory W-HfO2 metamaterial, which controls thermal emission through an engineered dielectric response function. The epsilon-near-zero frequency of a metamaterial and the connected optical topological transition (OTT) are adjusted to selectively enhance and suppress the thermal emission in the near-infrared spectrum, crucial for improved TPV efficiency. The near-omnidirectional and spectrally selective emitter is obtained as the emission changes due to material properties and not due to resonances or interference effects, marking a paradigm shift in thermal engineering approaches. We experimentally demonstrate the OTT in a thermally stable metamaterial at high temperatures of 1,000 °C.
Transition Induced by Fence Geometrics on Shuttle Orbiter at Mach 10
NASA Technical Reports Server (NTRS)
Everhart, Joel L.
2010-01-01
Fence-induced transition data simulating a raised gap filler have been acquired on the wing lower surface of a Shuttle Orbiter model in the Langley 31-Inch Mach 10 Tunnel to compare with the Shuttle Boundary Layer Transition Flight and HYTHIRM Experiments, and to provide additional correlation data for the Boundary Layer Transition Tool. In a qualitative assessment, the data exhibit the expected response to all parameter variations; however, it is unclear whether fully effective tripping at the fence was ever realized at any test condition with the present model hardware. A preliminary, qualitative comparison of the ground-based transition measurements with those obtained from the STS-128 HYTHIRM imagery at Mach 15 reveal similar transition-wake response characteristics in terms of the spreading and the path along the vehicle surface.
Magnetic transitions in the topological magnon insulator Cu(1,3-bdc)
NASA Astrophysics Data System (ADS)
Chisnell, R.; Helton, J. S.; Freedman, D. E.; Singh, D. K.; Demmel, F.; Stock, C.; Nocera, D. G.; Lee, Y. S.
2016-06-01
Topological magnon insulators are a new class of magnetic materials that possess topologically nontrivial magnon bands. As a result, magnons in these materials display properties analogous to those of electrons in topological insulators. Here we present magnetization, specific heat, and neutron scattering measurements of the ferromagnetic kagome magnet Cu(1,3-bdc). Our measurements provide a detailed description of the magnetic structure and interactions in this material and confirm that it is an ideal prototype for topological magnon physics in a system with a simple spin Hamiltonian.
Kim, Youngwook; Herlinger, Patrick; Moon, Pilkyung; Koshino, Mikito; Taniguchi, Takashi; Watanabe, Kenji; Smet, Jurgen H
2016-08-10
van Hove singularities (VHS's) in the density of states play an outstanding and diverse role for the electronic and thermodynamic properties of crystalline solids. At the critical point the Fermi surface connectivity changes, and topological properties undergo a transition. Opportunities to systematically pass a VHS at the turn of a voltage knob and study its diverse impact are however rare. With the advent of van der Waals heterostructures, control over the atomic registry of neighboring graphene layers offers an unprecedented tool to generate a low energy VHS easily accessible with conventional gating. Here we have addressed magnetotransport when the chemical potential crosses the twist angle induced VHS in twisted bilayer graphene. A topological phase transition is experimentally disclosed in the abrupt conversion of electrons to holes or vice versa, a loss of a nonzero Berry phase and distinct sequences of integer quantum Hall states above and below the singularity.
Qi, Yanpeng; Shi, Wujun; Naumov, Pavel G; Kumar, Nitesh; Sankar, Raman; Schnelle, Walter; Shekhar, Chandra; Chou, Fang-Cheng; Felser, Claudia; Yan, Binghai; Medvedev, Sergey A
2017-03-06
A pressure-induced topological quantum phase transition has been theoretically predicted for the semiconductor bismuth tellurohalide BiTeI with giant Rashba spin splitting. In this work, evolution of the electrical transport properties in BiTeI and BiTeBr is investigated under high pressure. The pressure-dependent resistivity in a wide temperature range passes through a minimum at around 3 GPa, indicating the predicted topological quantum phase transition in BiTeI. Superconductivity is observed in both BiTeI and BiTeBr, while resistivity at higher temperatures still exhibits semiconducting behavior. Theoretical calculations suggest that superconductivity may develop from the multivalley semiconductor phase. The superconducting transition temperature, Tc , increases with applied pressure and reaches a maximum value of 5.2 K at 23.5 GPa for BiTeI (4.8 K at 31.7 GPa for BiTeBr), followed by a slow decrease. The results demonstrate that BiTeX (X = I, Br) compounds with nontrivial topology of electronic states display new ground states upon compression.
NASA Astrophysics Data System (ADS)
Lee, Kyu Won; Lee, Cheol Eui
2015-12-01
We have investigated the effect of electronic topological transition on the electric field-induced band gap in sliding bilayer graphene by using the density functional theory calculations. The electric field-induced band gap was found to be extremely sensitive to the electronic topological transition. At the electronic topological transition induced by layer sliding, four Dirac cones in the Bernal-stacked bilayer graphene reduces to two Dirac cones with equal or unequal Dirac energies depending on the sliding direction. While the critical electric field required for the band gap opening increases with increasing lateral shift for the two Dirac cones with unequal Dirac energies, the critical field is essentially zero with or without a lateral shift for the two Dirac cones with equal Dirac energies. The critical field is determined by the Dirac energy difference and the electronic screening effect. The electronic screening effect was also found to be enhanced with increasing lateral shift, apparently indicating that the massless helical and massive chiral fermions are responsible for the perfect and imperfect electronic screening, respectively.
Photo-electrons unveil topological transitions in graphene-like systems
Peralta Gavensky, Lucila; Usaj, Gonzalo; Balseiro, C. A.
2016-01-01
The topological structure of the wavefunctions of particles in periodic potentials is characterized by the Berry curvature Ωkn whose integral on the Brillouin zone is a topological invariant known as the Chern number. The bulk-boundary correspondence states that these numbers define the number of edge or surface topologically protected states. It is then of primary interest to find experimental techniques able to measure the Berry curvature. However, up to now, there are no spectroscopic experiments that proved to be capable to obtain information on Ωkn to distinguish different topological structures of the bulk wavefunctions of semiconducting materials. Based on experimental results of the dipolar matrix elements for graphene, here we show that ARPES experiments with the appropriate x-ray energies and polarization can unambiguously detect changes of the Chern numbers in dynamically driven graphene and graphene-like materials opening new routes towards the experimental study of topological properties of condensed matter systems. PMID:27833125
Photo-electrons unveil topological transitions in graphene-like systems
NASA Astrophysics Data System (ADS)
Peralta Gavensky, Lucila; Usaj, Gonzalo; Balseiro, C. A.
2016-11-01
The topological structure of the wavefunctions of particles in periodic potentials is characterized by the Berry curvature Ωkn whose integral on the Brillouin zone is a topological invariant known as the Chern number. The bulk-boundary correspondence states that these numbers define the number of edge or surface topologically protected states. It is then of primary interest to find experimental techniques able to measure the Berry curvature. However, up to now, there are no spectroscopic experiments that proved to be capable to obtain information on Ωkn to distinguish different topological structures of the bulk wavefunctions of semiconducting materials. Based on experimental results of the dipolar matrix elements for graphene, here we show that ARPES experiments with the appropriate x-ray energies and polarization can unambiguously detect changes of the Chern numbers in dynamically driven graphene and graphene-like materials opening new routes towards the experimental study of topological properties of condensed matter systems.
NASA Astrophysics Data System (ADS)
Zuhail, K. P.; Sathyanarayana, P.; Seč, D.; Čopar, S.; Škarabot, M.; Muševič, I.; Dhara, S.
2015-03-01
We observe that topological defects in nematic colloids are strongly influenced by the elasticity and onset of smectic layering across the nematic (N ) to smectic-A (Sm A ) phase transition. When approaching the Sm A phase from above, the nematic hyperbolic hedgehog defect that accompanies a spherical colloidal inclusion is transformed into a focal conic line in the Sm A phase. This phase transformation has a strong influence on the pairwise colloidal interaction and is responsible for a structural transition of two-dimensional colloidal crystals. The pretransitional behavior of the point defect is supported by Landau-de Gennes Q -tensor modeling accounting for the increasing elastic anisotropy.
Wang, Hai Tao; Cho, Sam Young
2015-01-14
In order to investigate the quantum phase transition in the one-dimensional quantum compass model, we numerically calculate non-local string correlations, entanglement entropy and fidelity per lattice site by using the infinite matrix product state representation with the infinite time evolving block decimation method. In the whole range of the interaction parameters, we find that four distinct string orders characterize the four different Haldane phases and the topological quantum phase transition occurs between the Haldane phases. The critical exponents of the string order parameters β = 1/8 and the cental charges c = 1/2 at the critical points show that the topological phase transitions between the phases belong to an Ising type of universality classes. In addition to the string order parameters, the singularities of the second derivative of the ground state energies per site, the continuous and singular behaviors of the Von Neumann entropy and the pinch points of the fidelity per lattice site manifest that the phase transitions between the phases are of the second-order, in contrast to the first-order transition suggested in previous studies.
NASA Astrophysics Data System (ADS)
Cortés, Joaquín.; Valencia, Eliana
1999-04-01
Two novel phenomena are discussed in this paper. The first one refers to the effect of the catalyst's surface heterogeneity on the smoothing of the first-order transition observed in the ( A+ B2) reaction (ZGB model). The second effect corresponds to obtaining information on the surface heterogeneity from the shape of the transition curve. Two types of heterogeneity were considered: the structure obtained by the random blocking of reactive sites, and the existence of a distribution in independent strips or terraces on the catalyst's surface.
Synthetic Antimicrobial Oligomers Induce a Composition-Dependent Topological Transition in Membranes
Yang, L.; Gordon, V.D.; Mishra, A.; Som, A.; Purdy, K.R.; Davis, M.A.; Tew, G.N.; Wong, G.C.L.
2009-06-04
Antimicrobial peptides (AMPs) are cationic amphiphiles that comprise a key component of innate immunity. Synthetic analogues of AMPs, such as the family of phenylene ethynylene antimicrobial oligomers (AMOs), recently demonstrated broad-spectrum antimicrobial activity, but the underlying molecular mechanism is unknown. Homologues in this family can be inactive, specifically active against bacteria, or nonspecifically active against bacteria and eukaryotic cells. Using synchrotron small-angle X-ray scattering (SAXS), we show that observed antibacterial activity correlates with an AMO-induced topological transition of small unilamellar vesicles into an inverted hexagonal phase, in which hexagonal arrays of 3.4-nm water channels defined by lipid tubes are formed. Polarized and fluorescence microscopy show that AMO-treated giant unilamellar vesicles remain intact, instead of reconstructing into a bulk 3D phase, but are selectively permeable to encapsulated macromolecules that are smaller than 3.4 nm. Moreover, AMOs with different activity profiles require different minimum threshold concentrations of phosphoethanolamine (PE) lipids to reconstruct the membrane. Using ternary membrane vesicles composed of DOPG:DOPE:DOPC with a charge density fixed at typical bacterial values, we find that the inactive AMO cannot generate the inverted hexagonal phase even when DOPE completely replaces DOPC. The specifically active AMO requires a threshold ratio of DOPE:DOPC = 4:1, and the nonspecifically active AMO requires a drastically lower threshold ratio of DOPE:DOPC = 1.5:1. Since most gram-negative bacterial membranes have more PE lipids than do eukaryotic membranes, our results imply that there is a relationship between negative-curvature lipids such as PE and antimicrobial hydrophobicity that contributes to selective antimicrobial activity.
The dynamic and geometric phase transition in the cellular network of pancreatic islet
NASA Astrophysics Data System (ADS)
Wang, Xujing
2013-03-01
The pancreatic islet is a micro-organ that contains several thousands of endocrine cells, majority of which being the insulin releasing β - cells . - cellsareexcitablecells , andarecoupledtoeachother through gap junctional channels. Here, using percolation theory, we investigate the role of network structure in determining the dynamics of the β-cell network. We show that the β-cell synchronization depends on network connectivity. More specifically, as the site occupancy is reducing, initially the β-cell synchronization is barely affected, until it reaches around a critical value, where the synchronization exhibit a sudden rapid decline, followed by an slow exponential tail. This critical value coincides with the critical site open probability for percolation transition. The dependence over bond strength is similar, exhibiting critical-behavior like dependence around a certain value of bond strength. These results suggest that the β-cell network undergoes a dynamic phase transition when the network is percolated. We further apply the findings to study diabetes. During the development of diabetes, the β - cellnetworkconnectivitydecreases . Siteoccupancyreducesfromthe reducing β-cell mass, and the bond strength is increasingly impaired from β-cell stress and chronic hyperglycemia. We demonstrate that the network dynamics around the percolation transition explain the disease dynamics around onset, including a long time mystery in diabetes, the honeymoon phenomenon.
NASA Astrophysics Data System (ADS)
Ospina-Londoño, D. A.; Fulla, M. R.; Marín, J. H.
2013-03-01
In this work it is considered a versatile model to study two different ionization processes starting from a D20 homonuclear hydrogenic molecule confined in double concentric quantum donuts. Very narrow quantum donut circular cross sections are considered to separate the radial and angular variables in the D20 Hamiltonian by using the well-known adiabatic approximation D20 total energy as a function of the inter donor spacing and the outer donut center line radius is calculated. The salient features of an artificial D20 hydrogenic molecule such as the dissociation energy and the equilibrium length are strongly dependent on the quantum donut geometrical parameters. By increasing systematically the quantum donut outer center line radius, it is possible to understand a first ionization process: D20→D2++e-. A second ionization process D20→D-+D+ can be carried out by fixing the first donor position and gradually moving away the second one. The results obtained in this study are in good agreement with those previously obtained in the limiting cases of very large inter donor separation. The model proposed here is computationally economical and provides a realistic description of both ionization processes and the few-particle system confined in double concentric quantum donuts.
Lin, S.; Zhang, G.; Li, C.; Song, Z.
2016-01-01
We study the tight-binding model for a graphene tube with perimeter N threaded by a magnetic field. We show exactly that this model has different nontrivial topological phases as the flux changes. The winding number, as an indicator of topological quantum phase transition (QPT) fixes at N/3 if N/3 equals to its integer part [N/3], otherwise it jumps between [N/3] and [N/3] + 1 periodically as the flux varies a flux quantum. For an open tube with zigzag boundary condition, exact edge states are obtained. There exist two perfect midgap edge states, in which the particle is completely located at the boundary, even for a tube with finite length. The threading flux can be employed to control the quantum states: transferring the perfect edge state from one end to the other, or generating maximal entanglement between them. PMID:27554930
Lin, S; Zhang, G; Li, C; Song, Z
2016-08-24
We study the tight-binding model for a graphene tube with perimeter N threaded by a magnetic field. We show exactly that this model has different nontrivial topological phases as the flux changes. The winding number, as an indicator of topological quantum phase transition (QPT) fixes at N/3 if N/3 equals to its integer part [N/3], otherwise it jumps between [N/3] and [N/3] + 1 periodically as the flux varies a flux quantum. For an open tube with zigzag boundary condition, exact edge states are obtained. There exist two perfect midgap edge states, in which the particle is completely located at the boundary, even for a tube with finite length. The threading flux can be employed to control the quantum states: transferring the perfect edge state from one end to the other, or generating maximal entanglement between them.
NASA Astrophysics Data System (ADS)
Gruzberg, I. A.; Klümper, A.; Nuding, W.; Sedrakyan, A.
2017-03-01
Recent results for the critical exponent of the localization length at the integer quantum Hall transition differ considerably between experimental (νexp≈2.38 ) and numerical (νCC≈2.6 ) values obtained in simulations of the Chalker-Coddington (CC) network model. The difference is at least partially due to effects of the electron-electron interaction present in experiments. Here, we propose a mechanism that changes the value of ν even within the single-particle picture. We revisit the arguments leading to the CC model and consider more general networks with structural disorder. Numerical simulations of the new model lead to the value ν ≈2.37 . We argue that in a continuum limit the structurally disordered model maps to free Dirac fermions coupled to various random potentials (similar to the CC model) but also to quenched two-dimensional quantum gravity. This explains the possible reason for the considerable difference between critical exponents for the CC model and the structurally disordered model. We extend our results to network models in other symmetry classes.
Temperature-driven topological quantum phase transitions in a phase-change material Ge2Sb2Te5.
Eremeev, S V; Rusinov, I P; Echenique, P M; Chulkov, E V
2016-12-13
The Ge2Sb2Te5 is a phase-change material widely used in optical memory devices and is a leading candidate for next generation non-volatile random access memory devices which are key elements of various electronics and portable systems. Despite the compound is under intense investigation its electronic structure is currently not fully understood. The present work sheds new light on the electronic structure of the Ge2Sb2Te5 crystalline phases. We demonstrate by predicting from first-principles calculations that stable crystal structures of Ge2Sb2Te5 possess different topological quantum phases: a topological insulator phase is realized in low-temperature structure and Weyl semimetal phase is a characteristic of the high-temperature structure. Since the structural phase transitions are caused by the temperature the switching between different topologically non-trivial phases can be driven by variation of the temperature. The obtained results reveal the rich physics of the Ge2Sb2Te5 compound and open previously unexplored possibility for spintronics applications of this material, substantially expanding its application potential.
Temperature-driven topological quantum phase transitions in a phase-change material Ge2Sb2Te5
Eremeev, S. V.; Rusinov, I. P.; Echenique, P. M.; Chulkov, E. V.
2016-01-01
The Ge2Sb2Te5 is a phase-change material widely used in optical memory devices and is a leading candidate for next generation non-volatile random access memory devices which are key elements of various electronics and portable systems. Despite the compound is under intense investigation its electronic structure is currently not fully understood. The present work sheds new light on the electronic structure of the Ge2Sb2Te5 crystalline phases. We demonstrate by predicting from first-principles calculations that stable crystal structures of Ge2Sb2Te5 possess different topological quantum phases: a topological insulator phase is realized in low-temperature structure and Weyl semimetal phase is a characteristic of the high-temperature structure. Since the structural phase transitions are caused by the temperature the switching between different topologically non-trivial phases can be driven by variation of the temperature. The obtained results reveal the rich physics of the Ge2Sb2Te5 compound and open previously unexplored possibility for spintronics applications of this material, substantially expanding its application potential. PMID:27958321
Temperature-driven topological quantum phase transitions in a phase-change material Ge2Sb2Te5
NASA Astrophysics Data System (ADS)
Eremeev, S. V.; Rusinov, I. P.; Echenique, P. M.; Chulkov, E. V.
2016-12-01
The Ge2Sb2Te5 is a phase-change material widely used in optical memory devices and is a leading candidate for next generation non-volatile random access memory devices which are key elements of various electronics and portable systems. Despite the compound is under intense investigation its electronic structure is currently not fully understood. The present work sheds new light on the electronic structure of the Ge2Sb2Te5 crystalline phases. We demonstrate by predicting from first-principles calculations that stable crystal structures of Ge2Sb2Te5 possess different topological quantum phases: a topological insulator phase is realized in low-temperature structure and Weyl semimetal phase is a characteristic of the high-temperature structure. Since the structural phase transitions are caused by the temperature the switching between different topologically non-trivial phases can be driven by variation of the temperature. The obtained results reveal the rich physics of the Ge2Sb2Te5 compound and open previously unexplored possibility for spintronics applications of this material, substantially expanding its application potential.
Fisher, Kaitlin M.; Haglund, Ellinor; Noel, Jeffrey K.; Hailey, Kendra L.; Onuchic, José N.; Jennings, Patricia A.
2015-01-01
Interleukin-33 (IL-33) is currently the focus of multiple investigations into targeting pernicious inflammatory disorders. This mediator of inflammation plays a prevalent role in chronic disorders such as asthma, rheumatoid arthritis, and progressive heart disease. In order to better understand the possible link between the folding free energy landscape and functional regions in IL-33, a combined experimental and theoretical approach was applied. IL-33 is a pseudo- symmetrical protein composed of three distinct structural elements that complicate the folding mechanism due to competition for nucleation on the dominant folding route. Trefoil 1 constitutes the majority of the binding interface with the receptor whereas Trefoils 2 and 3 provide the stable scaffold to anchor Trefoil 1. We identified that IL-33 folds with a three-state mechanism, leading to a rollover in the refolding arm of its chevron plots in strongly native conditions. In addition, there is a second slower refolding phase that exhibits the same rollover suggesting similar limitations in folding along parallel routes. Characterization of the intermediate state and the rate limiting steps required for folding suggests that the rollover is attributable to a moving transition state, shifting from a post- to pre-intermediate transition state as you move from strongly native conditions to the midpoint of the transition. On a structural level, we found that initially, all independent Trefoil units fold equally well until a QCA of 0.35 when Trefoil 1 will backtrack in order to allow Trefoils 2 and 3 to fold in the intermediate state, creating a stable scaffold for Trefoil 1 to fold onto during the final folding transition. The formation of this intermediate state and subsequent moving transition state is a result of balancing the difficulty in folding the functionally important Trefoil 1 onto the remainder of the protein. Taken together our results indicate that the functional element of the protein is
NASA Astrophysics Data System (ADS)
Shojaei, Borzoyeh; McFadden, Anthony P.; Lee, Joon Sue; Pendharkar, Mihir; Palmstrøm, Chris J.
When 2D electron and hole subbands in InAs/GaSb bilayers are tuned to the inverted regime the system is predicted to exhibit an insulating bulk and counter propagating helical 1D edge states. This work presents a dual-gate mapping of the topological-to-normal insulator phase transition for several InAs/GaSb bilayers wherein the InAs and GaSb layer thicknesses are varied. In-plane and out-of-plane magnetotransport experiments reveal the effect of heterostructure geometry on the magnitudes of the longitudinal and Hall magnetoresistances and on the shape and temperature dependence of the gate-tuned resistance map in the vicinity of the phase transition. This work was supported by Microsoft Research.
NASA Astrophysics Data System (ADS)
Kargarian, Mehdi; Langari, Abdollah; Fiete, Gregory A.
2013-03-01
The expected phenomenology of non-interacting topological band insulators (TBI) is now largely theoretically understood. However, the fate of TBIs in the presence of interactions remains an active area of research with novel, interaction-driven topological states possible, as well as new exotic magnetic states. In this work we study the magnetic phases of an exchange Hamiltonian arising in the strong interaction limit of a Hubbard model on the honeycomb lattice whose non-interacting limit is a two-dimensional TBI recently proposed for the layered heavy transition metal oxide compound, (Li,Na)2IrO3. By a combination of analytical methods and exact diagonalization studies on finite size clusters, we map out the magnetic phase diagram of the model. We find that strong spin-orbit coupling can lead to a phase transition from an antiferromagnetic Neél state to a spiral or stripy ordered state. We also discuss the conditions under which a quantum spin liquid may appear in our model, and we compare our results with the different but related Kitaev-Heisenberg-J2-J3 model which has recently been studied in a similar context. We gratefully acknowledge financial support from ARO Grant No. W911NF-09-1-0527 and NSF Grant No. DMR-0955778
NASA Astrophysics Data System (ADS)
Kargarian, Mehdi; Langari, Abdollah; Fiete, Gregory A.
2012-11-01
The expected phenomenology of noninteracting topological band insulators (TBIs) is now largely theoretically understood. However, the fate of TBIs in the presence of interactions remains an active area of research with novel, interaction-driven topological states possible, as well as new exotic magnetic states. In this work we study the magnetic phases of an exchange Hamiltonian arising in the strong interaction limit of a Hubbard model on the honeycomb lattice whose noninteracting limit is a two-dimensional TBI recently proposed for the layered heavy transition metal oxide compound (Li,Na)2IrO3. By a combination of analytical methods and exact diagonalization studies on finite-size clusters, we map out the magnetic phase diagram of the model. We find that strong spin-orbit coupling can lead to a phase transition from an antiferromagnetic Neél state to a spiral or stripy ordered state. We also discuss the conditions under which a quantum spin liquid may appear in our model, and we compare our results with the different but related Kitaev-Heisenberg-J2-J3 model which has recently been studied in a similar context.
Lifshitz transition and Van Hove singularity in a three-dimensional topological Dirac semimetal
NASA Astrophysics Data System (ADS)
Xu, Su-Yang; Liu, Chang; Belopolski, I.; Kushwaha, S. K.; Sankar, R.; Krizan, J. W.; Chang, T.-R.; Polley, C. M.; Adell, J.; Balasubramanian, T.; Miyamoto, K.; Alidoust, N.; Bian, Guang; Neupane, M.; Jeng, H.-T.; Huang, C.-Y.; Tsai, W.-F.; Okuda, T.; Bansil, A.; Chou, F. C.; Cava, R. J.; Lin, H.; Hasan, M. Z.
2015-08-01
A three-dimensional (3D) Dirac semimetal is a novel state of quantum matter which has recently attracted much attention as an apparent 3D version of graphene. In this paper, we report results on the electronic structure of the 3D Dirac semimetal Na3Bi at a surface that reveals its nontrivial ground state. Our studies reveal that the two 3D Dirac cones go through a topological change in the constant energy contour as a function of the binding energy, featuring a Lifshitz point, which is missing in a strict 3D analog of graphene. Our results identify an example of a band saddle-point singularity in 3D Dirac materials. This is in contrast to its two-dimensional analogs such as graphene and the Dirac surface states of a topological insulator. The observation of multiple Dirac nodes in Na3Bi connecting via a Lifshitz point along its crystalline rotational axis away from the Kramers point serves as a decisive signature for the symmetry-protected nature of the Dirac semimetal's topological bulk ground state.
NASA Astrophysics Data System (ADS)
Sim, Sangwan; Koirala, Nikesh; Brahlek, Matthew; Sung, Ji Ho; Park, Jun; Cha, Soonyoung; Jo, Moon-Ho; Oh, Seongshik; Choi, Hyunyong
2015-06-01
Asymmetric Fano resonance arises from quantum interference between discrete and continuum states. The characteristic asymmetry has attracted strong interests in understanding light-induced optoelectronic responses and corresponding applications. In conventional solids, however, the tunability of Fano resonance is generally limited by a material's intrinsic property. Topological insulators are unique states of matter embodying both conducting Dirac surface and underlying bulk. If it is possible to manipulate the two coexisting states, then it should form an ideal laboratory for realizing a tunable topological Fano system. Here, with the recently discovered topological phase transition in (Bi1-xI nx ) 2S e3 , we report tunable Fano interference phenomena. By engineering the spatial overlap between surface Dirac electrons (continuous terahertz transitions) and bulk phonon (discrete mode at ˜2 terahertz), we continuously tune, abruptly switch, and dynamically modulate the Fano resonance. Eliminating the topological surface via decreasing spin-orbit coupling―that is, across topological and nontopological phases, we find that the asymmetric Fano spectra return to the symmetric profile. Laser-excited ultrafast terahertz spectroscopy reveals that the controlled spatial overlap is responsible for the picosecond tunability of the Fano resonance, suggesting potentials toward optically controllable topological Fano systems.
NASA Astrophysics Data System (ADS)
Łepkowski, S. P.; Bardyszewski, W.
2017-02-01
Combining the k · p method with the third-order elasticity theory, we perform a theoretical study of the pressure-induced topological phase transition and the pressure evolution of topologically protected edge states in InN/GaN and In-rich InGaN/GaN quantum wells. We show that for a certain range of the quantum well parameters, thanks to a negative band gap pressure coefficient, it is possible to continuously drive the system from the normal insulator state through the topological insulator into the semimetal phase. The critical pressure for the topological phase transition depends not only on the quantum well thickness but also on the width of the Hall bar, which determines the coupling between the edge states localized at the opposite edges. We also find that in narrow Hall bar structures, near the topological phase transition, a significant Rashba-type spin splitting of the lower and upper branches of the edge state dispersion curve appears. This effect originates from the lack of the mirror symmetry of the quantum well potential caused by the built-in electric field, and can be suppressed by increasing the Hall bar width. When the pressure increases, the energy dispersion of the edge states becomes more parabolic-like and the spin splitting decreases. A further increase of pressure leads to the transition to a semimetal phase, which occurs due to the closure of the indirect 2D bulk band gap. The difference between the critical pressure at which the system becomes semimetallic, and the pressure for the topological phase transition, correlates with the variation of the pressure coefficient of the band gap in the normal insulator state.
Łepkowski, S P; Bardyszewski, W
2017-02-08
Combining the k · p method with the third-order elasticity theory, we perform a theoretical study of the pressure-induced topological phase transition and the pressure evolution of topologically protected edge states in InN/GaN and In-rich InGaN/GaN quantum wells. We show that for a certain range of the quantum well parameters, thanks to a negative band gap pressure coefficient, it is possible to continuously drive the system from the normal insulator state through the topological insulator into the semimetal phase. The critical pressure for the topological phase transition depends not only on the quantum well thickness but also on the width of the Hall bar, which determines the coupling between the edge states localized at the opposite edges. We also find that in narrow Hall bar structures, near the topological phase transition, a significant Rashba-type spin splitting of the lower and upper branches of the edge state dispersion curve appears. This effect originates from the lack of the mirror symmetry of the quantum well potential caused by the built-in electric field, and can be suppressed by increasing the Hall bar width. When the pressure increases, the energy dispersion of the edge states becomes more parabolic-like and the spin splitting decreases. A further increase of pressure leads to the transition to a semimetal phase, which occurs due to the closure of the indirect 2D bulk band gap. The difference between the critical pressure at which the system becomes semimetallic, and the pressure for the topological phase transition, correlates with the variation of the pressure coefficient of the band gap in the normal insulator state.
Yu, Na; Klepov, Vladislav V.; Villa, Eric M.; Bosbach, Dirk; Suleimanov, Evgeny V.; Depmeier, Wulf; Albrecht-Schmitt, Thomas E.; Alekseev, Evgeny V.
2014-07-01
The hydrothermal reaction of uranyl nitrate with rubidium nitrate and arsenic (III) oxide results in the formation of polymorphic α- and β-Rb[UO{sub 2}(AsO{sub 3}OH)(AsO{sub 2}(OH){sub 2})]·H{sub 2}O (α-, β-RbUAs) and the anhydrous phase Rb[UO{sub 2}(AsO{sub 3}OH)(AsO{sub 2}(OH){sub 2})] (RbUAs). These phases were structurally, chemically and spectroscopically characterized. The structures of all three compounds are based upon topologically identical, but geometrically isomeric layers. The layers are linked with each other by means of the Rb cations and hydrogen bonding. Dehydration experiments demonstrate that water deintercalation from hydrous α- and β-RbUAs yields anhydrous RbUAs via topotactic reactions. - Graphical abstract: Three different layer geometries observed in the structures of Rb[UO{sub 2}(AsO{sub 3}OH)(AsO{sub 2}(OH){sub 2})] and α- and β- Rb[UO{sub 2}(AsO{sub 3}OH)(AsO{sub 2}(OH){sub 2})]·H{sub 2}O. Two different coordination environments of uranium polyhedra (types I and II) are shown schematically on the top of the figure. - Highlights: • Three new uranyl arsenates were synthesized from the hydrothermal reactions. • The phases consist of the topologically identical but geometrically different layers. • Topotactic transitions were observed in the processes of mono-hyrates dehydration.
NASA Astrophysics Data System (ADS)
Tripathi, Swarnendu; Portman, John J.
2011-08-01
Conformational flexibility plays a central role in allosteric transition of proteins. In this paper, we extend the analysis of our previous study [S. Tripathi and J. J. Portman, Proc. Natl. Acad. Sci. U.S.A. 106, 2104 (2009)] to investigate how relatively minor structural changes of the meta-stable states can significantly influence the conformational flexibility and allosteric transition mechanism. We use the allosteric transitions of the domains of calmodulin as an example system to highlight the relationship between the transition mechanism and the inter-residue contacts present in the meta-stable states. In particular, we focus on the origin of transient local unfolding (cracking), a mechanism that can lower free energy barriers of allosteric transitions, in terms of the inter-residue contacts of the meta-stable states and the pattern of local strain that develops during the transition. We find that the magnitude of the local strain in the protein is not the sole factor determining whether a region will ultimately crack during the transition. These results emphasize that the residue interactions found exclusively in one of the two meta-stable states is the key in understanding the mechanism of allosteric conformational change.
Tripathi, Swarnendu; Portman, John J
2011-08-21
Conformational flexibility plays a central role in allosteric transition of proteins. In this paper, we extend the analysis of our previous study [S. Tripathi and J. J. Portman, Proc. Natl. Acad. Sci. U.S.A. 106, 2104 (2009)] to investigate how relatively minor structural changes of the meta-stable states can significantly influence the conformational flexibility and allosteric transition mechanism. We use the allosteric transitions of the domains of calmodulin as an example system to highlight the relationship between the transition mechanism and the inter-residue contacts present in the meta-stable states. In particular, we focus on the origin of transient local unfolding (cracking), a mechanism that can lower free energy barriers of allosteric transitions, in terms of the inter-residue contacts of the meta-stable states and the pattern of local strain that develops during the transition. We find that the magnitude of the local strain in the protein is not the sole factor determining whether a region will ultimately crack during the transition. These results emphasize that the residue interactions found exclusively in one of the two meta-stable states is the key in understanding the mechanism of allosteric conformational change.
NASA Astrophysics Data System (ADS)
Carpentier, David; Le Doussal, Pierre
2000-11-01
We study the two dimensional XY model with quenched random phases and its Coulomb gas formulation. A novel renormalization group (RG) method is developed which allows to study perturbatively the glassy low temperature XY phase and the transition at which frozen topological defects (vortices) proliferate. This RG approach is constructed both from the replicated Coulomb gas and, equivalently without the use of replicas, using the probability distribution of the local disorder (random defect core energy). By taking into account the fusion of environments (i.e., charge fusion in the replicated Coulomb gas) this distribution is shown to obey a Kolmogorov's type (KPP) non linear RG equation which admits traveling wave solutions and exhibits a freezing phenomenon analogous to glassy freezing in Derrida's random energy models. The resulting physical picture is that the distribution of local disorder becomes broad below a freezing temperature and that the transition is controlled by rare favorable regions for the defects, the density of which can be used as the new perturbative parameter. The determination of marginal directions at the disorder induced transition is shown to be related to the well studied front velocity selection problem in the KPP equation and the universality of the novel critical behaviour obtained here to the known universality of the corrections to the front velocity. Applications to other two dimensional problems are mentioned at the end.
Wang, Zhenhua; Tian, Changhai; Dhamala, Mukesh; Liu, Zonghua
2017-04-03
We here study explosive synchronization transitions and network activity propagation in networks of coupled neurons to provide a new understanding of the relationship between network topology and explosive dynamical transitions as in epileptic seizures and their propagations in the brain. We model local network motifs and configurations of coupled neurons and analyze the activity propagations between a group of active neurons to their inactive neuron neighbors in a variety of network configurations. We find that neuronal activity propagation is limited to local regions when network is highly clustered with modular structures as in the normal brain networks. When the network cluster structure is slightly changed, the activity propagates to the entire network, which is reminiscent of epileptic seizure propagation in the brain. Finally, we analyze intracranial electroencephalography (IEEG) recordings of a seizure episode from a epilepsy patient and uncover that explosive synchronization-like transition occurs around the clinically defined onset of seizure. These findings may provide a possible mechanism for the recurrence of epileptic seizures, which are known to be the results of aberrant neuronal network structure and/or function in the brain.
NASA Astrophysics Data System (ADS)
Enderlein, Carsten; Fontes, Magda; Baggio-Saitovich, Elisa; Continentino, Mucio A.
2016-01-01
The semimetal-to-semiconductor transition in fcc-Yb under modest pressure can be considered a picture book example of a metal-insulator transition of the Lifshitz type. We have performed transport measurements at low temperatures in the closest vicinity of the transition and related DFT calculations of the Fermi surface. Our resistivity measurements show a linear temperature dependence with an unusually low dρ / dT at low temperatures approaching the MIT. The calculations suggest fcc-ytterbium being an ultra-multi valley system with 24 electron and 6 hole pockets in the Brillouin zone. Such Fermi surface topology naturally supports the appearance of strongly correlated phases. An estimation of the quasiparticle-enhanced effective mass shows that the scattering rate is by at least two orders of magnitude lower than in other materials which exhibit linear-in-T behavior at a quantum critical point. However, we cannot exclude an excessive effective mass enhancement, when the van Hove singularity touches the Fermi level.
Finite-size driven topological and metal-insulator transition in (Bi1-xInx)2 Se3thin films
NASA Astrophysics Data System (ADS)
Salehi, Maryam; Shapourian, Hassan; Koirala, Nikesh; Brahlek, Matthew; Moon, Jisoo; Oh, Seongshik
In a topological insulator (TI), if one of its heavy elements is replaced by a light one, the spin-orbit coupling (SOC) strength decreases and eventually the TI transforms into a normal insulator beyond a critical level of substitution.This is the standard description of the topological phase transition (TPT). However, this notion of TPT, driven solely by the SOC (or something equivalent), is not complete for finite size samples considering that the thickness of the topological surface states diverges at the critical point. Here, on specially-engineered (BixIn1-x)2 Se3 thin films, using systematic transport measurments we show that not only the SOC but also the finite sample size can induce TPT. This study sheds light on the role of spatial confinement as an extra tuning parameter controlling the topological critical point.
Pressure induced Ag_{2}Te polymorphs in conjunction with topological non trivial to metal transition
Zhu, J.; Oganov, A. R.; Feng, W. X.; Yao, Y. G.; Zhang, S. J.; Yu, X. H.; Zhu, J. L.; Yu, R. C.; Jin, C. Q.; Dai, X.; Fang, Z.; Zhao, Y. S.
2016-08-01
Silver telluride (Ag_{2}Te) is well known as superionic conductor and topologica insulator with polymorphs. Pressure induced three phase transitions in Ag_{2}Te hav been reported in previous. Here, we experimentally identified high pressure phas above 13 GPa of Ag_{2}Te by using high pressure synchrotron x ray diffraction metho in combination with evolutionary crystal structure prediction, showing it crystallize into a monoclinic structure of space group C2/m with lattice parameters a = 6.081Å b = 5.744Å, c = 6.797 Å, β = 105.53°. The electronic properties measurements of Ag_{2}Te reveal that the topologically non-trivial semiconducting phase I and semimetalli phase II previously predicated by theory transformed into bulk metals fo high pressure phases in consistent with the first principles calculations
Zhao, Bao; Zhang, Jiayong; Wang, Yicheng; Yang, Zhongqin
2014-12-28
The electronic states and topological behaviors of Pt(Ni, Pd)-decorated silicene are investigated by using an ab-initio method. All the three kinds of the adatoms prefer hollow sites of the silicene, guaranteeing the Dirac cones unbroken. The Pt(Ni, Pd)-decorated silicene systems all present quantum valley Hall (QVH) states with the gap opened exactly at the Fermi level. The gaps of the QVH states can be increased substantially by applying a positive electric field. Very fascinating phase transitions from QVH to quantum spin Hall (QSH) and then to QVH again are achieved in the Pt/Ni-decorated silicene when a negative electric field is applied. The QSH state in the Pd case with a negative electric field is, however, quenched because of relatively larger Rashba spin-orbit coupling (SOC) than the intrinsic SOC in the system. Our findings may be useful for the applications of silicene-based devices in valleytronics and spintronics.
NASA Astrophysics Data System (ADS)
Chasapis, T. C.; Koumoulis, D.; Leung, B.; Calta, N. P.; Lo, S.-H.; Dravid, V. P.; Bouchard, L.-S.; Kanatzidis, M. G.
2015-08-01
The requirement for large bulk resistivity in topological insulators has led to the design of complex ternary and quaternary phases with balanced donor and acceptor levels. A common feature of the optimized phases is that they lie close to the p- to n-transition. The tetradymite Bi2Te3-xSex system exhibits minimum bulk conductance at the ordered composition Bi2Te2Se. By combining local and integral measurements of the density of states, we find that the point of minimum electrical conductivity at x = 1.0 where carriers change from hole-like to electron-like is characterized by conductivity of the mixed type. Our experimental findings, which are interpreted within the framework of a two-band model for the different carrier types, indicate that the mixed state originates from different types of native defects that strongly compensate at the crossover point.
Chasapis, T. C. E-mail: m-kanatzidis@northwestern.edu; Calta, N. P.; Kanatzidis, M. G. E-mail: m-kanatzidis@northwestern.edu; Koumoulis, D.; Leung, B.; Lo, S.-H.; Dravid, V. P.; Bouchard, L.-S.
2015-08-01
The requirement for large bulk resistivity in topological insulators has led to the design of complex ternary and quaternary phases with balanced donor and acceptor levels. A common feature of the optimized phases is that they lie close to the p- to n-transition. The tetradymite Bi{sub 2}Te{sub 3−x}Se{sub x} system exhibits minimum bulk conductance at the ordered composition Bi{sub 2}Te{sub 2}Se. By combining local and integral measurements of the density of states, we find that the point of minimum electrical conductivity at x = 1.0 where carriers change from hole-like to electron-like is characterized by conductivity of the mixed type. Our experimental findings, which are interpreted within the framework of a two-band model for the different carrier types, indicate that the mixed state originates from different types of native defects that strongly compensate at the crossover point.
Geodesic paths and topological charges in quantum systems
NASA Astrophysics Data System (ADS)
Grangeiro Souza Barbosa Lima, Tiago Aecio
This dissertation focuses on one question: how should one drive an experimentally prepared state of a generic quantum system into a different target-state, simultaneously minimizing energy dissipation and maximizing the fidelity between the target and evolved-states? We develop optimal adiabatic driving protocols for general quantum systems, and show that these are geodesic paths. Geometric ideas have always played a fundamental role in the understanding and unification of physical phenomena, and the recent discovery of topological insulators has drawn great interest to topology from the field of condensed matter physics. Here, we discuss the quantum geometric tensor, a mathematical object that encodes geometrical and topological properties of a quantum system. It is related to the fidelity susceptibility (an important quantity regarding quantum phase transitions) and to the Berry curvature, which enables topological characterization through Berry phases. A refined understanding of the interplay between geometry and topology in quantum mechanics is of direct relevance to several emergent technologies, such as quantum computers, quantum cryptography, and quantum sensors. As a demonstration of how powerful geometric and topological ideas can become when combined, we present the results of an experiment that we recently proposed. This experimental work was done at the Google Quantum Lab, where researchers were able to visualize the topological nature of a two-qubit system in sharp detail, a startling contrast with earlier methods. To achieve this feat, the optimal protocols described in this dissertation were used, allowing for a great improvement on the experimental apparatus, without the need for technical engineering advances. Expanding the existing literature on the quantum geometric tensor using notions from differential geometry and topology, we build on the subject nowadays known as quantum geometry. We discuss how slowly changing a parameter of a quantum
Topology trivialization transition in random non-gradient autonomous ODEs on a sphere
NASA Astrophysics Data System (ADS)
Fyodorov, Y. V.
2016-12-01
We calculate the mean total number of equilibrium points in a system of N random autonomous ODEs introduced by Cugliandolo et al [17] to describe non-relaxational glassy dynamics on the high-dimensional sphere. In doing it we suggest a new approach which allows such a calculation to be done most straightforwardly, and is based on efficiently incorporating the Langrange multiplier into the Kac-Rice framework. Analysing the asymptotic behaviour for large N we confirm that the phenomenon of ‘topology trivialization’ revealed earlier for other systems holds also in the present framework with nonrelaxational dynamics. Namely, by increasing the variance of the random ‘magnetic field’ term in dynamical equations we find a ‘phase transition’ from the exponentially abundant number of equilibria down to just two equilibria. Classifying the equilibria in the nontrivial phase by stability remains an open problem.
Topological phase transition from trigonal warping in van der Waals multilayers
NASA Astrophysics Data System (ADS)
Zeng, Junjie; Ren, Yafei; Zhang, Kunhua; Qiao, Zhenhua
2017-01-01
In van der Waals multilayers of triangular lattice, trigonal warping occurs universally due to the interlayer hopping. We theoretically investigate the effect of trigonal warping upon distinctive topological phases, such as the quantum anomalous Hall effect (QAHE) and the quantum valley Hall effect (QVHE). Taking Bernal-stacked bilayer graphene as an example, we find that the trigonal warping plays a crucial role in the formation of QAHE in a large exchange field and/or interlayer potential difference by inducing extra band inversion points at a momentum further away from the high-symmetry point. The presence of trigonal warping shrinks the phase space of QAHE and QVHE, leading to the emergence of a valley-polarized QAHE with high Chern numbers ranging from C =-7 to 7 . These results suggest that the universal trigonal warping may play an important role when the Bloch states at momenta deviated from high-symmetry points are involved.
Damski, Bogdan
2005-07-15
It can be shown that the dynamics of the Landau-Zener model can be accurately described in terms of the Kibble-Zurek theory of the topological defect production in nonequilibrium phase transitions. The simplest quantum model exhibiting the Kibble-Zurek mechanism is presented. A new intuitive description of Landau-Zener dynamics is found.
Damski, Bogdan
2005-07-15
It can be shown that the dynamics of the Landau-Zener model can be accurately described in terms of the Kibble-Zurek theory of the topological defect production in nonequilibrium phase transitions. The simplest quantum model exhibiting the Kibble-Zurek mechanism is presented. A new intuitive description of Landau-Zener dynamics is found.
Butterfly magnetoresistance, quasi-2D Dirac Fermi surface and topological phase transition in ZrSiS.
Ali, Mazhar N; Schoop, Leslie M; Garg, Chirag; Lippmann, Judith M; Lara, Erik; Lotsch, Bettina; Parkin, Stuart S P
2016-12-01
Magnetoresistance (MR), the change of a material's electrical resistance in response to an applied magnetic field, is a technologically important property that has been the topic of intense study for more than a quarter century. We report the observation of an unusual "butterfly"-shaped titanic angular magnetoresistance (AMR) in the nonmagnetic Dirac material, ZrSiS, which we find to be the most conducting sulfide known, with a 2-K resistivity as low as 48(4) nΩ⋅cm. The MR in ZrSiS is large and positive, reaching nearly 1.8 × 10(5) percent at 9 T and 2 K at a 45° angle between the applied current (I || a) and the applied field (90° is H || c). Approaching 90°, a "dip" is seen in the AMR, which, by analyzing Shubnikov de Haas oscillations at different angles, we find to coincide with a very sharp topological phase transition unlike any seen in other known Dirac/Weyl materials. We find that ZrSiS has a combination of two-dimensional (2D) and 3D Dirac pockets comprising its Fermi surface and that the combination of high-mobility carriers and multiple pockets in ZrSiS allows for large property changes to occur as a function of angle between applied fields. This makes it a promising platform to study the physics stemming from the coexistence of 2D and 3D Dirac electrons as well as opens the door to creating devices focused on switching between different parts of the Fermi surface and different topological states.
Butterfly magnetoresistance, quasi-2D Dirac Fermi surface and topological phase transition in ZrSiS
Ali, Mazhar N.; Schoop, Leslie M.; Garg, Chirag; Lippmann, Judith M.; Lara, Erik; Lotsch, Bettina; Parkin, Stuart S. P.
2016-01-01
Magnetoresistance (MR), the change of a material’s electrical resistance in response to an applied magnetic field, is a technologically important property that has been the topic of intense study for more than a quarter century. We report the observation of an unusual “butterfly”-shaped titanic angular magnetoresistance (AMR) in the nonmagnetic Dirac material, ZrSiS, which we find to be the most conducting sulfide known, with a 2-K resistivity as low as 48(4) nΩ⋅cm. The MR in ZrSiS is large and positive, reaching nearly 1.8 × 105 percent at 9 T and 2 K at a 45° angle between the applied current (I || a) and the applied field (90° is H || c). Approaching 90°, a “dip” is seen in the AMR, which, by analyzing Shubnikov de Haas oscillations at different angles, we find to coincide with a very sharp topological phase transition unlike any seen in other known Dirac/Weyl materials. We find that ZrSiS has a combination of two-dimensional (2D) and 3D Dirac pockets comprising its Fermi surface and that the combination of high-mobility carriers and multiple pockets in ZrSiS allows for large property changes to occur as a function of angle between applied fields. This makes it a promising platform to study the physics stemming from the coexistence of 2D and 3D Dirac electrons as well as opens the door to creating devices focused on switching between different parts of the Fermi surface and different topological states. PMID:28028541
NASA Astrophysics Data System (ADS)
Slagle, Kevin
2015-03-01
Using determinant quantum Monte Carlo simulations, we demonstrate that an extended Hubbard model on a bilayer honeycomb lattice has two novel quantum phase transitions, each with connections to symmetry protected topological states. 1) The first is a continuous phase transition between the weakly interacting gapless Dirac fermion phase and a strongly interacting fully gapped and symmetric trivial phase. Because there is no spontaneous symmetry breaking, this transition cannot be described by the standard Gross-Neveu model. We argue that this phase transition is related to the Z16 classification of the topological superconductor 3He-B phase with interactions. 2) The second is a quantum critical point between a quantum spin Hall insulator with spin Sz conservation and the previously mentioned strongly interacting gapped phase. At the critical point the single particle excitations remain gapped, while spin and charge gaps close. We argue that this transition is described by a bosonic O(4) nonlinear sigma model field theory with a topological Θ-term.
Quantum computation using geometric algebra
NASA Astrophysics Data System (ADS)
Matzke, Douglas James
This dissertation reports that arbitrary Boolean logic equations and operators can be represented in geometric algebra as linear equations composed entirely of orthonormal vectors using only addition and multiplication Geometric algebra is a topologically based algebraic system that naturally incorporates the inner and anticommutative outer products into a real valued geometric product, yet does not rely on complex numbers or matrices. A series of custom tools was designed and built to simplify geometric algebra expressions into a standard sum of products form, and automate the anticommutative geometric product and operations. Using this infrastructure, quantum bits (qubits), quantum registers and EPR-bits (ebits) are expressed symmetrically as geometric algebra expressions. Many known quantum computing gates, measurement operators, and especially the Bell/magic operators are also expressed as geometric products. These results demonstrate that geometric algebra can naturally and faithfully represent the central concepts, objects, and operators necessary for quantum computing, and can facilitate the design and construction of quantum computing tools.
Geometric diffusion of quantum trajectories
Yang, Fan; Liu, Ren-Bao
2015-01-01
A quantum object can acquire a geometric phase (such as Berry phases and Aharonov–Bohm phases) when evolving along a path in a parameter space with non-trivial gauge structures. Inherent to quantum evolutions of wavepackets, quantum diffusion occurs along quantum trajectories. Here we show that quantum diffusion can also be geometric as characterized by the imaginary part of a geometric phase. The geometric quantum diffusion results from interference between different instantaneous eigenstate pathways which have different geometric phases during the adiabatic evolution. As a specific example, we study the quantum trajectories of optically excited electron-hole pairs in time-reversal symmetric insulators, driven by an elliptically polarized terahertz field. The imaginary geometric phase manifests itself as elliptical polarization in the terahertz sideband generation. The geometric quantum diffusion adds a new dimension to geometric phases and may have applications in many fields of physics, e.g., transport in topological insulators and novel electro-optical effects. PMID:26178745
NASA Astrophysics Data System (ADS)
Khazaei, Mohammad; Ranjbar, Ahmad; Arai, Masao; Yunoki, Seiji
2016-09-01
The family of two-dimensional transition metal carbides, so called MXenes, has recently found new members with ordered double transition metals M2'M″C2 , where M' and M″ stand for transition metals. Here, using a set of first-principles calculations, we demonstrate that some of the newly added members, oxide M2'M″C2 (M'=Mo , W; M″=Ti , Zr, Hf) MXenes, are topological insulators. The nontrivial topological states of the predicted MXenes are revealed by the Z2 index, which is evaluated from the parities of the occupied bands below the Fermi energy at time reversal invariant momenta, and also by the presence of the edge states. The predicted M2'M″C2O2 MXenes show nontrivial gaps in the range of 0.041-0.285 eV within the generalized gradient approximation and 0.119-0.409 eV within the hybrid functional. The band gaps are induced by the spin-orbit coupling within the degenerate states with dx2-y2 and dx y characters of M' and M″, while the band inversion occurs at the Γ point among the degenerate dx2-y2/dx y orbitals and a nondegenerate d3 z2-r2 orbital, which is driven by the hybridization of the neighboring orbitals. The phonon dispersion calculations find that the predicted topological insulators are structurally stable. The predicted W-based MXenes with large band gaps might be suitable candidates for many topological applications at room temperature. In addition, we study the electronic structures of thicker ordered double transition metals M2'M2″C3O2 (M'=Mo , W; M″=Ti , Zr, Hf) and find that they are nontrivial topological semimetals. Among the predicted topological insulators and topological semimetals, Mo2TiC2 and Mo2Ti2C3 functionalized with a mixture of F, O, and OH have already been synthesized, and therefore some of the topological materials proposed here can be experimentally accessed.
NASA Astrophysics Data System (ADS)
Fink, Herman J.; Haley, Stephen B.; Giuraniuc, Claudiu V.; Kozhevnikov, Vladimir F.; Indekeu, Joseph O.
2005-11-01
For various sample geometries (slabs, cylinders, spheres, hypercubes), de Gennes' boundary condition parameter b is used to study its effect upon the transition temperature Tc of a superconductor. For b > 0 the order parameter at the surface is decreased, and as a consequence Tc is reduced, while for b < 0 the order parameter at the surface is increased, thereby enhancing Tc of a specimen in zero magnetic field. Exact solutions, derived by Fink and Haley (Int. J. mod. Phys. B, 17, 2171 (2003)), of the order parameter of a slab of finite thickness as a function of temperature are presented, both for reduced and enhanced transition (nucleation) temperatures. At the nucleation temperature the order parameter approaches zero. This concise review closes with a link established between de Gennes' microscopic boundary condition and the Ginzburg-Landau phenomenological approach, and a discussion of some relevant experiments. For example, applying the boundary condition with b < 0 to tin whiskers elucidates the increase of Tc with strain.
NASA Astrophysics Data System (ADS)
Kimme, Lukas; Hyart, Timo
2016-01-01
We consider the effects of impurities on topological insulators and superconductors. We start by identifying the general conditions under which the eigenenergies of an arbitrary Hamiltonian H belonging to one of the Altland-Zirnbauer symmetry classes undergo a robust zero energy crossing as a function of an external parameter which can be, for example, the impurity strength. We define a generalized root of detH and use it to predict or rule out robust zero-energy crossings in all symmetry classes. We complement this result with an analysis based on almost degenerate perturbation theory, which allows a derivation of the asymptotic low-energy behavior of the ensemble averaged density of states ρ ˜Eα for all symmetry classes and makes it transparent that the exponent α does not depend on the choice of the random matrix ensemble. Finally, we show that a lattice of impurities can drive a topologically trivial system into a nontrivial phase, and in particular we demonstrate that impurity bands carrying extremely large Chern numbers can appear in different symmetry classes of two-dimensional topological insulators and superconductors. We use the generalized root of detH (k ) to reveal a spiderweblike momentum space structure of the energy gap closings that separate the topologically distinct phases in px+i py superconductors in the presence of an impurity lattice.
Finite-Size and Composition-Driven Topological Phase Transition in (Bi1-xInx)2Se3 Thin Films.
Salehi, Maryam; Shapourian, Hassan; Koirala, Nikesh; Brahlek, Matthew J; Moon, Jisoo; Oh, Seongshik
2016-09-14
In a topological insulator (TI), if its spin-orbit coupling (SOC) strength is gradually reduced, the TI eventually transforms into a trivial insulator beyond a critical point of SOC, at which point the bulk gap closes: this is the standard description of the topological phase transition (TPT). However, this description of TPT, driven solely by the SOC (or something equivalent) and followed by closing and reopening of the bulk band gap, is valid only for infinite-size samples, and little is known how TPT occurs for finite-size samples. Here, using both systematic transport measurements on interface-engineered (Bi1-xInx)2Se3 thin films and theoretical simulations (with animations in the Supporting Information), we show that description of TPT in finite-size samples needs to be substantially modified from the conventional picture of TPT due to surface-state hybridization and bulk confinement effects. We also show that the finite-size TPT is composed of two separate transitions, topological-normal transition (TNT) and metal-insulator transition (MIT), by providing a detailed phase diagram in the two-dimensional phase space of sample size and SOC strength.
NASA Astrophysics Data System (ADS)
Wang, Na; Wang, JianFeng; Si, Chen; Gu, Bing-Lin; Duan, WenHui
2016-08-01
The introduction of magnetism in SnTe-class topological crystalline insulators is a challenging subject with great importance in the quantum device applications. Based on the first-principles calculations, we have studied the defect energetics and magnetic properties of 3 d transition-metal (TM)-doped SnTe. We find that the doped TM atoms prefer to stay in the neutral states and have comparatively high formation energies, suggesting that the uniform TMdoping in SnTe with a higher concentration will be difficult unless clustering. In the dilute doping regime, all the magnetic TMatoms are in the high-spin states, indicating that the spin splitting energy of 3 d TM is stronger than the crystal splitting energy of the SnTe ligand. Importantly, Mn-doped SnTe has relatively low defect formation energy, largest local magnetic moment, and no defect levels in the bulk gap, suggesting that Mn is a promising magnetic dopant to realize the magnetic order for the theoretically-proposed large-Chern-number quantum anomalous Hall effect (QAHE) in SnTe.
NASA Astrophysics Data System (ADS)
Mangiarotti, Sylvain
2014-05-01
A low-dimensional chaotic model was recently obtained for the dynamics of cereal crops cycles in semi-arid region [1]. This model was obtained from one single time series of vegetation index measured from space. The global modeling approach [2] was used based on powerful algorithms recently developed for this purpose [3]. The resulting model could be validated by comparing its predictability (a data assimilation scheme was used for this purpose) with a statistical prediction approach based on the search of analogous states in the phase space [4]. The cereal crops model exhibits a weakly dissipative chaos (DKY = 2.68) and a toroidal-like structure. At present, quite few cases of such chaos are known and these are exclusively theoretical. The first case was introduced by Lorenz in 1984 to model the global circulation dynamics [5], which attractor's structure is remained poorly understood. Indeed, one very powerful way to characterize low-dimensional chaos is based on the topological analysis of the attractors' flow [6]. Unfortunately, such approach does not apply to weakly dissipative chaos. In this work, a color tracer method is introduced and used to perform a complete topological analysis of both the Lorenz-84 system and the cereal crops model. The usual stretching and squeezing mechanisms are easily detected in the attractors' structure. A stretching taking place in the globally contracting direction of the flow is also found in both attractors. Such stretching is unexpected and was not reported previously. The analysis also confirms the toroidal type of chaos and allows producing both the skeleton and algebraic descriptions of the two attractors. Their comparison shows that the cereal crops attractor is a new attractor. References [1] Mangiarotti S., Drapreau L., Letellier C., 2014. Two chaotic global models for cereal crops cycles observed from satellite in Northern Morocco. revision submitted. [2] Letellier C., Aguirre L.A., Freitas U.S., 2009. Frequently
Ozhovan, M. I.
2006-11-15
Using the Angell model of broken bonds (configurons), configuron clustering in a topologically disordered lattice (network) of amorphous SiO{sub 2} and GeO{sub 2} upon a glass-liquid transition is considered. It is shown that the glass-liquid transition is accompanied by the formation of a macroscopic (percolation) configuron cluster penetrating the entire bulk of the material and possessing fractal geometry. The glass-liquid (overcooled liquid) percolation phase transition in the amorphous substance is accompanied by a change in the Hausdorff dimension of the bond network structure for configurons from the three-dimensional Euclidean dimension in the glassy state to a fractal dimension of 2.55 {+-} 0.05 in the liquidlike state. Contrary to the kinetic character of the liquid-glass transition, the glass-transition temperature is a thermodynamic parameter of the amorphous substance, depending parametrically on the cooling rate.
Collectively induced many-vortices topology via rotatory Dicke quantum phase transition
NASA Astrophysics Data System (ADS)
Das, Priyam; Emre Tasgin, Mehmet; Müstecaplıoğlu, Özgür E.
2016-09-01
We examine the superradiance of a Bose-Einstein condensate pumped with a Laguerre-Gaussian laser of high winding number, e.g., {\\ell }=7. The laser beam transfers its orbital angular momentum (OAM) to the condensate at once due to the collectivity of the superradiance. An ℓ-fold rotational symmetric structure emerges with the rotatory superradiance. ℓ number of single-charge vortices appear at the arms of this structure. Even though the pump and the condensate profiles initially have cylindrical symmetry, we observe that it is broken to ℓ-fold rotational symmetry at the superradiance. Breaking of the cylindrical symmetry into the ℓ-fold symmetry and OAM transfer to the condensate become significant after the same critical pump strength. Reorganization of the condensate resembles the ordering in the experiment by Esslinger and colleagues (2010 Nature 264 1301). We numerically verify that the critical point for the onset of the reorganization, as well as the properties of the emitted pulse, conform to the characteristics of superradiant quantum phase transition.
NASA Astrophysics Data System (ADS)
Parisi, Filippo; Sciascia, Luciana; Princivalle, Francesco; Merli, Marcello
2012-02-01
In order to characterize the pressure-induced decomposition of ringwoodite (γ-Mg2SiO4), the topological analysis of the electron density ρ( r), based upon the theory of atoms in molecules (AIM) developed by Bader in the framework of the catastrophe theory, has been performed. Calculations have been carried out by means of the ab initio CRYSTAL09 code at the HF/DFT level, using Hamiltonians based on the Becke- LYP scheme containing hybrid Hartree-Fock/density functional exchange-correlation terms. The equation of state at 0 K has been constructed for the three phases involved in the post-spinel phase transition (ringwoodite → Mg-perovskite + periclase) occurring at the transition zone-lower mantel boundary. The topological results show that the decomposition of the ringwoodite at high pressures is caused by a conflict catastrophe. Furthermore, topological evidences of the central role played by the oxygen atoms to facilitate the pressure-induced ringwoodite decomposition and the subsequent phase transition have been noticed.
Da Silva, David; Han, Liqi; Faivre, Robert; Costes, Evelyne
2014-01-01
Background and Aims The impact of a fruit tree's architecture on its performance is still under debate, especially with regard to the definition of varietal ideotypes and the selection of architectural traits in breeding programmes. This study aimed at providing proof that a modelling approach can contribute to this debate, by using in silico exploration of different combinations of traits and their consequences on light interception, here considered as one of the key parameters to optimize fruit tree production. Methods The variability of organ geometrical traits, previously described in a bi-parental population, was used to simulate 1- to 5-year-old apple trees (Malus × domestica). Branching sequences along trunks observed during the first year of growth of the same hybrid trees were used to initiate the simulations, and hidden semi-Markov chains previously parameterized were used in subsequent years. Tree total leaf area (TLA) and silhouette to total area ratio (STAR) values were estimated, and a sensitivity analysis was performed, based on a metamodelling approach and a generalized additive model (GAM), to analyse the relative impact of organ geometry and lateral shoot types on STAR. Key Results A larger increase over years in TLA mean and variance was generated by varying branching along trunks than by varying organ geometry, whereas the inverse was observed for STAR, where mean values stabilized from year 3 to year 5. The internode length and leaf area had the highest impact on STAR, whereas long sylleptic shoots had a more significant effect than proleptic shoots. Although the GAM did not account for interactions, the additive effects of the geometrical factors explained >90% of STAR variation, but much less in the case of branching factors. Conclusions This study demonstrates that the proposed modelling approach could contribute to screening architectural traits and their relative impact on tree performance, here viewed through light interception. Even
Bermejo, Rodrigo; Doksani, Ylli; Capra, Thelma; Katou, Yuki-Mori; Tanaka, Hirokazu; Shirahige, Katsuhiko; Foiani, Marco
2007-08-01
DNA topoisomerases solve topological problems during chromosome metabolism. We investigated where and when Top1 and Top2 are recruited on replicating chromosomes and how their inactivation affects fork integrity and DNA damage checkpoint activation. We show that, in the context of replicating chromatin, Top1 and Top2 act within a 600-base-pair (bp) region spanning the moving forks. Top2 exhibits additional S-phase clusters at specific intergenic loci, mostly containing promoters. TOP1 ablation does not affect fork progression and stability and does not cause activation of the Rad53 checkpoint kinase. top2 mutants accumulate sister chromatid junctions in S phase without affecting fork progression and activate Rad53 at the M-G1 transition. top1 top2 double mutants exhibit fork block and processing and phosphorylation of Rad53 and gamma H2A in S phase. The exonuclease Exo1 influences fork processing and DNA damage checkpoint activation in top1 top2 mutants. Our data are consistent with a coordinated action of Top1 and Top2 in counteracting the accumulation of torsional stress and sister chromatid entanglement at replication forks, thus preventing the diffusion of topological changes along large chromosomal regions. A failure in resolving fork-related topological constrains during S phase may therefore result in abnormal chromosome transitions, DNA damage checkpoint activation, and chromosome breakage during segregation.
Souma, S; Komatsu, M; Nomura, M; Sato, T; Takayama, A; Takahashi, T; Eto, K; Segawa, Kouji; Ando, Yoichi
2012-11-02
We performed systematic spin- and angle-resolved photoemission spectroscopy of TlBi(S(1-x)Se(x))(2) which undergoes a topological phase transition at x ~ 0.5. In TlBiSe(2) (x = 1.0), we revealed a helical spin texture of Dirac-cone surface states with an intrinsic in-plane spin polarization of ~0.8. The spin polarization still survives in the gapped surface states at x > 0.5, although it gradually weakens upon approaching x = 0.5 and vanishes in the nontopological phase. No evidence for the out-of-plane spin polarization was found, irrespective of x and momentum. The present results unambiguously indicate the topological origin of the gapped Dirac surface states, and also impose a constraint on models to explain the origin of mass acquisition of Dirac fermions.
Kim, Youngjae; Yun, Won Seok; Lee, J. D.
2016-01-01
Functionalized X-Bi bilayers (X = Ga, In, and Tl) with halogens bonded on their both sides have been recently claimed to be the giant topological insulators due to the strong band inversion strengths. Employing the first-principles electronic structure calculation, we find the topological band order transition from the order p – p – s of the X-Bi bilayers with halogens on their both sides to the new order p – s – p of the bilayers (especially for X = Ga and In) with halogen on one side and hydrogen on the other side, where the asymmetric hydrogen bonding simulates the substrate. We further find that the p – s bulk band gap of the bilayer bearing the new order p – s – p sensitively depends on the electric field, which enables a meaningful engineering of the quantum spin Hall edge state by controlling the external electric field. PMID:27623710
Kim, Youngjae; Yun, Won Seok; Lee, J D
2016-09-14
Functionalized X-Bi bilayers (X = Ga, In, and Tl) with halogens bonded on their both sides have been recently claimed to be the giant topological insulators due to the strong band inversion strengths. Employing the first-principles electronic structure calculation, we find the topological band order transition from the order p - p - s of the X-Bi bilayers with halogens on their both sides to the new order p - s - p of the bilayers (especially for X = Ga and In) with halogen on one side and hydrogen on the other side, where the asymmetric hydrogen bonding simulates the substrate. We further find that the p - s bulk band gap of the bilayer bearing the new order p - s - p sensitively depends on the electric field, which enables a meaningful engineering of the quantum spin Hall edge state by controlling the external electric field.
Xu, Shuigang; Han, Yu; Chen, Xiaolong; Wu, Zefei; Wang, Lin; Han, Tianyi; Ye, Weiguang; Lu, Huanhuan; Long, Gen; Wu, Yingying; Lin, Jiangxiazi; Cai, Yuan; Ho, K M; He, Yuheng; Wang, Ning
2015-04-08
Two-dimensional (2D) atomic-layered heterostructures stacked by van der Waals interactions recently introduced new research fields, which revealed novel phenomena and provided promising applications for electronic, optical, and optoelectronic devices. In this study, we report the van der Waals epitaxial growth of high-quality atomically thin Bi2Se3 on single crystalline hexagonal boron nitride (h-BN) by chemical vapor deposition. Although the in-plane lattice mismatch between Bi2Se3 and h-BN is approximately 65%, our transmission electron microscopy analysis revealed that Bi2Se3 single crystals epitaxially grew on h-BN with two commensurate states; that is, the (1̅21̅0) plane of Bi2Se3 was preferably parallel to the (1̅100) or (1̅21̅0) plane of h-BN. In the case of the Bi2Se3 (2̅110) ∥ h-BN (11̅00) state, the Moiré pattern wavelength in the Bi2Se3/h-BN superlattice can reach 5.47 nm. These naturally formed thin crystals facilitated the direct assembly of h-BN/Bi2Se3/h-BN sandwiched heterostructures without introducing any impurity at the interfaces for electronic property characterization. Our quantum capacitance (QC) measurements showed a compelling phenomenon of thickness-dependent topological phase transition, which was attributed to the coupling effects of two surface states from Dirac Fermions at/or above six quintuple layers (QLs) to gapped Dirac Fermions below six QLs. Moreover, in ultrathin Bi2Se3 (e.g., 3 QLs), we observed the midgap states induced by intrinsic defects at cryogenic temperatures. Our results demonstrated that QC measurements based on h-BN/Bi2Se3/h-BN sandwiched structures provided rich information regarding the density of states of Bi2Se3, such as quantum well states and Landau quantization. Our approach in fabricating h-BN/Bi2Se3/h-BN sandwiched device structures through the combination of bottom-up growth and top-down dry transferring techniques can be extended to other two-dimensional layered heterostructures.
NASA Astrophysics Data System (ADS)
Laurita, N. J.; Arpino, K. A.; Koopayeh, S. M.; McQueen, T. M.; Armitage, N. P.
The search for an intrinsic single crystal topological superconductor is one of the most dynamic areas of modern condensed matter physics. One of the best candidates of such a material is Tl5Te3 (Tc = 2 . 3 K), which previous ARPES measurements have shown possesses a Dirac cone within its superconducting gap. However, the fundamental nature of superconductivity, i.e. the superconducting order parameter, in Tl5Te3 remains unknown. Additionally, it has been shown that Tl5Te3 undergoes a superconducting-insulator transition upon doping with Sn. With no band parity inversion expected in the fully Sn doped compound one expects a topological supercondutor - trivial insulator transition, the nature of which is also unknown. In this work we use highly sensitive microwave cavity perturbation measurements, a direct probe of the superfluid density, to study the low energy electrodynamics of superconductivity in Tl5Te3 and its corresponding superconductor-insulator transition upon Sn doping. Work at Johns Hopkins was supported by the Gordon and Betty Moore Foundation through Grant GBMF2628, the DOE-BES through DE-FG02-08ER46544, and the ARCS Foundation.
Efthimiopoulos, Ilias; Buchan, Cienna; Wang, Yuejian
2016-04-06
High-pressure Raman spectroscopy and x-ray diffraction of Sb_{2}S_{3} 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 Sb_{2}S_{3} near 5 GPa. Close comparison between Sb_{2}S_{3} and Sb_{2}S_{3} 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 Sb_{2}S_{3} and Sb_{2}S_{3} up to 10 GPa, i.e. the absence of an insulator-metal transition in Sb_{2}S_{3} 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.
Werneburg, Ingmar; Wilson, Laura A B; Parr, William C H; Joyce, Walter G
2015-03-01
The unique ability of modern turtles to retract their head and neck into the shell through a side-necked (pleurodiran) or hidden-necked (cryptodiran) motion is thought to have evolved independently in crown turtles. The anatomical changes that led to the vertebral shapes of modern turtles, however, are still poorly understood. Here we present comprehensive geometric morphometric analyses that trace turtle vertebral evolution and reconstruct disparity across phylogeny. Disparity of vertebral shape was high at the dawn of turtle evolution and decreased after the modern groups evolved, reflecting a stabilization of morphotypes that correspond to the two retraction modes. Stem turtles, which had a very simple mode of retraction, the lateral head tuck, show increasing flexibility of the neck through evolution towards a pleurodiran-like morphotype. The latter was the precondition for evolving pleurodiran and cryptodiran vertebrae. There is no correlation between the construction of formed articulations in the cervical centra and neck mobility. An increasing mobility between vertebrae, associated with changes in vertebral shape, resulted in a more advanced ability to retract the neck. In this regard, we hypothesize that the lateral tucking retraction of stem turtles was not only the precondition for pleurodiran but also of cryptodiran retraction. For the former, a kink in the middle third of the neck needed to be acquired, whereas for the latter modification was necessary between the eighth cervical vertebra and first thoracic vertebra. Our paper highlights the utility of 3D shape data, analyzed in a phylogenetic framework, to examine the magnitude and mode of evolutionary modifications to vertebral morphology. By reconstructing and visualizing ancestral anatomical shapes, we provide insight into the anatomical features underlying neck retraction mode, which is a salient component of extant turtle classification.
NASA Astrophysics Data System (ADS)
Wang, Xujing
Living systems are characterized by complexity in structure and emergent dynamic orders. In many aspects the onset of a chronic disease resembles phase transition in a dynamic system: quantitative changes accumulate largely unnoticed until a critical threshold is reached, which causes abrupt qualitative changes of the system. In this study we investigate this idea in a real example, the insulin-producing pancreatic islet β-cells and the onset of type 1 diabetes. Within each islet, the β-cells are electrically coupled to each other, and function as a network with synchronized actions. Using percolation theory we show how normal islet function is intrinsically linked to network connectivity, and the critical point where the islet cellular network loses site percolation, is consistent with laboratory and clinical observations of the threshold β-cell loss that causes islet functional failure. Numerical simulations confirm that the islet cellular network needs to be percolated for β-cells to synchronize. Furthermore, the interplay between site percolation and bond strength predicts the existence of a transient phase of islet functional recovery after disease onset and introduction of treatment, potentially explaining a long time mystery in the clinical study of type 1 diabetes: the honeymoon phenomenon. Based on these results, we hypothesized that the onset of T1D may be the result of a phase transition of the islet β-cell network. We further discuss the potential applications in identifying disease-driving factors, and the critical parameters that are predictive of disease onset.
NASA Astrophysics Data System (ADS)
Zhang, Shengli; Xie, Meiqiu; Cai, Bo; Zhang, Haijun; Ma, Yandong; Chen, Zhongfang; Zhu, Zhen; Hu, Ziyu; Zeng, Haibo
2016-06-01
A stibarsen [derived from Latin stibium (antimony) and arsenic] or allemontite, is a natural form of arsenic antimonide (SbAs) with the same layered structure as arsenic and antimony. Thus, exploring the two-dimensional SbAs nanosheets is of great importance to gain insights into the properties of group V-V compounds at the atomic scale. Here, we propose a class of two-dimensional V-V honeycomb binary compounds, SbAs monolayers, which can be tuned from semiconductor to topological insulator. By ab initio density functional theory, both α-SbAs and γ-SbAs display a significant direct band gap, while others are indirect semiconductors. Interestingly, in an atomically thin β-SbAs polymorph, spin-orbital coupling is significant, which reduces its band gap by 200 meV. Especially under biaxial tensile strain, the gap of β-SbAs can be closed and reopened with concomitant change of band shapes, which is reminiscent of band inversion known in many topological insulators. In addition, we find that the Z2 topological invariant is 1 for β-SbAs under the tensile strain of 12%, and the nontrivial topological feature of β-SbAs is also confirmed by the gapless edge states which cross linearly at the Γ point. These ultrathin group-V-V semiconductors with outstanding properties are highly favorable for applications in alternative optoelectronic and quantum spin Hall devices.
You, Jia-Bin; Chan, A.H.; Oh, C.H.; Vedral, Vlatko
2014-10-15
We examine the topological properties of a spin–singlet superconductor with Rashba and Dresselhaus (110) spin–orbit couplings. We demonstrate that there are several topological invariants in the Bogoliubov–de Gennes (BdG) Hamiltonian by symmetry analysis. In particular, the Pfaffian invariant P for the particle–hole symmetry can be used to demonstrate all the possible phase diagrams of the BdG Hamiltonian. We find that the edge spectrum is either Dirac cone or flat band which supports the emergence of the Majorana fermion in this system. For the Majorana flat bands, an edge index, namely the Pfaffian invariant P(k{sub y}) or the winding number W(k{sub y}), is needed to make them topologically stable. These edge indices can also be used in determining the location of the Majorana flat bands. - Highlights: • Majorana fermion can emerge in the spin–orbit coupled singlet superconductor. • Pfaffian invariant and 1D winding number can be used to identify the nontrivial topological phase where Majorana flat band exists. • All the possible phase diagrams in the spin–orbit coupled singlet superconductor are demonstrated. • Majorana flat band only exists in the y direction in our model. • Majorana flat band has a significant experimental signature in the tunneling conductance measurement.
Strain-induced topological transition in SrRu_{2}O_{6} and CaOs_{2}O_{6}
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 way to realize a topological insulating state in a complex oxide, which has not been experimentally demonstrated so far.
NASA Astrophysics Data System (ADS)
Tanda, Satoshi; Matsuyama, Toyoki; Oda, Migaku; Asano, Yasuhiro; Yakubo, Kousuke
2006-08-01
.]. Nanofibers of hydrogen storage alloy / I. Saita ... [et al.]. Synthesis of stable icosahedral quasicrystals in Zn-Sc based alloys and their magnetic properties / S. Kashimoto and T. Ishimasa. One-armed spiral wave excited by eam pressure in accretion disks in Be/X-Ray binaries / K. Hayasaki and A. T. Okazaki -- IV. Topological defects and excitations. Topological excitations in the ground state of charge density wave systems / P. Monceau. Soliton transport in nanoscale charge-density-wave systems / K. Inagaki, T. Toshima and S. Tanda. Topological defects in triplet superconductors UPt3, Sr[symbol]RuO[symbol], etc. / K. Maki ... [et al.]. Microscopic structure of vortices in type II superconductors / K. Machida ... [et al.]. Microscopic neutron investigation of the Abrikosov state of high-temperature superconductors / J. Mesot. Energy dissipation at nano-scale topological defects of high-Tc superconductors: microwave study / A. Maeda. Pressure induced topological phase transition in the heavy Fermion compound CeAl[symbol] / H. Miyagawa ... [et al.]. Explanation for the unusual orientation of LSCO square vortex lattice in terms of nodal superconductivity / M. Oda. Local electronic states in Bi[symbol]Sr[symbol]CaCu[symbol]O[symbol] / A. Hashimoto ... [et al.] -- V. Topology in quantum phenomena. Topological vortex formation in a Bose-Einstein condensate of alkali-metal atoms / M. Nakahara. Quantum phase transition of [symbol]He confined in nano-porous media / K. Shirahama, K. Yamamoto and Y. Shibayama. A new mean-field theory for Bose-Einstein condensates / T. Kita. Spin current in topological cristals / Y. Asano. Antiferromagnetic defects in non-magnetic hidden order of the heavy-electron system URu[symbol]Si[symbol] / H. Amitsuka, K. Tenya and M. Yokoyama. Magnetic-field dependences of thermodynamic quantities in the vortex state of Type-II superconductors / K. Watanabe, T. Kita and M. Arai. Three-magnon-mediated nuclear spin relaxation in quantum ferrimagnets of topological
Hybrid Topological Lie-Hamiltonian Learning in Evolving Energy Landscapes
NASA Astrophysics Data System (ADS)
Ivancevic, Vladimir G.; Reid, Darryn J.
2015-11-01
In this Chapter, a novel bidirectional algorithm for hybrid (discrete + continuous-time) Lie-Hamiltonian evolution in adaptive energy landscape-manifold is designed and its topological representation is proposed. The algorithm is developed within a geometrically and topologically extended framework of Hopfield's neural nets and Haken's synergetics (it is currently designed in Mathematica, although with small changes it could be implemented in Symbolic C++ or any other computer algebra system). The adaptive energy manifold is determined by the Hamiltonian multivariate cost function H, based on the user-defined vehicle-fleet configuration matrix W, which represents the pseudo-Riemannian metric tensor of the energy manifold. Search for the global minimum of H is performed using random signal differential Hebbian adaptation. This stochastic gradient evolution is driven (or, pulled-down) by `gravitational forces' defined by the 2nd Lie derivatives of H. Topological changes of the fleet matrix W are observed during the evolution and its topological invariant is established. The evolution stops when the W-topology breaks down into several connectivity-components, followed by topology-breaking instability sequence (i.e., a series of phase transitions).
NASA Astrophysics Data System (ADS)
Zhang, Xiaowei; Xing, Peiqi; Geng, Xiujuan; Sun, Daofeng; Xiao, Zhenyu; Wang, Lei
2015-09-01
Eight new coordination polymers (CPs), namely, [Zn(1,2-mbix)(tbtpa)]n (1), [Co(1,2-mbix)(tbtpa)]n (2), [CdCl(1,2-mbix)(tbtpa)0.5]n (3), {[Cd(1,2-bix)(tbtpa)]·H2O}n (4), {[Cd0.5(1,2-bix)(tbtpa)0.5]·H2O}n (5), {[Co0.5(1,2-bix)(tbtpa)0.5]·2H2O}n (6), {[Co(1,2-bix)(tbtpa)]·H2O}n (7) and {[Co(1,2-bix)(tbtpa)]·Diox·2H2O}n (8), were synthesized under solvothermal conditions based on mix-ligand strategy (H2tbtpa=tetrabromoterephthalic acid and 1,2-mbix=1,2-bis((2-methyl-1H-imidazol-1-yl)methyl)benzene, 1,2-bix=1,2-bis(imidazol-1-ylmethyl)benzene). All of the CPs have been structurally characterized by single-crystal X-ray diffraction analyses and further characterized by elemental analyses, IR spectroscopy, powder X-ray diffraction (PXRD), and thermogravimetric analyses (TGA). X-ray diffraction analyses show that 1 and 2 are isotypics which have 2D highly undulated networks with (4,4)-sql topology with the existence of C-H ⋯Br interactions; for 3, it has a 2D planar network with (4,4)-sql topology with the occurrence of C-H ⋯Cl interactions other than C-H ⋯Br interactions; 4 shows a 3D 2-fold interpenetrated nets with rare 65·8-mok topology which has a self-catention property. As the same case as 1 and 2, 5 and 6 are also isostructural with planar layers with 44-sql topology which further assembled into 3D supramolecular structure through the interdigitated stacking fashion and the C-Br ⋯Cph interactions. As for 7, it has a 2D slightly undulated networks with (4,4)-sql topology which has one dimension channel. While 8 has a 2-fold interpenetrated networks with (3,4)-connect jeb topology with point symbol {63}{65·8}. And their structures can be tuned by conformations of bis(imidazol) ligands and solvent mixture. Besides, the TGA properties for all compounds and the luminescent properties for 1, 3, 4, 5 are discussed in detail.
Geometrical methods in soft condensed-matter physics
NASA Astrophysics Data System (ADS)
Kung, William
We propose a geometrical picture of understanding the thermodynamic and elastic properties of charged and fuzzy colloidal crystals, by analogy to foams, as well as perform a computational exercise to confirm a new universality class for long polymers with non-trivial topologies. By the foam analogy, we relate the problem of thermodynamic stability to the Kelvin's problem of partitioning space into equal-volume cells of minimal surface area. In particular, we consider the face-centered cubic (FCC), body-centered cubic (BCC) and the beta-tungsten (A15) lattices. We write down the free energy of these solid phases directly in terms of geometric and microscopic parameters of the system, and we derive the theoretical phase diagram of an experimental charged colloidal systems [Phys. Rev. Lett. 62, 1524 (1989)]. By considering deformations to the foam cells, we also compute the cubic elastic constants of these three lattices for charged and fuzzy colloids. In the polymer problem, we consider the critical behavior of polymers much longer than their persistence length, with built-in topological constraint in the form of Fuller's relation: Lk = Tw + Wr in a theta-solvent. We map the problem to the three-dimensional symmetric U( N)-Chern Simons theory as N → 0. To two-loop order, we find a new scaling regime for the topologically constrained polymers, with critical exponents that depend on the chemical potential for writhe which gives way to a fluctuation-induced first-order transition.
Chakraborty, Shibalik; Boolchand, P
2014-02-27
Binary GexS100-x glasses reveal a richness of elastic and chemical phase transitions driven by network topology. With increasing Ge content (x), well-defined rigidity at xc(1) = 19.3(5)% and a stress transition at xc(2) = 24.9(5)% are observed in Raman scattering. In modulated DSC measurements, the nonreversing enthalpy of relaxation at Tg reveals a square-well-like minimum (reversibility window) with window walls that coincide with the two elastic phase transitions. Molar volumes show a trapezoidal-like minimum (volumetric window) with edges that nearly coincide with the reversibility window. These optical, thermal, and volumetric results are consistent with an isostatically rigid elastic phase (intermediate phase, IP) present between the rigidity (xc(1)) and stress (xc(2)) transitions. Complex Cp measurements show melt fragility index, m(x) to also show a global minimum in the reversibility window with m < 20, underscoring that melt dynamics encode the elastic behavior of the glass formed at Tg. The strong nature of melts formed in the IP has an important practical consequence; they lead to slow homogenization (over days not hours) of nonstoichiometric Ge-S batch compositions reacted at high temperatures. Homogenization of chalcogenide melts/glasses over a scale of a few micrometers is a prerequisite to observe the intrinsic physical properties of these materials.
NASA Astrophysics Data System (ADS)
Lu, Ying-Bo; Li, Y. H.; Ling, Z. C.; Cong, Wei-Yan; Zhang, Peng; Xin, Y. Q.; Yang, T. L.
2016-02-01
As transparent conducting oxides (TCOs), In2O3 in the high pressure phase attracts extensive research interests. Because physical properties are determined by the geometric structures, we investigate the electronic and optical properties of Zn/Sn codoped In2O3 materials (IZTO) being modulated by the bixbyite/corundum phase transition via Density Functional Theory calculations. For IZTO in high pressure phase, i.e. corundum phase, Sn/Zn dopant pair tends to form face-sharing ZnO6 and SnO6 octahedrons. The radius differences between Zn2+/Sn4+ dopants and In3+ host cations make Jahn-Teller effect occur and IZTO transform from bixbyite to corundum phase under a slight higher pressure than that of pure In2O3. Although Zn/Sn cosubstitution of In ions may increase the free carrier effective mass m * near the band edge, when IZTO crystal transforms to corundum phase, the more dense packing structure results in stronger cation s-orbital overlaps than in bixbyite phase, which makes m * recover to a smaller value. In addition, corundum IZTO has a larger indirect band gap and a high dopant solubility. So these investigations may open a new way to search for TCOs materials with low indium content.
NASA Astrophysics Data System (ADS)
Talman, Richard
1999-10-01
Mechanics for the nonmathematician-a modern approach For physicists, mechanics is quite obviously geometric, yet the classical approach typically emphasizes abstract, mathematical formalism. Setting out to make mechanics both accessible and interesting for nonmathematicians, Richard Talman uses geometric methods to reveal qualitative aspects of the theory. He introduces concepts from differential geometry, differential forms, and tensor analysis, then applies them to areas of classical mechanics as well as other areas of physics, including optics, crystal diffraction, electromagnetism, relativity, and quantum mechanics. For easy reference, Dr. Talman treats separately Lagrangian, Hamiltonian, and Newtonian mechanics-exploring their geometric structure through vector fields, symplectic geometry, and gauge invariance respectively. Practical perturbative methods of approximation are also developed. Geometric Mechanics features illustrative examples and assumes only basic knowledge of Lagrangian mechanics. Of related interest . . . APPLIED DYNAMICS With Applications to Multibody and Mechatronic Systems Francis C. Moon A contemporary look at dynamics at an intermediate level, including nonlinear and chaotic dynamics. 1998 (0-471-13828-2) 504 pp. MATHEMATICAL PHYSICS Applied Mathematics for Scientists and Engineers Bruce Kusse and Erik Westwig A comprehensive treatment of the mathematical methods used to solve practical problems in physics and engineering. 1998 (0-471-15431-8) 680 pp.
Perspective: Geometrically frustrated assemblies
NASA Astrophysics Data System (ADS)
Grason, Gregory M.
2016-09-01
This perspective will overview an emerging paradigm for self-organized soft materials, geometrically frustrated assemblies, where interactions between self-assembling elements (e.g., particles, macromolecules, proteins) favor local packing motifs that are incompatible with uniform global order in the assembly. This classification applies to a broad range of material assemblies including self-twisting protein filament bundles, amyloid fibers, chiral smectics and membranes, particle-coated droplets, curved protein shells, and phase-separated lipid vesicles. In assemblies, geometric frustration leads to a host of anomalous structural and thermodynamic properties, including heterogeneous and internally stressed equilibrium structures, self-limiting assembly, and topological defects in the equilibrium assembly structures. The purpose of this perspective is to (1) highlight the unifying principles and consequences of geometric frustration in soft matter assemblies; (2) classify the known distinct modes of frustration and review corresponding experimental examples; and (3) describe outstanding questions not yet addressed about the unique properties and behaviors of this broad class of systems.
Emergent geometric frustration of artificial magnetic skyrmion crystals
Ma, Fusheng; Reichhardt, Charles; Gan, Weiliang; Reichhardt, Cynthia Jane Olson; Lew, Wen Siang
2016-10-05
Magnetic skyrmions have been receiving growing attention as potential information storage and magnetic logic devices since an increasing number of materials have been identified that support skyrmion phases. Explorations of artificial frustrated systems have led to new insights into controlling and engineering new emergent frustration phenomena in frustrated and disordered systems. Here, we propose a skyrmion spin ice, giving a unifying framework for the study of geometric frustration of skyrmion crystals (SCs) in a nonfrustrated artificial geometrical lattice as a consequence of the structural confinement of skyrmions in magnetic potential wells. The emergent ice rules from the geometrically frustrated SCs highlight a novel phenomenon in this skyrmion system: emergent geometrical frustration. We demonstrate how SC topology transitions between a nonfrustrated periodic configuration and a frustrated icelike ordering can also be realized reversibly. The proposed artificial frustrated skyrmion systems can be annealed into different ice phases with an applied current-induced spin-transfer torque, including a long-range ordered ice rule obeying ground state, as-relaxed random state, biased state, and monopole state. In conclusion, the spin-torque reconfigurability of the artificial skyrmion ice states, difficult to achieve in other artificial spin ice systems, is compatible with standard spintronic device fabrication technology, which makes the semiconductor industrial integration straightforward.
Emergent geometric frustration of artificial magnetic skyrmion crystals
NASA Astrophysics Data System (ADS)
Ma, Fusheng; Reichhardt, C.; Gan, Weiliang; Reichhardt, C. J. Olson; Lew, Wen Siang
2016-10-01
Magnetic skyrmions have been receiving growing attention as potential information storage and magnetic logic devices since an increasing number of materials have been identified that support skyrmion phases. Explorations of artificial frustrated systems have led to new insights into controlling and engineering new emergent frustration phenomena in frustrated and disordered systems. Here, we propose a skyrmion spin ice, giving a unifying framework for the study of geometric frustration of skyrmion crystals (SCs) in a nonfrustrated artificial geometrical lattice as a consequence of the structural confinement of skyrmions in magnetic potential wells. The emergent ice rules from the geometrically frustrated SCs highlight a novel phenomenon in this skyrmion system: emergent geometrical frustration. We demonstrate how SC topology transitions between a nonfrustrated periodic configuration and a frustrated icelike ordering can also be realized reversibly. The proposed artificial frustrated skyrmion systems can be annealed into different ice phases with an applied current-induced spin-transfer torque, including a long-range ordered ice rule obeying ground state, as-relaxed random state, biased state, and monopole state. The spin-torque reconfigurability of the artificial skyrmion ice states, difficult to achieve in other artificial spin ice systems, is compatible with standard spintronic device fabrication technology, which makes the semiconductor industrial integration straightforward.
Emergent geometric frustration of artificial magnetic skyrmion crystals
Ma, Fusheng; Reichhardt, Charles; Gan, Weiliang; ...
2016-10-05
Magnetic skyrmions have been receiving growing attention as potential information storage and magnetic logic devices since an increasing number of materials have been identified that support skyrmion phases. Explorations of artificial frustrated systems have led to new insights into controlling and engineering new emergent frustration phenomena in frustrated and disordered systems. Here, we propose a skyrmion spin ice, giving a unifying framework for the study of geometric frustration of skyrmion crystals (SCs) in a nonfrustrated artificial geometrical lattice as a consequence of the structural confinement of skyrmions in magnetic potential wells. The emergent ice rules from the geometrically frustrated SCsmore » highlight a novel phenomenon in this skyrmion system: emergent geometrical frustration. We demonstrate how SC topology transitions between a nonfrustrated periodic configuration and a frustrated icelike ordering can also be realized reversibly. The proposed artificial frustrated skyrmion systems can be annealed into different ice phases with an applied current-induced spin-transfer torque, including a long-range ordered ice rule obeying ground state, as-relaxed random state, biased state, and monopole state. In conclusion, the spin-torque reconfigurability of the artificial skyrmion ice states, difficult to achieve in other artificial spin ice systems, is compatible with standard spintronic device fabrication technology, which makes the semiconductor industrial integration straightforward.« less
NASA Astrophysics Data System (ADS)
Merli, Marcello; Sciascia, Luciana
2013-06-01
In this work, the Bader's topological analysis of the electron density, coupled with Thom's catastrophe theory, was used to characterize the pressure-induced transformations in α-quartz. In particular, ab initio calculations of the α-quartz structures in the range 0-105 Gpa have been performed at the HF/DFT exchange-correlation terms level, using Hamiltonians based on a WC1LYP hybrid scheme. The electron densities calculated throughout the ab initio wave functions have been analysed by means of the Bader's theory, seeking for some catastrophic mechanism in the sense of Thom's theory. The analysis mainly showed that there is a typical fold catastrophe feature involving an O-O interaction at the quartz-coesite transition pressure, while the amorphization of α-quartz is coincident with an average distribution of the gradient field of the electron density around the oxygen atom which is typically observed in the free atoms. This approach is addressed to depict a phase transition from a novel viewpoint, particularly useful in predicting the stability of a compound at extreme conditions, especially in the absence of experimental data.
Dziarmaga, Jacek; Zurek, Wojciech H
2014-08-05
Kibble-Zurek mechanism (KZM) uses critical scaling to predict density of topological defects and other excitations created in second order phase transitions. We point out that simply inserting asymptotic critical exponents deduced from the immediate vicinity of the critical point to obtain predictions can lead to results that are inconsistent with a more careful KZM analysis based on causality - on the comparison of the relaxation time of the order parameter with the "time distance" from the critical point. As a result, scaling of quench-generated excitations with quench rates can exhibit behavior that is locally (i.e., in the neighborhood of any given quench rate) well approximated by the power law, but with exponents that depend on that rate, and that are quite different from the naive prediction based on the critical exponents relevant for asymptotically long quench times. Kosterlitz-Thouless scaling (that governs e.g. Mott insulator to superfluid transition in the Bose-Hubbard model in one dimension) is investigated as an example of this phenomenon.
Geometrical Pumping with a Bose-Einstein Condensate.
Lu, H-I; Schemmer, M; Aycock, L M; Genkina, D; Sugawa, S; Spielman, I B
2016-05-20
We realized a quantum geometric "charge" pump for a Bose-Einstein condensate (BEC) in the lowest Bloch band of a novel bipartite magnetic lattice. Topological charge pumps in filled bands yield quantized pumping set by the global-topological-properties of the bands. In contrast, our geometric charge pump for a BEC occupying just a single crystal momentum state exhibits nonquantized charge pumping set by local-geometrical-properties of the band structure. Like topological charge pumps, for each pump cycle we observed an overall displacement (here, not quantized) and a temporal modulation of the atomic wave packet's position in each unit cell, i.e., the polarization.
Topological string theory revisited I: The stage
NASA Astrophysics Data System (ADS)
Jia, Bei
2016-08-01
In this paper, we reformulate topological string theory using supermanifolds and supermoduli spaces, following the approach worked out by Witten (Superstring perturbation theory revisited, arXiv:1209.5461). We intend to make the construction geometrical in nature, by using supergeometry techniques extensively. The goal is to establish the foundation of studying topological string amplitudes in terms of integration over appropriate supermoduli spaces.
Topological Characterization of Extended Quantum Ising Models.
Zhang, G; Song, Z
2015-10-23
We show that a class of exactly solvable quantum Ising models, including the transverse-field Ising model and anisotropic XY model, can be characterized as the loops in a two-dimensional auxiliary space. The transverse-field Ising model corresponds to a circle and the XY model corresponds to an ellipse, while other models yield cardioid, limacon, hypocycloid, and Lissajous curves etc. It is shown that the variation of the ground state energy density, which is a function of the loop, experiences a nonanalytical point when the winding number of the corresponding loop changes. The winding number can serve as a topological quantum number of the quantum phases in the extended quantum Ising model, which sheds some light upon the relation between quantum phase transition and the geometrical order parameter characterizing the phase diagram.
Second-quantized formulation of geometric phases
Deguchi, Shinichi; Fujikawa, Kazuo
2005-07-15
The level crossing problem and associated geometric terms are neatly formulated by the second-quantized formulation. This formulation exhibits a hidden local gauge symmetry related to the arbitrariness of the phase choice of the complete orthonormal basis set. By using this second-quantized formulation, which does not assume adiabatic approximation, a convenient exact formula for the geometric terms including off-diagonal geometric terms is derived. The analysis of geometric phases is then reduced to a simple diagonalization of the Hamiltonian, and it is analyzed both in the operator and path-integral formulations. If one diagonalizes the geometric terms in the infinitesimal neighborhood of level crossing, the geometric phases become trivial (and thus no monopole singularity) for arbitrarily large but finite time interval T. The integrability of Schroedinger equation and the appearance of the seemingly nonintegrable phases are thus consistent. The topological proof of the Longuet-Higgins' phase-change rule, for example, fails in the practical Born-Oppenheimer approximation where a large but finite ratio of two time scales is involved and T is identified with the period of the slower system. The difference and similarity between the geometric phases associated with level crossing and the exact topological object such as the Aharonov-Bohm phase become clear in the present formulation. A crucial difference between the quantum anomaly and the geometric phases is also noted.
PREFACE: Geometrically frustrated magnetism Geometrically frustrated magnetism
NASA Astrophysics Data System (ADS)
Gardner, Jason S.
2011-04-01
Frustrated magnetism is an exciting and diverse field in condensed matter physics that has grown tremendously over the past 20 years. This special issue aims to capture some of that excitement in the field of geometrically frustrated magnets and is inspired by the 2010 Highly Frustrated Magnetism (HFM 2010) meeting in Baltimore, MD, USA. Geometric frustration is a broad phenomenon that results from an intrinsic incompatibility between some fundamental interactions and the underlying lattice geometry based on triangles and tetrahedra. Most studies have centred around the kagomé and pyrochlore based magnets but recent work has looked at other structures including the delafossite, langasites, hyper-kagomé, garnets and Laves phase materials to name a few. Personally, I hope this issue serves as a great reference to scientist both new and old to this field, and that we all continue to have fun in this very frustrated playground. Finally, I want to thank the HFM 2010 organizers and all the sponsors whose contributions were an essential part of the success of the meeting in Baltimore. Geometrically frustrated magnetism contents Spangolite: an s = 1/2 maple leaf lattice antiferromagnet? T Fennell, J O Piatek, R A Stephenson, G J Nilsen and H M Rønnow Two-dimensional magnetism and spin-size effect in the S = 1 triangular antiferromagnet NiGa2S4 Yusuke Nambu and Satoru Nakatsuji Short range ordering in the modified honeycomb lattice compound SrHo2O4 S Ghosh, H D Zhou, L Balicas, S Hill, J S Gardner, Y Qi and C R Wiebe Heavy fermion compounds on the geometrically frustrated Shastry-Sutherland lattice M S Kim and M C Aronson A neutron polarization analysis study of moment correlations in (Dy0.4Y0.6)T2 (T = Mn, Al) J R Stewart, J M Hillier, P Manuel and R Cywinski Elemental analysis and magnetism of hydronium jarosites—model kagome antiferromagnets and topological spin glasses A S Wills and W G Bisson The Herbertsmithite Hamiltonian: μSR measurements on single crystals
Topological Methods for Visualization
Berres, Anne Sabine
2016-04-07
This slide presentation describes basic topological concepts, including topological spaces, homeomorphisms, homotopy, betti numbers. Scalar field topology explores finding topological features and scalar field visualization, and vector field topology explores finding topological features and vector field visualization.
NASA Astrophysics Data System (ADS)
Gonnelli, R. S.; Daghero, D.; Tortello, M.; Ummarino, G. A.; Bukowski, Z.; Karpinski, J.; Reuvekamp, P. G.; Kremer, R. K.; Profeta, G.; Suzuki, K.; Kuroki, K.
2016-05-01
Iron-based compounds (IBS) display a surprising variety of superconducting properties that seems to arise from the strong sensitivity of these systems to tiny details of the lattice structure. In this respect, systems that become superconducting under pressure, like CaFe2As2, are of particular interest. Here we report on the first directional point-contact Andreev-reflection spectroscopy (PCARS) measurements on CaFe2As2 crystals under quasi-hydrostatic pressure, and on the interpretation of the results using a 3D model for Andreev reflection combined with ab-initio calculations of the Fermi surface (within the density functional theory) and of the order parameter symmetry (within a random-phase-approximation approach in a ten-orbital model). The almost perfect agreement between PCARS results at different pressures and theoretical predictions highlights the intimate connection between the changes in the lattice structure, a topological transition in the holelike Fermi surface sheet, and the emergence on the same sheet of an order parameter with a horizontal node line.
NASA Astrophysics Data System (ADS)
Senyuk, B.; Wonderly, H.; Mathews, M.; Li, Q.; Shiyanovskii, S. V.; Lavrentovich, O. D.
2010-10-01
We study optical, structural, and surface anchoring properties of thermotropic nematic bent-core material A131. The focus is on the features associated with orientational order as the material has been reported to exhibit not only the usual uniaxial nematic but also the biaxial nematic phase. We demonstrate that A131 experiences a surface anchoring transition from a perpendicular to tilted alignment when the temperature decreases. The features of the tilted state are consistent with surface-induced birefringence associated with smectic layering near the surface and a molecular tilt that changes along the normal to the substrates. The surface-induced birefringence is reduced to zero by a modest electric field that establishes a uniform uniaxial nematic state. Both refractive and absorptive optical properties of A131 are consistent with the uniaxial order. We found no evidence of the “polycrystalline” biaxial behavior in the cells placed in crossed electric and magnetic fields. We observe stable topological point defects (boojums and hedgehogs) and nonsingular “escaped” disclinations pertinent only to the uniaxial order. Finally, freely suspended films of A131 show uniaxial nematic and smectic textures; a decrease in the film thickness expands the temperature range of stability of smectic textures, supporting the idea of surface-induced smectic layering. Our conclusion is that A131 features only a uniaxial nematic phase and that the apparent biaxiality is caused by subtle surface effects rather than by the bulk biaxial phase.
NASA Astrophysics Data System (ADS)
Pakmehr, M.; Bruene, C.; Buhmann, H.; Molenkamp, L. W.; Stier, A. V.; McCombe, B. D.
2014-12-01
We report a detailed low-temperature study of the two-dimensional (2D) electron gas in a 6.1-nm-wide HgTe quantum well with H g0.3C d0.7Te barriers by terahertz magnetophotoconductivity and magnetotransmission combined with magnetotransport measurements (Rx x and Rx y) in magnetic fields up to 10 T. This well width, close to that at the topological phase transition, corresponds to conventional band ordering, and we probe the "bulk" quasi-2D Landau-level (LL) spectrum of the conduction band at high energies (≈135 -160 meV ) above the Dirac point. The calculated separations between adjacent LLs of the same spin based on published parameters for this structure are in fair agreement with the measured cyclotron resonance energies. However, the very large spin splittings observed (Espin>Ecyclotron) require a significantly larger g -parameter ge for electrons. Tilted field coincidence experiments are consistent with the large spin splitting showing coincidences at 3/2 and twice the cyclotron energy. This large value of ge also leads to interesting crossings of the calculated LLs, and we find direct evidence of these crossings in the Rx x measurements at lower electron densities (Fermi energies) produced by negative gate bias.
Gonnelli, R. S.; Daghero, D.; Tortello, M.; Ummarino, G. A.; Bukowski, Z.; Karpinski, J.; Reuvekamp, P. G.; Kremer, R. K.; Profeta, G.; Suzuki, K.; Kuroki, K.
2016-01-01
Iron-based compounds (IBS) display a surprising variety of superconducting properties that seems to arise from the strong sensitivity of these systems to tiny details of the lattice structure. In this respect, systems that become superconducting under pressure, like CaFe2As2, are of particular interest. Here we report on the first directional point-contact Andreev-reflection spectroscopy (PCARS) measurements on CaFe2As2 crystals under quasi-hydrostatic pressure, and on the interpretation of the results using a 3D model for Andreev reflection combined with ab-initio calculations of the Fermi surface (within the density functional theory) and of the order parameter symmetry (within a random-phase-approximation approach in a ten-orbital model). The almost perfect agreement between PCARS results at different pressures and theoretical predictions highlights the intimate connection between the changes in the lattice structure, a topological transition in the holelike Fermi surface sheet, and the emergence on the same sheet of an order parameter with a horizontal node line. PMID:27216477
Rendering the Topological Spines
Nieves-Rivera, D.
2015-05-05
Many tools to analyze and represent high dimensional data already exits yet most of them are not flexible, informative and intuitive enough to help the scientists make the corresponding analysis and predictions, understand the structure and complexity of scientific data, get a complete picture of it and explore a greater number of hypotheses. With this in mind, N-Dimensional Data Analysis and Visualization (ND²AV) is being developed to serve as an interactive visual analysis platform with the purpose of coupling together a number of these existing tools that range from statistics, machine learning, and data mining, with new techniques, in particular with new visualization approaches. My task is to create the rendering and implementation of a new concept called topological spines in order to extend ND²AV's scope. Other existing visualization tools create a representation preserving either the topological properties or the structural (geometric) ones because it is challenging to preserve them both simultaneously. Overcoming such challenge by creating a balance in between them, the topological spines are introduced as a new approach that aims to preserve them both. Its render using OpenGL and C++ and is currently being tested to further on be implemented on ND²AV. In this paper I will present what are the Topological Spines and how they are rendered.
How Do Young Children Learn Geometric Concepts.
ERIC Educational Resources Information Center
Ohe, Pia
Twenty children (ages 5 and 6) from each of seven cultural groups (Caucasian, Black, Jewish, Puerto Rican, Chinese, Korean-American and native Korean) were given a copying task of 21 geometric shapes to test the cultural invariancy of Piaget's topological-projective-Euclidean concept acquisition sequence. All subjects were either middle or lower…
Reflections on representing non-geometric data
NASA Technical Reports Server (NTRS)
Emnett, R. F.; Shu, H. H.
1984-01-01
The American National Standard Y14.26M-1981 on Digital Representation for Communication of Product Definition Data includes an introduction, three sections corresponding to IGES (Initial Graphics Exchange Specification) Version 1.0, and Section 5, which is a constructive, relational, language based representation for geometric and topological entitles.
Comprehensible Presentation of Topological Information
Weber, Gunther H.; Beketayev, Kenes; Bremer, Peer-Timo; Hamann, Bernd; Haranczyk, Maciej; Hlawitschka, Mario; Pascucci, Valerio
2012-03-05
Topological information has proven very valuable in the analysis of scientific data. An important challenge that remains is presenting this highly abstract information in a way that it is comprehensible even if one does not have an in-depth background in topology. Furthermore, it is often desirable to combine the structural insight gained by topological analysis with complementary information, such as geometric information. We present an overview over methods that use metaphors to make topological information more accessible to non-expert users, and we demonstrate their applicability to a range of scientific data sets. With the increasingly complex output of exascale simulations, the importance of having effective means of providing a comprehensible, abstract overview over data will grow. The techniques that we present will serve as an important foundation for this purpose.
Prediction of a strain-tunable 2D Topological Dirac semimetal in monolayers of black phosphorus
NASA Astrophysics Data System (ADS)
Zhang, Xiuwen; Liu, Qihang; Zunger, Alex; Theory Team
2015-03-01
N-dimensional Topological Nonmetals (TNM) such as N = 2D HgTe/CdTe quantum wells or N = 3D Bi2Se3 have a finite (often tiny) band gap between occupied and unoccupied bands, and show conductive Dirac cones in their N-1 dimensional geometric boundaries. On the other hand, examples of topological semimetals (TSM) are known for 3D solids (Cd3As2) where they have Dirac cones in the 3D system itself. Using density functional calculation of bands and the topological invariant Z2 we predict the existence of 2D topological Dirac semimetal in few monolayers of strain tuned black phosphorus (BP), with Dirac cones induced by band inversion. The band structures of few monolayers and bulk crystal of BP under a few percent biaxial and uniaxial strains were calculated using state-of-art electronic structure methods. The critical strain of the transition to TSM was found to decrease as the layer thickness increases. We will discuss the protection of the Dirac cones by the crystalline symmetry in the 2D TSM and the manipulation of crystalline symmetry, which induces further topological phase transitions. Supported by the NSF-DMREF-13-34170.
NASA Astrophysics Data System (ADS)
Tiwari, S. C.
2008-03-01
We associate intrinsic energy equal to hν /2 with the spin angular momentum of photon, and propose a topological model based on orbifold in space and tifold in time as topological obstructions. The model is substantiated using vector wavefield disclinations. The physical photon is suggested to be a particlelike topological photon and a propagating wave such that the energy hν of photon is equally divided between spin energy and translational energy, corresponding to linear momentum of hν /c. The enigma of wave-particle duality finds natural resolution, and the proposed model gives new insights into the phenomena of interference and emission of radiation.
Jin, Dafei; Lu, Ling; Wang, Zhong; Fang, Chen; Joannopoulos, John D.; Soljačić, Marin; Fu, Liang; Fang, Nicholas X.
2016-01-01
Classical wave fields are real-valued, ensuring the wave states at opposite frequencies and momenta to be inherently identical. Such a particle–hole symmetry can open up new possibilities for topological phenomena in classical systems. Here we show that the historically studied two-dimensional (2D) magnetoplasmon, which bears gapped bulk states and gapless one-way edge states near-zero frequency, is topologically analogous to the 2D topological p+ip superconductor with chiral Majorana edge states and zero modes. We further predict a new type of one-way edge magnetoplasmon at the interface of opposite magnetic domains, and demonstrate the existence of zero-frequency modes bounded at the peripheries of a hollow disk. These findings can be readily verified in experiment, and can greatly enrich the topological phases in bosonic and classical systems. PMID:27892453
NASA Astrophysics Data System (ADS)
Jin, Dafei; Lu, Ling; Wang, Zhong; Fang, Chen; Joannopoulos, John D.; Soljačić, Marin; Fu, Liang; Fang, Nicholas X.
2016-11-01
Classical wave fields are real-valued, ensuring the wave states at opposite frequencies and momenta to be inherently identical. Such a particle-hole symmetry can open up new possibilities for topological phenomena in classical systems. Here we show that the historically studied two-dimensional (2D) magnetoplasmon, which bears gapped bulk states and gapless one-way edge states near-zero frequency, is topologically analogous to the 2D topological p+ip superconductor with chiral Majorana edge states and zero modes. We further predict a new type of one-way edge magnetoplasmon at the interface of opposite magnetic domains, and demonstrate the existence of zero-frequency modes bounded at the peripheries of a hollow disk. These findings can be readily verified in experiment, and can greatly enrich the topological phases in bosonic and classical systems.
Signatures of topological Josephson junctions
NASA Astrophysics Data System (ADS)
Peng, Yang; Pientka, Falko; Berg, Erez; Oreg, Yuval; von Oppen, Felix
2016-08-01
Quasiparticle poisoning and diabatic transitions may significantly narrow the window for the experimental observation of the 4 π -periodic dc Josephson effect predicted for topological Josephson junctions. Here, we show that switching-current measurements provide accessible and robust signatures for topological superconductivity which persist in the presence of quasiparticle poisoning processes. Such measurements provide access to the phase-dependent subgap spectrum and Josephson currents of the topological junction when incorporating it into an asymmetric SQUID together with a conventional Josephson junction with large critical current. We also argue that pump-probe experiments with multiple current pulses can be used to measure the quasiparticle poisoning rates of the topological junction. The proposed signatures are particularly robust, even in the presence of Zeeman fields and spin-orbit coupling, when focusing on short Josephson junctions. Finally, we also consider microwave excitations of short topological Josephson junctions which may complement switching-current measurements.
Distance measures and evolution of polymer chains in their topological space
NASA Astrophysics Data System (ADS)
Mashaghi, Alireza; Ramezanpour, Abolfazl
Conformational transitions are ubiquitous in biomolecular systems, have significant functional roles and are subject to evolutionary pressures. Here we provide a first theoretical framework for topological transition, i.e. conformational transitions that are associated with changes in molecular topology. For folded linear biomolecules, arrangement of intramolecular contacts is identified as a key topological property, termed as circuit topology. Distance measures are proposed as reaction coordinates to represent progress along a pathway from initial topology to final topology. Certain topological classes are shown to be more accessible from a random topology. We study dynamic stability and pathway degeneracy associated with a topological reaction and found that off-pathways might seriously hamper evolution to desired topologies. Finally we present an algorithm for estimating the number of intermediate topologies visited during a topological reaction. The results of this study are relevant to, among others, structural studies of RNA and proteins, analysis of topologically associated domains in chromosomes, and molecular evolution.
Topological strength of magnetic skyrmions
NASA Astrophysics Data System (ADS)
Bazeia, D.; Ramos, J. G. G. S.; Rodrigues, E. I. B.
2017-02-01
This work deals with magnetic structures that attain integer and half-integer skyrmion numbers. We model and solve the problem analytically, and show how the solutions appear in materials that engender distinct, very specific physical properties, and use them to describe their topological features. In particular, we found a way to model skyrmion with a large transition region correlated with the presence of a two-peak skyrmion number density. Moreover, we run into the issue concerning the topological strength of a vortex-like structure and suggest an experimental realization, important to decide how to modify and measure the topological strength of the magnetic structure.
Luo, H.; Yan, K.; Pletikosic, I.; Xie, W.; Phelan, B. F.; Valla, T.; Cava, R. J.
2016-05-13
We report the characterization of the misfit compound (Pb_{1-x}Sn_{x}Se_{2})1.16(TiSe_{2})_{2} for 0 ≤ x ≤ 0.6, in which a [100] rocksalt-structure bilayer of Pb1-xSnxSe, which is a topological crystalline insulator in bulk form, alternates with a double layer of the normally nonsuperconducting transition metal dichalcogenide TiSe_{2}. The x dependence of Tc displays a weak dome-like shape with a maximum Tc of 4.5 K at x = 0.2; there is only a subtle change in Tc at the composition where the trivial to topological transition occurs in bulk Pb1-xSnxSe. We present the characterization of the superconductor at x = 0.4, for which the bulk Pb1-xSnxSe phase is in the topological crystalline insulator regime. For this material, the Sommerfeld parameter γ = 11.06 mJ mol^{-1} K^{-2}, the Debye temperature Θ_{D} = 161 K, the normalized specific heat jump value ΔC/γT_{c} = 1.38 and the electron-phonon constant value γ_{ep} = 0.72, suggesting that (Pb_{0.6}Sn_{0.4}Se)_{1.16}(TiSe_{2})_{2} is a BCS-type weak coupling superconductor. This material may be of interest for probing the interaction of superconductivity with the surface states of a topological crystalline insulator.
Luo, H.; Yan, K.; Pletikosic, I.; ...
2016-05-13
We report the characterization of the misfit compound (Pb1-xSnxSe2)1.16(TiSe2)2 for 0 ≤ x ≤ 0.6, in which a [100] rocksalt-structure bilayer of Pb1-xSnxSe, which is a topological crystalline insulator in bulk form, alternates with a double layer of the normally nonsuperconducting transition metal dichalcogenide TiSe2. The x dependence of Tc displays a weak dome-like shape with a maximum Tc of 4.5 K at x = 0.2; there is only a subtle change in Tc at the composition where the trivial to topological transition occurs in bulk Pb1-xSnxSe. We present the characterization of the superconductor at x = 0.4, for whichmore » the bulk Pb1-xSnxSe phase is in the topological crystalline insulator regime. For this material, the Sommerfeld parameter γ = 11.06 mJ mol-1 K-2, the Debye temperature ΘD = 161 K, the normalized specific heat jump value ΔC/γTc = 1.38 and the electron-phonon constant value γep = 0.72, suggesting that (Pb0.6Sn0.4Se)1.16(TiSe2)2 is a BCS-type weak coupling superconductor. This material may be of interest for probing the interaction of superconductivity with the surface states of a topological crystalline insulator.« less
ERIC Educational Resources Information Center
Thompson, Sandy, Ed.; And Others
1990-01-01
This "feature issue" focuses on transition from school to adult life for persons with disabilities. Included are "success stories," brief program descriptions, and a list of resources. Individual articles include the following titles and authors: "Transition: An Energizing Concept" (Paul Bates); "Transition…
Topologies on quantum topoi induced by quantization
Nakayama, Kunji
2013-07-15
In the present paper, we consider effects of quantization in a topos approach of quantum theory. A quantum system is assumed to be coded in a quantum topos, by which we mean the topos of presheaves on the context category of commutative subalgebras of a von Neumann algebra of bounded operators on a Hilbert space. A classical system is modeled by a Lie algebra of classical observables. It is shown that a quantization map from the classical observables to self-adjoint operators on the Hilbert space naturally induces geometric morphisms from presheaf topoi related to the classical system to the quantum topos. By means of the geometric morphisms, we give Lawvere-Tierney topologies on the quantum topos (and their equivalent Grothendieck topologies on the context category). We show that, among them, there exists a canonical one which we call a quantization topology. We furthermore give an explicit expression of a sheafification functor associated with the quantization topology.
NASA Astrophysics Data System (ADS)
Pankratov, D. L.; Nizamov, R. S.; Harisov, I. Zh
2016-06-01
The cause of a pipe clip during the setting of the pipe is determined on the basis of modeling. The method, which excludes the formation of a defect in a semi finished product by changing the configuration of the setting transition, is developed.
Geometric formalism for DNA quadruplex folding.
Webba da Silva, Mateus
2007-01-01
Understanding the control of self-assembly and stereochemical properties of DNA higher order architectural folds is of fundamental importance in biology as well as biochemical technological applications. Guanine-rich DNA sequences can form tetrahelical architectures termed quadruplexes. A formalism is presented describing the interdependency of a set of structural descriptors as a geometric basis for folding of unimolecular quadruplex topologies. It represents a standard for interpretation of structural characteristics of quadruplexes, and is comprehensive in explicitly harmonizing the results of published literature with a unified language. The formalism is a fundamental step towards prediction of unimolecular quadruplex folding topologies from primary sequence.
Exploring complex networks via topological embedding on surfaces.
Aste, Tomaso; Gramatica, Ruggero; Di Matteo, T
2012-09-01
We demonstrate that graphs embedded on surfaces are a powerful and practical tool to generate, to characterize, and to simulate networks with a broad range of properties. Any network can be embedded on a surface with sufficiently high genus and therefore the study of topologically embedded graphs is non-restrictive. We show that the local properties of the network are affected by the surface genus which determines the average degree, which influences the degree distribution, and which controls the clustering coefficient. The global properties of the graph are also strongly affected by the surface genus which is constraining the degree of interwovenness, changing the scaling properties of the network from large-world kind (small genus) to small- and ultrasmall-world kind (large genus). Two elementary moves allow the exploration of all networks embeddable on a given surface and naturally introduce a tool to develop a statistical mechanics description for these networks. Within such a framework, we study the properties of topologically embedded graphs which dynamically tend to lower their energy towards a ground state with a given reference degree distribution. We show that the cooling dynamics between high and low "temperatures" is strongly affected by the surface genus with the manifestation of a glass-like transition occurring when the distance from the reference distribution is low. We prove, with examples, that topologically embedded graphs can be built in a way to contain arbitrary complex networks as subgraphs. This method opens a new avenue to build geometrically embedded networks on hyperbolic manifolds.
Classical light beams and geometric phases.
Mukunda, N; Chaturvedi, S; Simon, R
2014-06-01
We present a study of geometric phases in classical wave and polarization optics using the basic mathematical framework of quantum mechanics. Important physical situations taken from scalar wave optics, pure polarization optics, and the behavior of polarization in the eikonal or ray limit of Maxwell's equations in a transparent medium are considered. The case of a beam of light whose propagation direction and polarization state are both subject to change is dealt with, attention being paid to the validity of Maxwell's equations at all stages. Global topological aspects of the space of all propagation directions are discussed using elementary group theoretical ideas, and the effects on geometric phases are elucidated.
Semsarha, Farid; Raisali, Gholamreza; Goliaei, Bahram; Khalafi, Hossein
2016-05-01
In order to obtain the energy deposition pattern of ionizing radiation in the nanometric scale of genetic material and to investigate the different sensitivities of the DNA conformations, direct effects of (60)Co gamma rays on the three A, B and Z conformations of DNA have been studied. For this purpose, single-strand breaks (SSB), double-strand breaks (DSB), base damage (BD), hit probabilities and three microdosimetry quantities (imparted energy, mean chord length and lineal energy) in the mentioned DNA conformations have been calculated and compared by using GEometry ANd Tracking 4 (Geant4) toolkit. The results show that A-, B- and Z-DNA conformations have the highest yields of DSB (1.2 Gy(-1) Gbp(-1)), SSB (25.2 Gy(-1) Gbp(-1)) and BD (4.81 Gy(-1) Gbp(-1)), respectively. Based on the investigation of direct effects of radiation, it can be concluded that the DSB yield is largely correlated to the topological characteristics of DNA models, although the SSB yield is not. Moreover, according to the comparative results of the present study, a reliable candidate parameter for describing the relationship between DNA damage yields and geometry of DNA models in the theoretical radiation biology research studies would be the mean chord length (4 V/S) of the models.
Identifying and Fostering Higher Levels of Geometric Thinking
ERIC Educational Resources Information Center
Škrbec, Maja; Cadež, Tatjana Hodnik
2015-01-01
Pierre M. Van Hiele created five levels of geometric thinking. We decided to identify the level of geometric thinking in the students in Slovenia, aged 9 to 11 years. The majority of students (60.7%) are at the transition between the zero (visual) level and the first (descriptive) level of geometric thinking. Nearly a third (31.7%) of students is…
Geometric Landau-Zener interferometry.
Gasparinetti, S; Solinas, P; Pekola, J P
2011-11-11
We propose a new type of interferometry, based on geometric phases accumulated by a periodically driven two-level system undergoing multiple Landau-Zener transitions. As a specific example, we study its implementation in a superconducting charge pump. We find that interference patterns appear as a function of the pumping frequency and the phase bias, and clearly manifest themselves in the pumped charge. We also show that the effects described should persist in the presence of realistic decoherence.
Learning topological maps: An alternative approach
Buecken, A.; Thrun, S.
1996-12-31
Our goal is autonomous real-time control of a mobile robot. In this paper we want to show a possibility to learn topological maps of a large-scale indoor environment autonomously. In the literature there are two paradigms how to store information on the environment of a robot: as a grid-based (geometric) or as a topological map. While grid-based maps are considerably easy to learn and maintain, topological maps are quite compact and facilitate fast motion-planning.
Topological Mechanics of Origami and Kirigami.
Chen, Bryan Gin-Ge; Liu, Bin; Evans, Arthur A; Paulose, Jayson; Cohen, Itai; Vitelli, Vincenzo; Santangelo, C D
2016-04-01
Origami and kirigami have emerged as potential tools for the design of mechanical metamaterials whose properties such as curvature, Poisson ratio, and existence of metastable states can be tuned using purely geometric criteria. A major obstacle to exploiting this property is the scarcity of tools to identify and program the flexibility of fold patterns. We exploit a recent connection between spring networks and quantum topological states to design origami with localized folding motions at boundaries and study them both experimentally and theoretically. These folding motions exist due to an underlying topological invariant rather than a local imbalance between constraints and degrees of freedom. We give a simple example of a quasi-1D folding pattern that realizes such topological states. We also demonstrate how to generalize these topological design principles to two dimensions. A striking consequence is that a domain wall between two topologically distinct, mechanically rigid structures is deformable even when constraints locally match the degrees of freedom.
Topological Mechanics of Origami and Kirigami
NASA Astrophysics Data System (ADS)
Chen, Bryan Gin-ge; Liu, Bin; Evans, Arthur A.; Paulose, Jayson; Cohen, Itai; Vitelli, Vincenzo; Santangelo, C. D.
2016-04-01
Origami and kirigami have emerged as potential tools for the design of mechanical metamaterials whose properties such as curvature, Poisson ratio, and existence of metastable states can be tuned using purely geometric criteria. A major obstacle to exploiting this property is the scarcity of tools to identify and program the flexibility of fold patterns. We exploit a recent connection between spring networks and quantum topological states to design origami with localized folding motions at boundaries and study them both experimentally and theoretically. These folding motions exist due to an underlying topological invariant rather than a local imbalance between constraints and degrees of freedom. We give a simple example of a quasi-1D folding pattern that realizes such topological states. We also demonstrate how to generalize these topological design principles to two dimensions. A striking consequence is that a domain wall between two topologically distinct, mechanically rigid structures is deformable even when constraints locally match the degrees of freedom.
Topological Phenotypes in Complex Leaf Venation Networks
NASA Astrophysics Data System (ADS)
Ronellenfitsch, Henrik; Lasser, Jana; Daly, Douglas; Katifori, Eleni
2015-03-01
The leaves of vascular plants contain highly complex venation networks consisting of recursively nested, hierarchically organized loops. We analyze the topology of the venation of leaves from ca. 200 species belonging to ca. 10 families, defining topological metrics that quantify the hierarchical nestedness of the network cycles. We find that most of the venation variability can be described by a two dimensional phenotypic space, where one dimension consists of a linear combination of geometrical metrics and the other dimension of topological, previously uncharacterized metrics. We show how this new topological dimension in the phenotypic space significantly improves identification of leaves from fragments, by calculating a ``leaf fingerprint'' from the topology and geometry of the higher order veins. Further, we present a simple model suggesting that the topological phenotypic traits can be explained by noise effects and variations in the timing of higher order vein developmental events. This work opens the path to (a) new quantitative identification techniques for leaves which go beyond simple geometric traits such as vein density and (b) topological quantification of other planar or almost planar networks such as arterial vaculature in the neocortex and lung tissue.
Emergent Gauge Fields from Curvature in Single Layers of Transition-Metal Dichalcogenides
NASA Astrophysics Data System (ADS)
Ochoa, Héctor; Zarzuela, Ricardo; Tserkovnyak, Yaroslav
2017-01-01
We analyze the electron dynamics in corrugated layers of transition-metal dichalcogenides. Due to the strong spin-orbit coupling, the intrinsic (Gaussian) curvature leads to an emergent gauge field associated with the Berry connection of the spinor wave function. We discuss the gauge field created by topological defects of the lattice, namely, tetragonal and octogonal disclinations and edge dislocations. Ripples and topological disorder induce the same dephasing effects as a random magnetic field, suppressing the weak localization effects. This geometric magnetic field can be detected in an Aharonov-Bohm interferometry experiment by measuring the local density of states in the vicinity of corrugations.
Finite Topological Spaces as a Pedagogical Tool
ERIC Educational Resources Information Center
Helmstutler, Randall D.; Higginbottom, Ryan S.
2012-01-01
We propose the use of finite topological spaces as examples in a point-set topology class especially suited to help students transition into abstract mathematics. We describe how carefully chosen examples involving finite spaces may be used to reinforce concepts, highlight pathologies, and develop students' non-Euclidean intuition. We end with a…
Complex quantum network geometries: Evolution and phase transitions
NASA Astrophysics Data System (ADS)
Bianconi, Ginestra; Rahmede, Christoph; Wu, Zhihao
2015-08-01
Networks are topological and geometric structures used to describe systems as different as the Internet, the brain, or the quantum structure of space-time. Here we define complex quantum network geometries, describing the underlying structure of growing simplicial 2-complexes, i.e., simplicial complexes formed by triangles. These networks are geometric networks with energies of the links that grow according to a nonequilibrium dynamics. The evolution in time of the geometric networks is a classical evolution describing a given path of a path integral defining the evolution of quantum network states. The quantum network states are characterized by quantum occupation numbers that can be mapped, respectively, to the nodes, links, and triangles incident to each link of the network. We call the geometric networks describing the evolution of quantum network states the quantum geometric networks. The quantum geometric networks have many properties common to complex networks, including small-world property, high clustering coefficient, high modularity, and scale-free degree distribution. Moreover, they can be distinguished between the Fermi-Dirac network and the Bose-Einstein network obeying, respectively, the Fermi-Dirac and Bose-Einstein statistics. We show that these networks can undergo structural phase transitions where the geometrical properties of the networks change drastically. Finally, we comment on the relation between quantum complex network geometries, spin networks, and triangulations.
Geometrical pumping with a Bose-Einstein condensate
Lu, H.-I; Schemmer, M.; Aycock, L. M.; Genkina, D.; Sugawa, S.
2016-01-01
We realized a quantum geometric “charge” pump for a Bose-Einstein condensate (BEC) in the lowest Bloch band of a novel bipartite magnetic lattice. Topological charge pumps in filled bands yield quantized pumping set by the global – topological – properties of the bands. In contrast, our geometric charge pump for a BEC occupying just a single crystal momentum state exibits non-quantized charge pumping set by local – geometrical – properties of the band structure. Like topological charge pumps, for each pump cycle we observed an overall displacement (here, not quantized) and a temporal modulation of the atomic wavepacket’s position in each unit cell, i.e., the polarization. PMID:27258857
Geometrical Phases in Quantum Mechanics
NASA Astrophysics Data System (ADS)
Christian, Joy Julius
In quantum mechanics, the path-dependent geometrical phase associated with a physical system, over and above the familiar dynamical phase, was initially discovered in the context of adiabatically changing environments. Subsequently, Aharonov and Anandan liberated this phase from the original formulation of Berry, which used Hamiltonians, dependent on curves in a classical parameter space, to represent the cyclic variations of the environments. Their purely quantum mechanical treatment, independent of Hamiltonians, instead used the non-trivial topological structure of the projective space of one-dimensional subspaces of an appropriate Hilbert space. The geometrical phase, in their treatment, results from a parallel transport of the time-dependent pure quantum states along a curve in this space, which is endowed with an abelian connection. Unlike Berry, they were able to achieve this without resort to an adiabatic approximation or to a time-independent eigenvalue equation. Prima facie, these two approaches are conceptually quite different. After a review of both approaches, an exposition bridging this apparent conceptual gap is given; by rigorously analyzing a model composite system, it is shown that, in an appropriate correspondence limit, the Berry phase can be recovered as a special case from the Aharonov-Anandan phase. Moreover, the model composite system is used to show that Berry's correction to the traditional Born-Oppenheimer energy spectra indeed brings the spectra closer to the exact results. Then, an experimental arrangement to measure geometrical phases associated with cyclic and non-cyclic variations of quantum states of an entangled composite system is proposed, utilizing the fundamental ideas of the recently opened field of two-particle interferometry. This arrangement not only resolves the controversy regarding the true nature of the phases associated with photon states, but also unequivocally predicts experimentally accessible geometrical phases in a
The geometric nature of weights in real complex networks
NASA Astrophysics Data System (ADS)
Allard, Antoine; Serrano, M. Ángeles; García-Pérez, Guillermo; Boguñá, Marián
2017-01-01
The topology of many real complex networks has been conjectured to be embedded in hidden metric spaces, where distances between nodes encode their likelihood of being connected. Besides of providing a natural geometrical interpretation of their complex topologies, this hypothesis yields the recipe for sustainable Internet's routing protocols, sheds light on the hierarchical organization of biochemical pathways in cells, and allows for a rich characterization of the evolution of international trade. Here we present empirical evidence that this geometric interpretation also applies to the weighted organization of real complex networks. We introduce a very general and versatile model and use it to quantify the level of coupling between their topology, their weights and an underlying metric space. Our model accurately reproduces both their topology and their weights, and our results suggest that the formation of connections and the assignment of their magnitude are ruled by different processes.
The geometric nature of weights in real complex networks
Allard, Antoine; Serrano, M. Ángeles; García-Pérez, Guillermo; Boguñá, Marián
2017-01-01
The topology of many real complex networks has been conjectured to be embedded in hidden metric spaces, where distances between nodes encode their likelihood of being connected. Besides of providing a natural geometrical interpretation of their complex topologies, this hypothesis yields the recipe for sustainable Internet's routing protocols, sheds light on the hierarchical organization of biochemical pathways in cells, and allows for a rich characterization of the evolution of international trade. Here we present empirical evidence that this geometric interpretation also applies to the weighted organization of real complex networks. We introduce a very general and versatile model and use it to quantify the level of coupling between their topology, their weights and an underlying metric space. Our model accurately reproduces both their topology and their weights, and our results suggest that the formation of connections and the assignment of their magnitude are ruled by different processes. PMID:28098155
Topological Spin Glass in Diluted Spin Ice
NASA Astrophysics Data System (ADS)
Sen, Arnab; Moessner, R.
2015-06-01
It is a salient experimental fact that a large fraction of candidate spin liquid materials freeze as the temperature is lowered. The question naturally arises whether such freezing is intrinsic to the spin liquid ("disorder-free glassiness") or extrinsic, in the sense that a topological phase simply coexists with standard freezing of impurities. Here, we demonstrate a surprising third alternative, namely, that freezing and topological liquidity are inseparably linked. The topological phase reacts to the introduction of disorder by generating degrees of freedom of a new type (along with interactions between them), which in turn undergo a freezing transition while the topological phase supporting them remains intact.
Topological Spin Glass in Diluted Spin Ice.
Sen, Arnab; Moessner, R
2015-06-19
It is a salient experimental fact that a large fraction of candidate spin liquid materials freeze as the temperature is lowered. The question naturally arises whether such freezing is intrinsic to the spin liquid ("disorder-free glassiness") or extrinsic, in the sense that a topological phase simply coexists with standard freezing of impurities. Here, we demonstrate a surprising third alternative, namely, that freezing and topological liquidity are inseparably linked. The topological phase reacts to the introduction of disorder by generating degrees of freedom of a new type (along with interactions between them), which in turn undergo a freezing transition while the topological phase supporting them remains intact.
Topological Aspects of Information Retrieval.
ERIC Educational Resources Information Center
Egghe, Leo; Rousseau, Ronald
1998-01-01
Discusses topological aspects of theoretical information retrieval, including retrieval topology; similarity topology; pseudo-metric topology; document spaces as topological spaces; Boolean information retrieval as a subsystem of any topological system; and proofs of theorems. (LRW)
Minkowski vacuum transitions in (nongeometric) flux compactifications
Herrera-Suarez, Wilberth; Loaiza-Brito, Oscar
2010-02-15
In this work we study the generalization of twisted homology to geometric and nongeometric backgrounds. In the process, we describe the necessary conditions to wrap a network of D-branes on twisted cycles. If the cycle is localized in time, we show how by an instantonic brane mediation, some D-branes transform into fluxes on different backgrounds, including nongeometric fluxes. As a consequence, we show that in the case of a IIB six-dimensional torus compactification on a simple orientifold, the flux superpotential is not invariant by this brane-flux transition, allowing the connection among different Minkowski vacuum solutions. For the case in which nongeometric fluxes are turned on, we also discuss some topological restrictions for the transition to occur. In this context, we show that there are some vacuum solutions protected to change by a brane-flux transition.
Geometrical Pumping with a Bose-Einstein Condensate
NASA Astrophysics Data System (ADS)
Lu, H.-I.; Schemmer, M.; Aycock, L. M.; Genkina, D.; Sugawa, S.; Spielman, I. B.
2016-05-01
We realized a quantum geometric "charge" pump for a Bose-Einstein condensate (BEC) in the lowest Bloch band of a novel bipartite magnetic lattice. Topological charge pumps in filled bands yield quantized pumping set by the global—topological—properties of the bands. In contrast, our geometric charge pump for a BEC occupying just a single crystal momentum state exhibits nonquantized charge pumping set by local—geometrical—properties of the band structure. Like topological charge pumps, for each pump cycle we observed an overall displacement (here, not quantized) and a temporal modulation of the atomic wave packet's position in each unit cell, i.e., the polarization.
Thermoelectric effects and topological insulators
NASA Astrophysics Data System (ADS)
Xu, Yong
2016-11-01
The recent discovery of topological insulators (TIs) offers new opportunities for the development of thermoelectrics, because many TIs (like Bi2Te3) are excellent thermoelectric (TE) materials. In this review, we will first describe the general TE properties of TIs and show that the coexistence of the bulk and boundary states in TIs introduces unusual TE properties, including strong size effects and an anomalous Seebeck effect. Importantly, the TE figure of merit zT of TIs is no longer an intrinsic property, but depends strongly on the geometric size. The geometric parameters of two-dimensional TIs can be tuned to enhance zT to be significantly greater than 1. Then a few proof-of-principle experiments on three-dimensional TIs will be discussed, which observed unconventional TE phenomena that are closely related to the topological nature of the materials. However, current experiments indicate that the metallic surface states, if their advantage of high mobility is not fully utilized, would be detrimental to TE performance. Finally, we provide an outlook for future work on topological materials, which offers great possibilities to discover exotic TE effects and may lead to significant breakthroughs in improving zT. Project supported by the National Thousand-Young-Talents Program, China and Tsinghua University Initiative Scientific Research Program, China.
EDITORIAL: Topological data analysis Topological data analysis
NASA Astrophysics Data System (ADS)
Epstein, Charles; Carlsson, Gunnar; Edelsbrunner, Herbert
2011-12-01
Inverse problems can be defined as the area of mathematics that attempts to reconstruct a physical or mathematical object from derived data. Frequently, this means the evaluation of parameters or other numerical quantities (such as eigenvalues) that characterize or provide information about the system. There are, however, other aspects of a system that are important, but are not as readily summarized by numerical quantities. If one considers observations of diabetic patients (using metabolic quantities), one will find that the data breaks up into components, or pieces, corresponding to distinct forms of the disease. The decomposition of data sets into disjoint pieces, or clustering, is an aspect of the study of the shape of the data, albeit one that has been extensively studied. A more complex notion of shape appears in observations of a predator-prey system governed by a Lotka-Volterra equation. One would find that exact observations, consisting of (prey population, predator population) pairs, appear to lie along a simple closed curve in the plane. The fact that the data lies along such a closed curve is an important piece of information, since it suggests that the system displays recurrent behavior. If one did not know, a priori, that the system is governed by a Lotka-Volterra equation, then it would not be immediately obvious that the system is undergoing recurrent motion, and this deduction would constitute a significant insight. In this case, it is again the shape of the data, namely the fact that it lies on a simple closed curve, which is the key insight. Shape is a somewhat nebulous concept, which at first blush may be too intuitive to make precise mathematically, and describe quantitatively. Within pure mathematics, the disciplines of topology and differential geometry are designed exactly to address this problem. They provide explicit signatures which, in precise senses, quantify and describe the shape of a geometric object. In addition, they provide
EDITORIAL: Topological data analysis Topological data analysis
NASA Astrophysics Data System (ADS)
2011-12-01
Inverse problems can be defined as the area of mathematics that attempts to reconstruct a physical or mathematical object from derived data. Frequently, this means the evaluation of parameters or other numerical quantities (such as eigenvalues) that characterize or provide information about the system. There are, however, other aspects of a system that are important, but are not as readily summarized by numerical quantities. If one considers observations of diabetic patients (using metabolic quantities), one will find that the data breaks up into components, or pieces, corresponding to distinct forms of the disease. The decomposition of data sets into disjoint pieces, or clustering, is an aspect of the study of the shape of the data, albeit one that has been extensively studied. A more complex notion of shape appears in observations of a predator-prey system governed by a Lotka-Volterra equation. One would find that exact observations, consisting of (prey population, predator population) pairs, appear to lie along a simple closed curve in the plane. The fact that the data lies along such a closed curve is an important piece of information, since it suggests that the system displays recurrent behavior. If one did not know, a priori, that the system is governed by a Lotka-Volterra equation, then it would not be immediately obvious that the system is undergoing recurrent motion, and this deduction would constitute a significant insight. In this case, it is again the shape of the data, namely the fact that it lies on a simple closed curve, which is the key insight. Shape is a somewhat nebulous concept, which at first blush may be too intuitive to make precise mathematically, and describe quantitatively. Within pure mathematics, the disciplines of topology and differential geometry are designed exactly to address this problem. They provide explicit signatures which, in precise senses, quantify and describe the shape of a geometric object. In addition, they provide
Direct Measurement of Topological Numbers with Spins in Diamond.
Kong, Fei; Ju, Chenyong; Liu, Ying; Lei, Chao; Wang, Mengqi; Kong, Xi; Wang, Pengfei; Huang, Pu; Li, Zhaokai; Shi, Fazhan; Jiang, Liang; Du, Jiangfeng
2016-08-05
Topological numbers can characterize the transition between different topological phases, which are not described by Landau's paradigm of symmetry breaking. Since the discovery of the quantum Hall effect, more topological phases have been theoretically predicted and experimentally verified. However, it is still an experimental challenge to directly measure the topological numbers of various predicted topological phases. In this Letter, we demonstrate quantum simulation of topological phase transition of a quantum wire (QW), by precisely modulating the Hamiltonian of a single nitrogen-vacancy (NV) center in diamond. Deploying a quantum algorithm of finding eigenvalues, we reliably extract both the dispersion relations and topological numbers. This method can be further generalized to simulate more complicated topological systems.
Topological Superconductivity in Dirac Semimetals.
Kobayashi, Shingo; Sato, Masatoshi
2015-10-30
Dirac semimetals host bulk band-touching Dirac points and a surface Fermi loop. We develop a theory of superconducting Dirac semimetals. Establishing a relation between the Dirac points and the surface Fermi loop, we clarify how the nontrivial topology of Dirac semimetals affects their superconducting state. We note that the unique orbital texture of Dirac points and a structural phase transition of the crystal favor symmetry-protected topological superconductivity with a quartet of surface Majorana fermions. We suggest the possible application of our theory to recently discovered superconducting states in Cd_{3}As_{2}.
Brahlek, Matthew; Koirala, Nikesh; Salehi, Maryam; Moon, Jisoo; Zhang, Wenhan; Li, Haoxiang; Zhou, Xiaoqing; Han, Myung-Geun; Wu, Liang; Emge, Thomas; Lee, Hang-Dong; Xu, Can; Rhee, Seuk Joo; Gustafsson, Torgny; Armitage, N. Peter; Zhu, Yimei; Dessau, Daniel S.; Wu, Weida; Oh, Seongshik
2016-10-03
Topological insulators (TI) are a phase of matter that host unusual metallic states on their surfaces. Unlike the states that exist on the surface of conventional materials, these so-called topological surfaces states (TSS) are protected against disorder-related localization effects by time reversal symmetry through strong spin-orbit coupling. By combining transport measurements, angle-resolved photo-emission spectroscopy and scanning tunneling microscopy, we show that there exists a critical level of disorder beyond which the TI Bi_{2}Se_{3} loses its ability to protect the metallic TSS and transitions to a fully insulating state. The absence of the metallic surface channels dictates that there is a change in material’s topological character, implying that disorder can lead to a topological phase transition even without breaking the time reversal symmetry. This observation challenges the conventional notion of topologically-protected surface states, and will provoke new studies as to the fundamental nature of topological phase of matter in the presence of disorder.
Crystallographic topology and its applications
Johnson, C.K.; Burnett, M.N.; Dunbar, W.D.
1996-10-01
Geometric topology and structural crystallography concepts are combined to define a new area we call Structural Crystallographic Topology, which may be of interest to both crystallographers and mathematicians. In this paper, we represent crystallographic symmetry groups by orbifolds and crystal structures by Morse - functions. The Morse function uses mildly overlapping Gaussian thermal-motion probability density functions centered on atomic sites to form a critical net with peak, pass, pale, and pit critical points joined into a graph by density gradient-flow separatrices. Critical net crystal structure drawings can be made with the ORTEP-III graphics pro- An orbifold consists of an underlying topological space with an embedded singular set that represents the Wyckoff sites of the crystallographic group. An orbifold for a point group, plane group, or space group is derived by gluing together equivalent edges or faces of a crystallographic asymmetric unit. The critical-net-on-orbifold model incorporates the classical invariant lattice complexes of crystallography and allows concise quotient-space topological illustrations to be drawn without the repetition that is characteristic of normal crystal structure drawings.
Geared Topological Metamaterials with Tunable Mechanical Stability
NASA Astrophysics Data System (ADS)
Meeussen, Anne S.; Paulose, Jayson; Vitelli, Vincenzo
2016-10-01
The classification of materials into insulators and conductors has been shaken up by the discovery of topological insulators that conduct robustly at the edge but not in the bulk. In mechanics, designating a material as insulating or conducting amounts to asking if it is rigid or floppy. Although mechanical structures that display topological floppy modes have been proposed, they are all vulnerable to global collapse. Here, we design and build mechanical metamaterials that are stable and yet capable of harboring protected edge and bulk modes, analogous to those in electronic topological insulators and Weyl semimetals. To do so, we exploit gear assemblies that, unlike point masses connected by springs, incorporate both translational and rotational degrees of freedom. Global structural stability is achieved by eliminating geometrical frustration of collective gear rotations extending through the assembly. The topological robustness of the mechanical modes makes them appealing across scales from engineered macrostructures to networks of toothed microrotors of potential use in micromachines.
Geometry, topology, and string theory
Varadarajan, Uday
2003-01-01
A variety of scenarios are considered which shed light upon the uses and limitations of classical geometric and topological notions in string theory. The primary focus is on situations in which D-brane or string probes of a given classical space-time see the geometry quite differently than one might naively expect. In particular, situations in which extra dimensions, non-commutative geometries as well as other non-local structures emerge are explored in detail. Further, a preliminary exploration of such issues in Lorentzian space-times with non-trivial causal structures within string theory is initiated.
Topological approach of Jungian psychology.
Viret, Jacques
2010-09-01
In this work, we compare two global approaches which are usually considered as completely unconnected one with the other. The former is Thom's topology and the latter is Jung's psychology. More precisely, it seemed to us interesting to adapt some morphologies of Thom's catastrophe theory to some Jung's notions. Thus, we showed that the swallowtail, which is one of these morphologies, was able to describe geometrically the structural organisation of the psyche according to Jung, with its collective unconscious, personal unconscious and conscious. Moreover, we have correlated this morphology with Jung's evolutive processes like individualization and individuation. These comparisons incited us to think that some morphologies of Thom's catastrophe theory are the geometrical dealing of Jung's archetypes.
Topological Insulators from Electronic Superstructures
NASA Astrophysics Data System (ADS)
Sugita, Yusuke; Motome, Yukitoshi
2016-07-01
The possibility of realizing topological insulators by the spontaneous formation of electronic superstructures is theoretically investigated in a minimal two-orbital model including both the spin-orbit coupling and electron correlations on a triangular lattice. Using the mean-field approximation, we show that the model exhibits several different types of charge-ordered insulators, where the charge disproportionation forms a honeycomb or kagome superstructure. We find that the charge-ordered insulators in the presence of strong spin-orbit coupling can be topological insulators showing quantized spin Hall conductivity. Their band gap is dependent on electron correlations as well as the spin-orbit coupling, and even vanishes while showing the massless Dirac dispersion at the transition to a trivial charge-ordered insulator. Our results suggest a new route to realize and control topological states of quantum matter by the interplay between the spin-orbit coupling and electron correlations.
Induced topological pressure for topological dynamical systems
Xing, Zhitao; Chen, Ercai
2015-02-15
In this paper, inspired by the article [J. Jaerisch et al., Stochastics Dyn. 14, 1350016, pp. 1-30 (2014)], we introduce the induced topological pressure for a topological dynamical system. In particular, we prove a variational principle for the induced topological pressure.
Experimental Realizations of Magnetic Topological Insulator and Topological Crystalline Insulator
NASA Astrophysics Data System (ADS)
Xu, Suyang
2013-03-01
Over the past few years the experimental research on three-dimensional topological insulators have emerged as one of the most rapidly developing fields in condensed matter physics. In this talk, we report on two new developments in the field: The first part is on the dynamic interplay between ferromagnetism and the Z2 topological insulator state (leading to a magnetic topological insulator). We present our spin-resolved photoemission and magnetic dichroic experiments on MBE grown films where a hedgehog-like spin texture is revealed on the magnetically ordered surface of Mn-Bi2Se3 revealing a Berry's phase gradient in energy-momentum space of the crystal. A chemically/electrically tunable Berry's phase switch is further demonstrated via the tuning of the spin groundstate in Mn-Bi2Se3 revealed in our data (Nature Physics 8, 616 (2012)). The second part of this talk describes our experimental observation of a new topological phase of matter, namely a topological crystalline insulator where space group symmetries replace the role of time-reversal symmetry in an otherwise Z2 topological insulator predicted in theory. We experimentally investigate the possibility of a mirror symmetry protected topological phase transition in the Pb1-xSnxTe alloy system, which has long been known to contain an even number of band inversions based on band theory. Our experimental results show that at a composition below the theoretically predicted band inversion, the system is fully gapped, whereas in the band-inverted regime, the surface exhibits even number of spin-polarized Dirac cone states revealing mirror-protected topological order (Nature Communications 3, 1192 (2012)) distinct from that observed in Z2 topological insulators. We discuss future experimental possibilities opened up by these new developments in topological insulators research. This work is in collaboration with M. Neupane, C. Liu, N. Alidoust, I. Belopolski, D. Qian, D.M. Zhang, A. Richardella, A. Marcinkova, Q
Evolutionary Optimization of a Geometrically Refined Truss
NASA Technical Reports Server (NTRS)
Hull, P. V.; Tinker, M. L.; Dozier, G. V.
2007-01-01
Structural optimization is a field of research that has experienced noteworthy growth for many years. Researchers in this area have developed optimization tools to successfully design and model structures, typically minimizing mass while maintaining certain deflection and stress constraints. Numerous optimization studies have been performed to minimize mass, deflection, and stress on a benchmark cantilever truss problem. Predominantly traditional optimization theory is applied to this problem. The cross-sectional area of each member is optimized to minimize the aforementioned objectives. This Technical Publication (TP) presents a structural optimization technique that has been previously applied to compliant mechanism design. This technique demonstrates a method that combines topology optimization, geometric refinement, finite element analysis, and two forms of evolutionary computation: genetic algorithms and differential evolution to successfully optimize a benchmark structural optimization problem. A nontraditional solution to the benchmark problem is presented in this TP, specifically a geometrically refined topological solution. The design process begins with an alternate control mesh formulation, multilevel geometric smoothing operation, and an elastostatic structural analysis. The design process is wrapped in an evolutionary computing optimization toolset.
Exploring New Geometric Worlds
ERIC Educational Resources Information Center
Nirode, Wayne
2015-01-01
When students work with a non-Euclidean distance formula, geometric objects such as circles and segment bisectors can look very different from their Euclidean counterparts. Students and even teachers can experience the thrill of creative discovery when investigating these differences among geometric worlds. In this article, the author describes a…
Edge Detection and Geometric Methods in Computer Vision,
1985-02-01
anid espcially Ltme differenit meanings of the 2 types of arrows. In thin notatiom,, rather thani sayinig "the funtion a f (a, y)" Ceotnetric Methods in...a generative grammar . In fact, the only possible structures are shown In ,ig. (level). .. . . . . ... , Geometric Methods in Vision Topological
Effective Topological Charge Cancelation Mechanism
Mesarec, Luka; Góźdź, Wojciech; Iglič, Aleš; Kralj, Samo
2016-01-01
Topological defects (TDs) appear almost unavoidably in continuous symmetry breaking phase transitions. The topological origin makes their key features independent of systems’ microscopic details; therefore TDs display many universalities. Because of their strong impact on numerous material properties and their significant role in several technological applications it is of strong interest to find simple and robust mechanisms controlling the positioning and local number of TDs. We present a numerical study of TDs within effectively two dimensional closed soft films exhibiting in-plane orientational ordering. Popular examples of such class of systems are liquid crystalline shells and various biological membranes. We introduce the Effective Topological Charge Cancellation mechanism controlling localised positional assembling tendency of TDs and the formation of pairs {defect, antidefect} on curved surfaces and/or presence of relevant “impurities” (e.g. nanoparticles). For this purpose, we define an effective topological charge Δmeff consisting of real, virtual and smeared curvature topological charges within a surface patch Δς identified by the typical spatially averaged local Gaussian curvature K. We demonstrate a strong tendency enforcing Δmeff → 0 on surfaces composed of Δς exhibiting significantly different values of spatially averaged K. For Δmeff ≠ 0 we estimate a critical depinning threshold to form pairs {defect, antidefect} using the electrostatic analogy. PMID:27250777
A topologically driven glass in ring polymers
Michieletto, Davide; Turner, Matthew S.
2016-01-01
The static and dynamic properties of ring polymers in concentrated solutions remains one of the last deep unsolved questions in polymer physics. At the same time, the nature of the glass transition in polymeric systems is also not well understood. In this work, we study a novel glass transition in systems made of circular polymers by exploiting the topological constraints that are conjectured to populate concentrated solutions of rings. We show that such rings strongly interpenetrate through one another, generating an extensive network of topological interactions that dramatically affects their dynamics. We show that a kinetically arrested state can be induced by randomly pinning a small fraction of the rings. This occurs well above the classical glass transition temperature at which microscopic mobility is lost. Our work both demonstrates the existence of long-lived inter-ring penetrations and realizes a novel, topologically induced, glass transition. PMID:27118847
Enhanced baryon number violation due to gauged non-topological solitons.
NASA Astrophysics Data System (ADS)
Lee, C. H.; Yoon, S. U.
1993-12-01
In the context of the Callan-Rubakov effect, it is, in principle, possible for a gauged non-topological soliton (NTS) inside which a grand unified symmetry is realized to catalyse baryon decay. In this paper, assuming a gauged NTS which the localized FLS (Friedberg, Lee, and Sirlin)'s model admits to form during a grand unified phase transition, the authors calculate the cross-section for quark-to-lepton transition due to the gauged NTS, and learn that there is a range of parameters for which their cross-section gets away from a naive geometric one, and which is consistent with that for the existence of stable gauged NTSs.
Electrically tunable topological superconductivity and Majorana fermions in two dimensions
NASA Astrophysics Data System (ADS)
Wang, Jing
2016-12-01
The external controllability of topological superconductors and Majorana fermions would be important both for fundamental and practical interests. Here we predict the electric-field control of Majorana fermions in two-dimensional topological superconductors utilizing a topological insulator thin-film proximity coupled to a conventional s -wave superconductor. With ferromagnetic ordering, the tunable structure inversion asymmetry by vertical electric field could induce topological quantum phase transition and realize a chiral topological superconductor state. A zero-energy Majorana bound state appears at the boundary of an applied electric-field spot, which can be observed by scanning tunneling microscopy. Furthermore, the structure inversion asymmetry could also enlarge the helical topological superconductor state in the phase diagram, making the realization of such an exotic state more feasible. The electrical control of topological phases could further apply to van der Waals materials such as two-dimensional transition-metal dichalcogenides.
The topology of geology 1: Topological analysis
NASA Astrophysics Data System (ADS)
Thiele, Samuel T.; Jessell, Mark W.; Lindsay, Mark; Ogarko, Vitaliy; Wellmann, J. Florian; Pakyuz-Charrier, Evren
2016-10-01
Topology has been used to characterise and quantify the properties of complex systems in a diverse range of scientific domains. This study explores the concept and applications of topological analysis in geology. We have developed an automatic system for extracting first order 2D topological information from geological maps, and 3D topological information from models built with the Noddy kinematic modelling system, and equivalent analyses should be possible for other implicit modelling systems. A method is presented for describing the spatial and temporal topology of geological models using a set of adjacency relationships that can be expressed as a topology network, thematic adjacency matrix or hive diagram. We define three types of spatial topology (cellular, structural and lithological) that allow us to analyse different aspects of the geology, and then apply them to investigate the geology of the Hamersley Basin, Western Australia.
Topological order, entanglement, and quantum memory at finite temperature
Mazac, Dalimil Hamma, Alioscia
2012-09-15
We compute the topological entropy of the toric code models in arbitrary dimension at finite temperature. We find that the critical temperatures for the existence of full quantum (classical) topological entropy correspond to the confinement-deconfinement transitions in the corresponding Z{sub 2} gauge theories. This implies that the thermal stability of topological entropy corresponds to the stability of quantum (classical) memory. The implications for the understanding of ergodicity breaking in topological phases are discussed. - Highlights: Black-Right-Pointing-Pointer We calculate the topological entropy of a general toric code in any dimension. Black-Right-Pointing-Pointer We find phase transitions in the topological entropy. Black-Right-Pointing-Pointer The phase transitions coincide with the appearance of quantum/classical memory.
Deformations of Geometric Structures in Topological Sigma Models
NASA Astrophysics Data System (ADS)
Bytsenko, A. A.
2010-11-01
We study a Lie algebra of formal vector fields Wn with it application to the perturbative deformed holomorphic symplectic structure in the A-model, and a Calabi-Yau manifold with boundaries in the B-model. We show that equivalent classes of deformations are described by a Hochschild cohomology of the DG-algebra A = (A,Q), Q = ∂¯+∂deform, which is defined to be the cohomology of (-1)nQ+dHoch. Here ∂¯ is the initial non-deformed BRST operator while ∂deform is the deformed part whose algebra is a Lie algebra of linear vector fields gln.
Crystallographic parameters in geometrically and topologically close-packed superstructures
Knestaypin, Evgeny A. E-mail: 7mmm81@gmal.com; Morozov, Maksim M. E-mail: 7mmm81@gmal.com; Potekaev, Alexandr I.; Klopotov, Anatoly A.; Markova, Tatyana N.; Klopotov, Vladimir D.
2014-11-14
The structures of stoichiometric compositions AB, A{sub 2}B, and A{sub 3}B for structures, B19, L1{sub 0}, L1{sub 2}, D0{sub 19}, D0{sub 22}, D0{sub 23}, D0{sub 24}, A15, C14, C15 and C36 have been investigated based on the analysis of diagrams in coordinates of space-filling coefficients Ψ on superstructural compression ΔΩ/Ω. On the basis of the analysis of the abovementioned diagrams, the equation Ψ = f{sub 0}+f{sub 1}(ΔΩ/Ω) has been obtained, and coefficients f{sub 0} and f{sub 1} of the equation for the investigated structures have been determined. It has been established that values of coefficients f{sub 0} and f{sub 1} for Laves phases have higher values than for all other compounds.
Topological and Geometric Tools for the Analysis fo Complex Networks
2013-10-01
Vol. 55, No. 6, June 2010 A. Tahbaz- Salehi , and A. Jadbabaie," Consensus in ergodic-stationary graph processes," IEEE Transactions on...Preciado, A. Tahbaz- Salehi , and A. Jadbabaie, “On Asymptotic Consensus Value in Directed Random Networks,” IEEE Conference on Decision and Control...2010. V.M. Preciado , A. Tehbaz- Salehi and A. Jadbabaie, “Variance Analysis of Randomized Consensus in Switching Directed Networks,” American
NASA Astrophysics Data System (ADS)
Durand, Marc; Kraynik, Andrew M.; van Swol, Frank; Käfer, Jos; Quilliet, Catherine; Cox, Simon; Ataei Talebi, Shirin; Graner, François
2014-06-01
Bubble monolayers are model systems for experiments and simulations of two-dimensional packing problems of deformable objects. We explore the relation between the distributions of the number of bubble sides (topology) and the bubble areas (geometry) in the low liquid fraction limit. We use a statistical model [M. Durand, Europhys. Lett. 90, 60002 (2010), 10.1209/0295-5075/90/60002] which takes into account Plateau laws. We predict the correlation between geometrical disorder (bubble size dispersity) and topological disorder (width of bubble side number distribution) over an extended range of bubble size dispersities. Extensive data sets arising from shuffled foam experiments, surface evolver simulations, and cellular Potts model simulations all collapse surprisingly well and coincide with the model predictions, even at extremely high size dispersity. At moderate size dispersity, we recover our earlier approximate predictions [M. Durand, J. Kafer, C. Quilliet, S. Cox, S. A. Talebi, and F. Graner, Phys. Rev. Lett. 107, 168304 (2011), 10.1103/PhysRevLett.107.168304]. At extremely low dispersity, when approaching the perfectly regular honeycomb pattern, we study how both geometrical and topological disorders vanish. We identify a crystallization mechanism and explore it quantitatively in the case of bidisperse foams. Due to the deformability of the bubbles, foams can crystallize over a larger range of size dispersities than hard disks. The model predicts that the crystallization transition occurs when the ratio of largest to smallest bubble radii is 1.4.
Topological superconductors: a review.
Sato, Masatoshi; Ando, Yoichi
2017-04-03
This review elaborates pedagogically on the fundamental concept, basic theory, expected properties, and materials realizations of topological superconductors. The relation between topological superconductivity and Majorana fermions are explained, and the difference between dispersive Majorana fermions and a localized Majorana zero mode is emphasized. A variety of routes to topological superconductivity are explained with an emphasis on the roles of spin-orbit coupling. Present experimental situations and possible signatures of topological superconductivity are summarized with an emphasis on intrinsic topological superconductors.
Topological defects in extended inflation
NASA Technical Reports Server (NTRS)
Copeland, Edmund J.; Kolb, Edward W.; Liddle, Andrew R.
1990-01-01
The production of topological defects, especially cosmic strings, in extended inflation models was considered. In extended inflation, the Universe passes through a first-order phase transition via bubble percolation, which naturally allows defects to form at the end of inflation. The correlation length, which determines the number density of the defects, is related to the mean size of bubbles when they collide. This mechanism allows a natural combination of inflation and large scale structure via cosmic strings.
Geometrical description of algebraic structures: Applications to Quantum Mechanics
Carinena, J. F.; Ibort, A.; Marmo, G.; Morandi, G.
2009-05-06
Geometrization of physical theories have always played an important role in their analysis and development. In this contribution we discuss various aspects concerning the geometrization of physical theories: from classical mechanics to quantum mechanics. We will concentrate our attention into quantum theories and we will show how to use in a systematic way the transition from algebraic to geometrical structures to explore their geometry, mainly its Jordan-Lie structure.
Transformable topological mechanical metamaterials
NASA Astrophysics Data System (ADS)
Rocklin, D. Zeb; Zhou, Shangnan; Sun, Kai; Mao, Xiaoming
2017-01-01
Mechanical metamaterials are engineered materials whose structures give them novel mechanical properties, including negative Poisson's ratios, negative compressibilities and phononic bandgaps. Of particular interest are systems near the point of mechanical instability, which recently have been shown to distribute force and motion in robust ways determined by a nontrivial topological state. Here we discuss the classification of and propose a design principle for mechanical metamaterials that can be easily and reversibly transformed between states with dramatically different mechanical and acoustic properties via a soft strain. Remarkably, despite the low energetic cost of this transition, quantities such as the edge stiffness and speed of sound can change by orders of magnitude. We show that the existence and form of a soft deformation directly determines floppy edge modes and phonon dispersion. Finally, we generalize the soft strain to generate domain structures that allow further tuning of the material.
Transformable topological mechanical metamaterials
Rocklin, D. Zeb; Zhou, Shangnan; Sun, Kai; Mao, Xiaoming
2017-01-01
Mechanical metamaterials are engineered materials whose structures give them novel mechanical properties, including negative Poisson's ratios, negative compressibilities and phononic bandgaps. Of particular interest are systems near the point of mechanical instability, which recently have been shown to distribute force and motion in robust ways determined by a nontrivial topological state. Here we discuss the classification of and propose a design principle for mechanical metamaterials that can be easily and reversibly transformed between states with dramatically different mechanical and acoustic properties via a soft strain. Remarkably, despite the low energetic cost of this transition, quantities such as the edge stiffness and speed of sound can change by orders of magnitude. We show that the existence and form of a soft deformation directly determines floppy edge modes and phonon dispersion. Finally, we generalize the soft strain to generate domain structures that allow further tuning of the material. PMID:28112155
Correlation effects in two-dimensional topological insulators.
Hohenadler, M; Assaad, F F
2013-04-10
Topological insulators have become one of the most active research areas in condensed matter physics. This article reviews progress on the topic of electronic correlation effects in the two-dimensional case, with a focus on systems with intrinsic spin-orbit coupling and numerical results. Topics addressed include an introduction to the noninteracting case, an overview of theoretical models, correlated topological band insulators, interaction-driven phase transitions, topological Mott insulators and fractional topological states, correlation effects on helical edge states, and topological invariants of interacting systems.
Buckling in a topological metamaterial
NASA Astrophysics Data System (ADS)
Meeussen, Anne; Paulose, Jayson; Vitelli, Vincenzo
2015-03-01
Controlling the nonlinear response of mechanical metamaterials paves the way toward designing materials with adaptive and tunable mechanical properties. Buckling, a change in load-bearing state from axial compression to off-axis deformation, is a ubiquitous nonlinear instability that is often exploited to change the local or global mechanical response in metamaterials composed of slender elements. We create localized buckling regions in cellular metamaterials by engineering states of self-stress, regions where the response is dominated by stretching or compression of the constituent beams rather than bending at the stiff hinges connecting them. Unique to our approach is the use of topological states of self-stress, which originate in a topological invariant that characterizes the vibrational spectrum of the repeating unit cell. Unlike typical states of self-stress which result from additional geometric constraints induced by excess beams in a region, these topological states do not change the number of beams at each hinge. We demonstrate the phenomenon through numerical calculations of the linear response of the proposed metamaterial, and through experiments probing the nonlinear regime including localized buckling at specific regions.
A topological similarity measure for proteins.
Máté, Gabriell; Hofmann, Andreas; Wenzel, Nicolas; Heermann, Dieter W
2014-04-01
We introduce a new measure for assessing similarity among chemical structures, based on well-established computational-topology algorithms. We argue that although the method considers geometry, it is more than a mere geometric similarity measure, as it takes into account, on different geometric scales, the important topological features of the compared structures. We prove that our measure is rigorous and complies with the proper mathematical requirements. We validate the method through comparing different configurations of simple zinc finger proteins and present an application on ligands binding to membrane-proteINS extracted from the Directory of Useful Decoys: Enhanced database and corresponding decoys. This article is part of a Special Issue entitled: Viral membrane proteins - Channels for cellular networking.
Emergence of topological and topological crystalline phases in TlBiS2 and TlSbS2
Zhang, Qingyun; Cheng, Yingchun; Schwingenschlögl, Udo
2015-01-01
Using first-principles calculations, we investigate the band structure evolution and topological phase transitions in TlBiS2 and TlSbS2 under hydrostatic pressure as well as uniaxial and biaxial strain. The phase transitions are identified by parity analysis and by calculating the surface states. Zero, one, and four Dirac cones are found for the (111) surfaces of both TlBiS2 and TlSbS2 when the pressure grows, which confirms trivial-nontrivial-trivial phase transitions. The Dirac cones at the points are anisotropic with large out-of-plane component. TlBiS2 shows normal, topological, and topological crystalline insulator phases under hydrostatic pressure, thus being the first compound to exhibit a phase transition from a topological to a topological crystalline insulator. PMID:25669914
Linked topological colloids in a nematic host.
Martinez, Angel; Hermosillo, Leonardo; Tasinkevych, Mykola; Smalyukh, Ivan I
2015-04-14
Geometric shape and topology of constituent particles can alter many colloidal properties such as Brownian motion, self-assembly, and phase behavior. Thus far, only single-component building blocks of colloids with connected surfaces have been studied, although topological colloids, with constituent particles shaped as freestanding knots and handlebodies of different genus, have been recently introduced. Here we develop a topological class of colloids shaped as multicomponent links. Using two-photon photopolymerization, we fabricate colloidal microparticle analogs of the classic examples of links studied in the field of topology, the Hopf and Solomon links, which we disperse in nematic fluids that possess orientational ordering of anisotropic rod-like molecules. The surfaces of these particles are treated to impose tangential or perpendicular boundary conditions for the alignment of liquid crystal molecules, so that they generate a host of topologically nontrivial field and defect structures in the dispersing nematic medium, resulting in an elastic coupling between the linked constituents. The interplay between the topologies of surfaces of linked colloids and the molecular alignment field of the nematic host reveals that linking of particle rings with perpendicular boundary conditions is commonly accompanied by linking of closed singular defect loops, laying the foundations for fabricating complex composite materials with interlinking-based structural organization.
Direct Measurement of the Zak phase in Topological Bloch Bands
NASA Astrophysics Data System (ADS)
Aidelsburger, Monika; Atala, Marcos; Barreiro, Julio; Abanin, Dmitry; Kitagawa, Takuya; Demler, Eugene; Bloch, Immanuel
2013-05-01
Geometric phases that characterize the topological properties of Bloch bands play a fundamental role in the modern band theory of solids. We report on the direct measurement of the geometric phase acquired by cold atoms moving in one-dimensional optical lattices. Using a combination of Bloch oscillations and Ramsey interferometry, we extract the Zak phase--the Berry phase acquired during an adiabatic motion of a particle across the Brillouin zone--which can be viewed as an invariant characterizing the topological properties of the band. For a dimerized optical lattice, which models polyacetylene, we measure a difference of the Zak phase equal to 0.97(2) π for the two possible polyacetylene phases with different dimerization. This indicates that the two dimerized phases belong to different topological classes, such that for a filled band, domain walls have fractional quantum numbers. Our work establishes a new general approach for probing the topological structure of Bloch bands in optical lattices.
Direct measurement of the Zak phase in topological Bloch bands
NASA Astrophysics Data System (ADS)
Atala, Marcos; Aidelsburger, Monika; Barreiro, Julio T.; Abanin, Dmitry; Kitagawa, Takuya; Demler, Eugene; Bloch, Immanuel
2013-12-01
Geometric phases that characterize the topological properties of Bloch bands play a fundamental role in the band theory of solids. Here we report on the measurement of the geometric phase acquired by cold atoms moving in one-dimensional optical lattices. Using a combination of Bloch oscillations and Ramsey interferometry, we extract the Zak phase--the Berry phase gained during the adiabatic motion of a particle across the Brillouin zone--which can be viewed as an invariant characterizing the topological properties of the band. For a dimerized lattice, which models polyacetylene, we measure a difference of the Zak phase δφZak=0.97(2)π for the two possible polyacetylene phases with different dimerization. The two dimerized phases therefore belong to different topological classes, such that for a filled band, domain walls have fractional quantum numbers. Our work establishes a new general approach for probing the topological structure of Bloch bands inoptical lattices.
NASA Astrophysics Data System (ADS)
Meerman, E. R. W.; Spruyt, H. J. N.
1989-08-01
Dc to dc converters using an electrical switch to control power flow between a dc source and a dc load are discussed. Only Pulse Width Modulation (PWM) type converter topologies are considered. A basic three element, three terminal converter topology is defined followed by two universal rules allowing for derivation of a wide variety of different topologies. A summary of different topology types is provided with steady state and small signal relations given for each. The survey shows 46 converter topologies of which 18 are known and 28 are new (under, patent application). The number of topologies could be increased to 68 if negative input voltages are considered.
Protected gates for topological quantum field theories
NASA Astrophysics Data System (ADS)
Beverland, Michael E.; Buerschaper, Oliver; Koenig, Robert; Pastawski, Fernando; Preskill, John; Sijher, Sumit
2016-02-01
We study restrictions on locality-preserving unitary logical gates for topological quantum codes in two spatial dimensions. A locality-preserving operation is one which maps local operators to local operators — for example, a constant-depth quantum circuit of geometrically local gates, or evolution for a constant time governed by a geometrically local bounded-strength Hamiltonian. Locality-preserving logical gates of topological codes are intrinsically fault tolerant because spatially localized errors remain localized, and hence sufficiently dilute errors remain correctable. By invoking general properties of two-dimensional topological field theories, we find that the locality-preserving logical gates are severely limited for codes which admit non-abelian anyons, in particular, there are no locality-preserving logical gates on the torus or the sphere with M punctures if the braiding of anyons is computationally universal. Furthermore, for Ising anyons on the M-punctured sphere, locality-preserving gates must be elements of the logical Pauli group. We derive these results by relating logical gates of a topological code to automorphisms of the Verlinde algebra of the corresponding anyon model, and by requiring the logical gates to be compatible with basis changes in the logical Hilbert space arising from local F-moves and the mapping class group.
Protected gates for topological quantum field theories
Beverland, Michael E.; Pastawski, Fernando; Preskill, John; Buerschaper, Oliver; Koenig, Robert; Sijher, Sumit
2016-02-15
We study restrictions on locality-preserving unitary logical gates for topological quantum codes in two spatial dimensions. A locality-preserving operation is one which maps local operators to local operators — for example, a constant-depth quantum circuit of geometrically local gates, or evolution for a constant time governed by a geometrically local bounded-strength Hamiltonian. Locality-preserving logical gates of topological codes are intrinsically fault tolerant because spatially localized errors remain localized, and hence sufficiently dilute errors remain correctable. By invoking general properties of two-dimensional topological field theories, we find that the locality-preserving logical gates are severely limited for codes which admit non-abelian anyons, in particular, there are no locality-preserving logical gates on the torus or the sphere with M punctures if the braiding of anyons is computationally universal. Furthermore, for Ising anyons on the M-punctured sphere, locality-preserving gates must be elements of the logical Pauli group. We derive these results by relating logical gates of a topological code to automorphisms of the Verlinde algebra of the corresponding anyon model, and by requiring the logical gates to be compatible with basis changes in the logical Hilbert space arising from local F-moves and the mapping class group.
Topological insulators: Engineered heterostructures
NASA Astrophysics Data System (ADS)
Hesjedal, Thorsten; Chen, Yulin
2017-01-01
The combination of topological properties and magnetic order can lead to new quantum states and exotic physical phenomena. In particular, the coupling between topological insulators and antiferromagnets enables magnetic and electronic structural engineering.
Inflation from geometrical tachyons
Thomas, Steven; Ward, John
2005-10-15
We propose an alternative formulation of tachyon inflation using the geometrical tachyon arising from the time dependent motion of a BPS D3-brane in the background geometry due to k parallel NS5-branes arranged around a ring of radius R. Because of the fact that the mass of this geometrical tachyon field is {radical}(2/k) times smaller than the corresponding open-string tachyon mass, we find that the slow-roll conditions for inflation and the number of e-foldings can be satisfied in a manner that is consistent with an effective 4-dimensional model and with a perturbative string coupling. We also show that the metric perturbations produced at the end of inflation can be sufficiently small and do not lead to the inconsistencies that plague the open-string tachyon models. Finally we argue for the existence of a minimum of the geometrical tachyon potential which could give rise to a traditional reheating mechanism.
NASA Astrophysics Data System (ADS)
Bukhanko, F. N.; Bukhanko, A. F.
2016-10-01
Characteristic signs of the universal Nelson-Kosterlitz jump of the superconducting liquid density in the temperature dependences of the magnetization of La1- y Sm y MnO3 + δ samples with samarium concentrations y = 0.85 and 1.0, which are measured in magnetic fields 100 Oe ≤ H ≤ 3.5 kOe, are detected. As the temperature increases, the sample with y = 0.85 exhibits a crescent-shaped singularity in the dc magnetization curve near the critical temperature of decoupling vortex-antivortex pairs ( T KT ≡ T c ≈ 43 K), which is independent of measuring magnetic field H and is characteristic of the dissociation of 2D vortex pairs. A similar singularity is also detected in the sample with a samarium concentration y = 1.0 at a significantly lower temperature ( T KT ≈ 12 K). The obtained experimental results are explained in terms of the topological Kosterlitz-Thouless phase transition of dissociation of 2D vortex pairs in a quasi-two-dimensional weak Josephson coupling network.
NASA Technical Reports Server (NTRS)
Lieberman, R. N.
1972-01-01
Given a directed graph, a natural topology is defined and relationships between standard topological properties and graph theoretical concepts are studied. In particular, the properties of connectivity and separatedness are investigated. A metric is introduced which is shown to be related to separatedness. The topological notions of continuity and homeomorphism. A class of maps is studied which preserve both graph and topological properties. Applications involving strong maps and contractions are also presented.
Chiral models: Geometrical aspects
NASA Astrophysics Data System (ADS)
Perelomov, A. M.
1987-02-01
Two-dimensional classical chiral models of field theory are considered, the main attention being paid on geometrical aspects of such theories. A characteristic feature of these models is that the interaction is inserted not by adding the interaction Lagrangian to the free field Lagrangian, but has a purely geometrical origin and is related to the inner curvature of the manifold. These models are in many respects analogous to non-Abelian gauge theories and as became clear recently, they are also important for the superstring theory which nowadays is the most probable candidate for a truly unified theory of all interactions including gravitation.
Uhlmann phase as a topological measure for one-dimensional fermion systems.
Viyuela, O; Rivas, A; Martin-Delgado, M A
2014-04-04
We introduce the Uhlmann geometric phase as a tool to characterize symmetry-protected topological phases in one-dimensional fermion systems, such as topological insulators and superconductors. Since this phase is formulated for general mixed quantum states, it provides a way to extend topological properties to finite temperature situations. We illustrate these ideas with some paradigmatic models and find that there exists a critical temperature Tc at which the Uhlmann phase goes discontinuously and abruptly to zero. This stands as a borderline between two different topological phases as a function of the temperature. Furthermore, at small temperatures we recover the usual notion of topological phase in fermion systems.
Universalities of thermodynamic signatures in topological phases
Kempkes, S. N.; Quelle, A.; Smith, C. Morais
2016-01-01
Topological insulators (superconductors) are materials that host symmetry-protected metallic edge states in an insulating (superconducting) bulk. Although they are well understood, a thermodynamic description of these materials remained elusive, firstly because the edges yield a non-extensive contribution to the thermodynamic potential, and secondly because topological field theories involve non-local order parameters, and cannot be captured by the Ginzburg-Landau formalism. Recently, this challenge has been overcome: by using Hill thermodynamics to describe the Bernevig-Hughes-Zhang model in two dimensions, it was shown that at the topological phase transition the thermodynamic potential does not scale extensively due to boundary effects. Here, we extend this approach to different topological models in various dimensions (the Kitaev chain and Su-Schrieffer-Heeger model in one dimension, the Kane-Mele model in two dimensions and the Bernevig-Hughes-Zhang model in three dimensions) at zero temperature. Surprisingly, all models exhibit the same universal behavior in the order of the topological-phase transition, depending on the dimension. Moreover, we derive the topological phase diagram at finite temperature using this thermodynamic description, and show that it displays a good agreement with the one calculated from the Uhlmann phase. Our work reveals unexpected universalities and opens the path to a thermodynamic description of systems with a non-local order parameter. PMID:27929041
Universalities of thermodynamic signatures in topological phases
NASA Astrophysics Data System (ADS)
Kempkes, S. N.; Quelle, A.; Smith, C. Morais
2016-12-01
Topological insulators (superconductors) are materials that host symmetry-protected metallic edge states in an insulating (superconducting) bulk. Although they are well understood, a thermodynamic description of these materials remained elusive, firstly because the edges yield a non-extensive contribution to the thermodynamic potential, and secondly because topological field theories involve non-local order parameters, and cannot be captured by the Ginzburg-Landau formalism. Recently, this challenge has been overcome: by using Hill thermodynamics to describe the Bernevig-Hughes-Zhang model in two dimensions, it was shown that at the topological phase transition the thermodynamic potential does not scale extensively due to boundary effects. Here, we extend this approach to different topological models in various dimensions (the Kitaev chain and Su-Schrieffer-Heeger model in one dimension, the Kane-Mele model in two dimensions and the Bernevig-Hughes-Zhang model in three dimensions) at zero temperature. Surprisingly, all models exhibit the same universal behavior in the order of the topological-phase transition, depending on the dimension. Moreover, we derive the topological phase diagram at finite temperature using this thermodynamic description, and show that it displays a good agreement with the one calculated from the Uhlmann phase. Our work reveals unexpected universalities and opens the path to a thermodynamic description of systems with a non-local order parameter.
The singular cubical set of a topological space
NASA Astrophysics Data System (ADS)
Antolini, Rosa; Wiest, Bert
1999-01-01
For any topological space X let C(X) be the realization of the singular cubical set of X; let * be the topological space consisting of one point. In [1] Antolini proves, as a corollary to a general theorem about cubical sets, that C(X) and X×C(*) are homotopy equivalent, provided X is a CW-complex. In this note we give a short geometric proof that for any topological space X there is a natural weak homotopy equivalence between C(X) and X×C(*).
Sufficient symmetry conditions for Topological Quantum Order.
Nussinov, Zohar; Ortiz, Gerardo
2009-10-06
We prove sufficient conditions for Topological Quantum Order at zero and finite temperatures. The crux of the proof hinges on the existence of low-dimensional Gauge-Like Symmetries, thus providing a unifying framework based on a symmetry principle. These symmetries may be actual invariances of the system, or may emerge in the low-energy sector. Prominent examples of Topological Quantum Order display Gauge-Like Symmetries. New systems exhibiting such symmetries include Hamiltonians depicting orbital-dependent spin exchange and Jahn-Teller effects in transition metal orbital compounds, short-range frustrated Klein spin models, and p+ip superconducting arrays. We analyze the physical consequences of Gauge-Like Symmetries (including topological terms and charges) and show the insufficiency of the energy spectrum, topological entanglement entropy, maximal string correlators, and fractionalization in establishing Topological Quantum Order. General symmetry considerations illustrate that not withstanding spectral gaps, thermal fluctuations may impose restrictions on suggested quantum computing schemes. Our results allow us to go beyond standard topological field theories and engineer systems with Topological Quantum Order.
Topological Signatures in the Electronic Structure of Graphene Spirals
Avdoshenko, Stas M.; Koskinen, Pekka; Sevinçli, Haldun; Popov, Alexey A.; Rocha, Claudia G.
2013-01-01
Topology is familiar mostly from mathematics, but also natural sciences have found its concepts useful. Those concepts have been used to explain several natural phenomena in biology and physics, and they are particularly relevant for the electronic structure description of topological insulators and graphene systems. Here, we introduce topologically distinct graphene forms - graphene spirals - and employ density-functional theory to investigate their geometric and electronic properties. We found that the spiral topology gives rise to an intrinsic Rashba spin-orbit splitting. Through a Hamiltonian constrained by space curvature, graphene spirals have topologically protected states due to time-reversal symmetry. In addition, we argue that the synthesis of such graphene spirals is feasible and can be achieved through advanced bottom-up experimental routes that we indicate in this work. PMID:23568379
Topological computation based on direct magnetic logic communication
Zhang, Shilei; Baker, Alexander A.; Komineas, Stavros; Hesjedal, Thorsten
2015-01-01
Non-uniform magnetic domains with non-trivial topology, such as vortices and skyrmions, are proposed as superior state variables for nonvolatile information storage. So far, the possibility of logic operations using topological objects has not been considered. Here, we demonstrate numerically that the topology of the system plays a significant role for its dynamics, using the example of vortex-antivortex pairs in a planar ferromagnetic film. Utilising the dynamical properties and geometrical confinement, direct logic communication between the topological memory carriers is realised. This way, no additional magnetic-to-electrical conversion is required. More importantly, the information carriers can spontaneously travel up to ~300 nm, for which no spin-polarised current is required. The derived logic scheme enables topological spintronics, which can be integrated into large-scale memory and logic networks capable of complex computations. PMID:26508375
Mapping of topological quantum circuits to physical hardware.
Paler, Alexandru; Devitt, Simon J; Nemoto, Kae; Polian, Ilia
2014-04-11
Topological quantum computation is a promising technique to achieve large-scale, error-corrected computation. Quantum hardware is used to create a large, 3-dimensional lattice of entangled qubits while performing computation requires strategic measurement in accordance with a topological circuit specification. The specification is a geometric structure that defines encoded information and fault-tolerant operations. The compilation of a topological circuit is one important aspect of programming a quantum computer, another is the mapping of the topological circuit into the operations performed by the hardware. Each qubit has to be controlled, and measurement results are needed to propagate encoded quantum information from input to output. In this work, we introduce an algorithm for mapping an topological circuit to the operations needed by the physical hardware. We determine the control commands for each qubit in the computer and the relevant measurements that are needed to track information as it moves through the circuit.
Geometric Series via Probability
ERIC Educational Resources Information Center
Tesman, Barry
2012-01-01
Infinite series is a challenging topic in the undergraduate mathematics curriculum for many students. In fact, there is a vast literature in mathematics education research on convergence issues. One of the most important types of infinite series is the geometric series. Their beauty lies in the fact that they can be evaluated explicitly and that…
ERIC Educational Resources Information Center
Smart, Julie; Marshall, Jeff
2007-01-01
Children possess a genuine curiosity for exploring the natural world around them. One third grade teacher capitalized on this inherent trait by leading her students on "A Geometric Scavenger Hunt." The four-lesson inquiry investigation described in this article integrates mathematics and science. Among the students' discoveries was the fact that…
NASA Technical Reports Server (NTRS)
Ives, David
1995-01-01
This paper presents a highly automated hexahedral grid generator based on extensive geometrical and solid modeling operations developed in response to a vision of a designer-driven one day turnaround CFD process which implies a designer-driven one hour grid generation process.
ERIC Educational Resources Information Center
Burgess, Claudia R.
2014-01-01
Designed for a broad audience, including educators, camp directors, afterschool coordinators, and preservice teachers, this investigation aims to help individuals experience mathematics in unconventional and exciting ways by engaging them in the physical activity of building geometric shapes using ropes. Through this engagement, the author…
Electrically Tunable Magnetism in Magnetic Topological Insulators
NASA Astrophysics Data System (ADS)
Zhang, Shou-Cheng; Wang, Jing; Lian, Biao
2015-03-01
The external controllability of the magnetic properties in topological insulators would be important both for fundamental and practical interests. Here we predict the electric-field control of ferromagnetism in a thin film of insulating magnetic topological insulators. The decrease of band inversion by the application of electric fields results in a reduction of magnetic susceptibility, and hence in the modication of magnetism. Remarkably, the electric field could even induce the magnetic quantum phase transition from ferromagnetism to paramagnetism. We further propose a topological transistor device in which the dissipationless charge transport of chiral edge states is controlled by an electric field. The simultaneous electrical control of magnetic order and chiral edge transport in such a device may lead to electronic and spintronic applications for topological insulators. This work is supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering, under Contract No. DE-AC02-76SF00515.
Pragmatic geometric model evaluation
NASA Astrophysics Data System (ADS)
Pamer, Robert
2015-04-01
Quantification of subsurface model reliability is mathematically and technically demanding as there are many different sources of uncertainty and some of the factors can be assessed merely in a subjective way. For many practical applications in industry or risk assessment (e. g. geothermal drilling) a quantitative estimation of possible geometric variations in depth unit is preferred over relative numbers because of cost calculations for different scenarios. The talk gives an overview of several factors that affect the geometry of structural subsurface models that are based upon typical geological survey organization (GSO) data like geological maps, borehole data and conceptually driven construction of subsurface elements (e. g. fault network). Within the context of the trans-European project "GeoMol" uncertainty analysis has to be very pragmatic also because of different data rights, data policies and modelling software between the project partners. In a case study a two-step evaluation methodology for geometric subsurface model uncertainty is being developed. In a first step several models of the same volume of interest have been calculated by omitting successively more and more input data types (seismic constraints, fault network, outcrop data). The positions of the various horizon surfaces are then compared. The procedure is equivalent to comparing data of various levels of detail and therefore structural complexity. This gives a measure of the structural significance of each data set in space and as a consequence areas of geometric complexity are identified. These areas are usually very data sensitive hence geometric variability in between individual data points in these areas is higher than in areas of low structural complexity. Instead of calculating a multitude of different models by varying some input data or parameters as it is done by Monte-Carlo-simulations, the aim of the second step of the evaluation procedure (which is part of the ongoing work) is to
Kalb, Jeffrey L.; Lee, David S.
2008-01-01
Emerging high-bandwidth, low-latency network technology has made network-based architectures both feasible and potentially desirable for use in satellite payload architectures. The selection of network topology is a critical component when developing these multi-node or multi-point architectures. This study examines network topologies and their effect on overall network performance. Numerous topologies were reviewed against a number of performance, reliability, and cost metrics. This document identifies a handful of good network topologies for satellite applications and the metrics used to justify them as such. Since often multiple topologies will meet the requirements of the satellite payload architecture under development, the choice of network topology is not easy, and in the end the choice of topology is influenced by both the design characteristics and requirements of the overall system and the experience of the developer.
Statistical mechanics of topologically constrained DNA and nucleoprotein complexes
NASA Astrophysics Data System (ADS)
Giovan, Stefan Michael
A complex connection exists between the 3 dimensional topological state of DNA in living organisms and biological processes including gene expression, DNA replication, recombination and repair. A significant limitation in developing a detailed, quantitative understanding of this connection is due to a lack of rigorous methods to calculate statistical mechanical properties of DNA molecules with complex topologies, including supercoiling, looping and knotting. This dissertation's main focus is on developing such methods and applying them to realistic DNA and nucleoprotein models. In chapter 2, a method is presented to calculate free energies and J factors of protein mediated DNA loops by normal mode analysis (NMA). This method is similar to calculations performed previously but with several significant advances. We apply the method to the specific case of DNA looping mediated by Cre recombinase protein. J factors calculated by our method are compared to experimental measurements to extract geometric and elastic properties of the Cre-DNA synaptic complex. In particular, the results suggest the existence of a synaptic complex that is more flexible than previously expected and may be explained by a stable intermediate in the reaction pathway that deviates significantly from the planar crystal structure. Calculating free energies of DNA looping is difficult in general, especially when considering intermediate length scales such as plasmid sized DNA which may readily adopt multiple topological states. In chapter 3, a novel method is presented to obtain free energies of semiflexible biopolymers with fixed topologies and arbitrary ratios of contour length L to persistence length P. High accuracy is demonstrated by calculating free energies of specific DNA knots with L/P = 20 and L/P = 40, corresponding to DNA lengths of 3000 and 6000 base pairs, respectively. We then apply the method to study the free-energy landscape for a model of a synaptic nucleoprotein complex
A quantum dot in topological insulator nanofilm.
Herath, Thakshila M; Hewageegana, Prabath; Apalkov, Vadym
2014-03-19
We introduce a quantum dot in topological insulator nanofilm as a bump at the surface of the nanofilm. Such a quantum dot can localize an electron if the size of the dot is large enough, ≳5 nm. The quantum dot in topological insulator nanofilm has states of two types, which belong to two ('conduction' and 'valence') bands of the topological insulator nanofilm. We study the energy spectra of such defined quantum dots. We also consider intraband and interband optical transitions within the dot. The optical transitions of the two types have the same selection rules. While the interband absorption spectra have multi-peak structure, each of the intraband spectra has one strong peak and a few weak high frequency satellites.
Edge anisotropy and the geometric perspective on flow networks
NASA Astrophysics Data System (ADS)
Molkenthin, Nora; Kutza, Hannes; Tupikina, Liubov; Marwan, Norbert; Donges, Jonathan F.; Feudel, Ulrike; Kurths, Jürgen; Donner, Reik V.
2017-03-01
Spatial networks have recently attracted great interest in various fields of research. While the traditional network-theoretic viewpoint is commonly restricted to their topological characteristics (often disregarding the existing spatial constraints), this work takes a geometric perspective, which considers vertices and edges as objects in a metric space and quantifies the corresponding spatial distribution and alignment. For this purpose, we introduce the concept of edge anisotropy and define a class of measures characterizing the spatial directedness of connections. Specifically, we demonstrate that the local anisotropy of edges incident to a given vertex provides useful information about the local geometry of geophysical flows based on networks constructed from spatio-temporal data, which is complementary to topological characteristics of the same flow networks. Taken both structural and geometric viewpoints together can thus assist the identification of underlying flow structures from observations of scalar variables.
Classification and characterization of topological insulators and superconductors
NASA Astrophysics Data System (ADS)
Mong, Roger
surface spectrum can be computed from bulk quantities. Specifically, we present an analytic prescription for computing the edge dispersion
Geometric aspects of charged black holes in Palatini theories
NASA Astrophysics Data System (ADS)
Olmo, Gonzalo J.; Rubiera-Garcia, D.; Sanchez-Puente, Antonio
2015-04-01
Charged black holes in gravity theories in the Palatini formalism present a number of unique properties. Their innermost structure is topologically nontrivial, representing a wormhole supported by a sourceless electric flux. For certain values of their effective mass and charge curvature divergences may be absent, and their event horizon may also disappear yielding a remnant. We give an overview of the mathematical derivation of these solutions and discuss their geodesic structure and other geometric properties.
CAM - Geometric systems integration
NASA Astrophysics Data System (ADS)
Dunlap, G. C.
The integration of geometric and nongeometric information for efficient use of CAM is examined. Requirements for engineering drawings requested by management are noted to involve large volumes of nongeometric data to define the materials and quantity variables which impinge on the required design, so that the actual design may be the last and smaller step in the CAM process. Geometric classification and coding are noted to offer an alpha/numeric identifier for integrating the engineering design, manufacturing, and quality assurance functions. An example is provided of a turbine gear part coding in terms of polycode and monocode displays, showing a possible covering of more than 10 trillion features. Software is stressed as the key to integration of company-wide data.
Topological Winding and Unwinding in Metastable Bose-Einstein Condensates
Kanamoto, Rina; Carr, Lincoln D.; Ueda, Masahito
2008-02-15
Topological winding and unwinding in a quasi-one-dimensional metastable Bose-Einstein condensate are shown to be manipulated by changing the strength of interaction or the frequency of rotation. Exact diagonalization analysis reveals that quasidegenerate states emerge spontaneously near the transition point, allowing a smooth crossover between topologically distinct states. On a mean-field level, the transition is accompanied by formation of gray solitons, or density notches, which serve as an experimental signature of this phenomenon.
Topological structure of dictionary graphs
NASA Astrophysics Data System (ADS)
Fukś, Henryk; Krzemiński, Mark
2009-09-01
We investigate the topological structure of the subgraphs of dictionary graphs constructed from WordNet and Moby thesaurus data. In the process of learning a foreign language, the learner knows only a subset of all words of the language, corresponding to a subgraph of a dictionary graph. When this subgraph grows with time, its topological properties change. We introduce the notion of the pseudocore and argue that the growth of the vocabulary roughly follows decreasing pseudocore numbers—that is, one first learns words with a high pseudocore number followed by smaller pseudocores. We also propose an alternative strategy for vocabulary growth, involving decreasing core numbers as opposed to pseudocore numbers. We find that as the core or pseudocore grows in size, the clustering coefficient first decreases, then reaches a minimum and starts increasing again. The minimum occurs when the vocabulary reaches a size between 103 and 104. A simple model exhibiting similar behavior is proposed. The model is based on a generalized geometric random graph. Possible implications for language learning are discussed.
Geometric measures of entanglement
Uyanik, K.; Turgut, S.
2010-03-15
The geometric measure of entanglement, which expresses the minimum distance to product states, has been generalized to distances to sets that remain invariant under the stochastic reducibility relation. For each such set, an associated entanglement monotone can be defined. The explicit analytical forms of these measures are obtained for bipartite entangled states. Moreover, the three-qubit case is discussed and it is argued that the distance to the W states is a new monotone.
Geometrical deuteron stripping revisited
Neoh, Y. S.; Yap, S. L.
2014-03-05
We investigate the reality of the idea of geometrical deuteron stripping originally envisioned by Serber. By taking into account of realistic deuteron wavefunction, nuclear density, and nucleon stopping mean free path, we are able to estimate inclusive deuteron stripping cross section for deuteron energy up to before pion production. Our semiclassical model contains only one global parameter constant for all nuclei which can be approximated by Woods-Saxon or any other spherically symmetric density distribution.
Strain tuning of topological band order in cubic semiconductors
Feng, wanxiang; Zhu, Wenguang; Weitering, Hanno; Stocks, George Malcolm; Yao, yugui; Xiao, Di
2012-01-01
We theoretically explore the possibility of tuning the topological order of cubic diamond/zinc-blende semi- conductors with external strain. Based on a simple tight-binding model, we analyze the evolution of the cubic semiconductor band structure under hydrostatic or biaxial lattice expansion, by which a generic guiding princi- ple is established that biaxial lattice expansion can induce a topological phase transition of small band-gap cubic semiconductors via a band inversion and symmetry breaking at point. Using density functional theory cal- culations, we demonstrate that a prototype topological trivial semiconductor, InSb, is converted to a nontrivial topological semiconductor with a 2% 3% biaxial lattice expansion.
Destroying a topological quantum bit by condensing Ising vortices.
Hao, Zhihao; Inglis, Stephen; Melko, Roger
2014-12-09
The imminent realization of topologically protected qubits in fabricated systems will provide not only an elementary implementation of fault-tolerant quantum computing architecture, but also an experimental vehicle for the general study of topological order. The simplest topological qubit harbours what is known as a Z2 liquid phase, which encodes information via a degeneracy depending on the system's topology. Elementary excitations of the phase are fractionally charged objects called spinons, or Ising flux vortices called visons. At zero temperature, a Z2 liquid is stable under deformations of the Hamiltonian until spinon or vison condensation induces a quantum-phase transition destroying the topological order. Here we use quantum Monte Carlo to study a vison-induced transition from a Z2 liquid to a valence-bond solid in a quantum dimer model on the kagome lattice. Our results indicate that this critical point is beyond the description of the standard Landau paradigm.
The topological Anderson insulator phase in the Kane-Mele model
Orth, Christoph P.; Sekera, Tibor; Bruder, Christoph; Schmidt, Thomas L.
2016-01-01
It has been proposed that adding disorder to a topologically trivial mercury telluride/cadmium telluride (HgTe/CdTe) quantum well can induce a transition to a topologically nontrivial state. The resulting state was termed topological Anderson insulator and was found in computer simulations of the Bernevig-Hughes-Zhang model. Here, we show that the topological Anderson insulator is a more universal phenomenon and also appears in the Kane-Mele model of topological insulators on a honeycomb lattice. We numerically investigate the interplay of the relevant parameters, and establish the parameter range in which the topological Anderson insulator exists. A staggered sublattice potential turns out to be a necessary condition for the transition to the topological Anderson insulator. For weak enough disorder, a calculation based on the lowest-order Born approximation reproduces quantitatively the numerical data. Our results thus considerably increase the number of candidate materials for the topological Anderson insulator phase. PMID:27045779
Superfluidity in topologically nontrivial flat bands
NASA Astrophysics Data System (ADS)
Peotta, Sebastiano; Törmä, Päivi
2015-11-01
Topological invariants built from the periodic Bloch functions characterize new phases of matter, such as topological insulators and topological superconductors. The most important topological invariant is the Chern number that explains the quantized conductance of the quantum Hall effect. Here we provide a general result for the superfluid weight Ds of a multiband superconductor that is applicable to topologically nontrivial bands with nonzero Chern number C. We find that the integral over the Brillouin-zone of the quantum metric, an invariant calculated from the Bloch functions, gives the superfluid weight in a flat band, with the bound Ds>=|C|. Thus, even a flat band can carry finite superfluid current, provided the Chern number is nonzero. As an example, we provide Ds for the time-reversal invariant attractive Harper-Hubbard model that can be experimentally tested in ultracold gases. In general, our results establish that a topologically nontrivial flat band is a promising concept for increasing the critical temperature of the superconducting transition.
Superfluidity in topologically nontrivial flat bands
Peotta, Sebastiano; Törmä, Päivi
2015-01-01
Topological invariants built from the periodic Bloch functions characterize new phases of matter, such as topological insulators and topological superconductors. The most important topological invariant is the Chern number that explains the quantized conductance of the quantum Hall effect. Here we provide a general result for the superfluid weight Ds of a multiband superconductor that is applicable to topologically nontrivial bands with nonzero Chern number C. We find that the integral over the Brillouin-zone of the quantum metric, an invariant calculated from the Bloch functions, gives the superfluid weight in a flat band, with the bound Ds⩾|C|. Thus, even a flat band can carry finite superfluid current, provided the Chern number is nonzero. As an example, we provide Ds for the time-reversal invariant attractive Harper–Hubbard model that can be experimentally tested in ultracold gases. In general, our results establish that a topologically nontrivial flat band is a promising concept for increasing the critical temperature of the superconducting transition. PMID:26586543
Frustration and Self-Ordering of Topological Defects in Ferroelectrics.
Nahas, Y; Prokhorenko, S; Bellaiche, L
2016-03-18
A first-principles-based effective Hamiltonian technique is used to investigate the interplay between geometrical frustration and the ordering of topological defects in a ferroelectric nanocomposite consisting of a square array of BaTiO_{3} nanowires embedded in a Ba_{0.15}Sr_{0.85}TiO_{3} matrix. Different arrangements of the wires' chiralities geometrically frustrate the matrix, which in response exhibits point topological defects featuring self-assembled ordered structures spatially fluctuating down to the lowest temperatures. These fluctuations thereby endow the system with residual configurational entropy from which many properties characteristic of geometric frustration, such as the ground state degeneracy and the broadness of the dielectric response, are further found to originate.
Spatially-protected Topology and Group Cohomology in Band Insulators
NASA Astrophysics Data System (ADS)
Alexandradinata, A.
This thesis investigates band topologies which rely fundamentally on spatial symmetries. A basic geometric property that distinguishes spatial symmetry regards their transformation of the spatial origin. Point groups consist of spatial transformations that preserve the spatial origin, while un-split extensions of the point groups by spatial translations are referred to as nonsymmorphic space groups. The first part of the thesis addresses topological phases with discretely-robust surface properties: we introduce theories for the Cnv point groups, as well as certain nonsymmorphic groups that involve glide reflections. These band insulators admit a powerful characterization through the geometry of quasimomentum space; parallel transport in this space is represented by the Wilson loop. The non-symmorphic topology we study is naturally described by a further extension of the nonsymmorphic space group by quasimomentum translations (the Wilson loop), thus placing real and quasimomentum space on equal footing -- here, we introduce the language of group cohomology into the theory of band insulators. The second part of the thesis addresses topological phases without surface properties -- their only known physical consequences are discrete signatures in parallel transport. We provide two such case studies with spatial-inversion and discrete-rotational symmetries respectively. One lesson learned here regards the choice of parameter loops in which we carry out transport -- the loop must be chosen to exploit the symmetry that protects the topology. While straight loops are popular for their connection with the geometric theory of polarization, we show that bent loops also have utility in topological band theory.
Representing geometrical knowledge.
Anderson, J A
1997-08-29
This paper introduces perspex algebra which is being developed as a common representation of geometrical knowledge. A perspex can currently be interpreted in one of four ways. First, the algebraic perspex is a generalization of matrices, it provides the most general representation for all of the interpretations of a perspex. The algebraic perspex can be used to describe arbitrary sets of coordinates. The remaining three interpretations of the perspex are all related to square matrices and operate in a Euclidean model of projective space-time, called perspex space. Perspex space differs from the usual Euclidean model of projective space in that it contains the point at nullity. It is argued that the point at nullity is necessary for a consistent account of perspective in top-down vision. Second, the geometric perspex is a simplex in perspex space. It can be used as a primitive building block for shapes, or as a way of recording landmarks on shapes. Third, the transformational perspex describes linear transformations in perspex space that provide the affine and perspective transformations in space-time. It can be used to match a prototype shape to an image, even in so called 'accidental' views where the depth of an object disappears from view, or an object stays in the same place across time. Fourth, the parametric perspex describes the geometric and transformational perspexes in terms of parameters that are related to everyday English descriptions. The parametric perspex can be used to obtain both continuous and categorical perception of objects. The paper ends with a discussion of issues related to using a perspex to describe logic.
Representing geometrical knowledge.
Anderson, J A
1997-01-01
This paper introduces perspex algebra which is being developed as a common representation of geometrical knowledge. A perspex can currently be interpreted in one of four ways. First, the algebraic perspex is a generalization of matrices, it provides the most general representation for all of the interpretations of a perspex. The algebraic perspex can be used to describe arbitrary sets of coordinates. The remaining three interpretations of the perspex are all related to square matrices and operate in a Euclidean model of projective space-time, called perspex space. Perspex space differs from the usual Euclidean model of projective space in that it contains the point at nullity. It is argued that the point at nullity is necessary for a consistent account of perspective in top-down vision. Second, the geometric perspex is a simplex in perspex space. It can be used as a primitive building block for shapes, or as a way of recording landmarks on shapes. Third, the transformational perspex describes linear transformations in perspex space that provide the affine and perspective transformations in space-time. It can be used to match a prototype shape to an image, even in so called 'accidental' views where the depth of an object disappears from view, or an object stays in the same place across time. Fourth, the parametric perspex describes the geometric and transformational perspexes in terms of parameters that are related to everyday English descriptions. The parametric perspex can be used to obtain both continuous and categorical perception of objects. The paper ends with a discussion of issues related to using a perspex to describe logic. PMID:9304680
Babichev, E.
2006-10-15
We consider global topological defects in symmetry-breaking models with a noncanonical kinetic term. Apart from a mass parameter entering the potential, one additional dimensional parameter arises in such models - a kinetic mass. The properties of defects in these models are quite different from standard global domain walls, vortices, and monopoles, if their kinetic mass scale is smaller than their symmetry-breaking scale. In particular, depending on the concrete form of the kinetic term, the typical size of such a defect can be either much larger or much smaller than the size of a standard defect with the same potential term. The characteristic mass of a nonstandard defect, which might have been formed during a phase transition in the early universe, depends on both the temperature of a phase transition and the kinetic mass.
Direct imaging of magnetic field-driven transitions of skyrmion cluster states in FeGe nanodisks
Zhao, Xuebing; Jin, Chiming; Wang, Chao; Du, Haifeng; Zang, Jiadong; Tian, Mingliang; Che, Renchao; Zhang, Yuheng
2016-01-01
Magnetic skyrmion is a nanosized magnetic whirl with nontrivial topology, which is highly relevant for applications on future memory devices. To enable the applications, theoretical efforts have been made to understand the dynamics of individual skyrmions in magnetic nanostructures. However, directly imaging the evolution of highly geometrically confined individual skyrmions is challenging. Here, we report the magnetic field-driven dynamics of individual skyrmions in FeGe nanodisks with diameters on the order of several skyrmion sizes by using Lorentz transmission electron microscopy. In contrast to the conventional skyrmion lattice in bulk, a series of skyrmion cluster states with different geometrical configurations and the field-driven cascading phase transitions are identified at temperatures far below the magnetic transition temperature. Furthermore, a dynamics, namely the intermittent jumps between the neighboring skyrmion cluster states, is found at elevated temperatures, at which the thermal energy competes with the energy barrier between the skyrmion cluster states. PMID:27051067
Attracting manifold for a viscous topology transition
Goldstein, R.E.; Pesci, A.I.; Shelley, M.J. ||
1995-11-13
An analytical method is developed describing the approach to a finite-time singularity associated with collapse of a narrow fluid layer in an unstable Hele-Shaw flow. Under the separation of time scales near a bifurcation point, a long-wavelength mode entrains higher-frequency modes, as described by a version of Hill`s equation. In the slaved dynamics, the initial-value problem is solved explicitly, yielding the time and analytical structure of a singularity which is associated with the motion of zeros in the complex plane. This suggests a general mechanism of singularity formation in this system. {copyright} {ital 1995} {ital The} {ital American} {ital Physical} {ital Society}.
Geometric phase in Bohmian mechanics
Chou, Chia-Chun; Wyatt, Robert E.
2010-10-15
Using the quantum kinematic approach of Mukunda and Simon, we propose a geometric phase in Bohmian mechanics. A reparametrization and gauge invariant geometric phase is derived along an arbitrary path in configuration space. The single valuedness of the wave function implies that the geometric phase along a path must be equal to an integer multiple of 2{pi}. The nonzero geometric phase indicates that we go through the branch cut of the action function from one Riemann sheet to another when we locally travel along the path. For stationary states, quantum vortices exhibiting the quantized circulation integral can be regarded as a manifestation of the geometric phase. The bound-state Aharonov-Bohm effect demonstrates that the geometric phase along a closed path contains not only the circulation integral term but also an additional term associated with the magnetic flux. In addition, it is shown that the geometric phase proposed previously from the ensemble theory is not gauge invariant.
NASA Astrophysics Data System (ADS)
Bietenholz, W.; Gerber, U.; Pepe, M.; Wiese, U.-J.
2010-12-01
We consider lattice field theories with topological actions, which are invariant against small deformations of the fields. Some of these actions have infinite barriers separating different topological sectors. Topological actions do not have the correct classical continuum limit and they cannot be treated using perturbation theory, but they still yield the correct quantum continuum limit. To show this, we present analytic studies of the 1-d O(2) and O(3) model, as well as Monte Carlo simulations of the 2-d O(3) model using topological lattice actions. Some topological actions obey and others violate a lattice Schwarz inequality between the action and the topological charge Q. Irrespective of this, in the 2-d O(3) model the topological susceptibility {χ_t} = {{{left< {{Q^2}} rightrangle }} left/ {V} right.} is logarithmically divergent in the continuum limit. Still, at non-zero distance the correlator of the topological charge density has a finite continuum limit which is consistent with analytic predictions. Our study shows explicitly that some classically important features of an action are irrelevant for reaching the correct quantum continuum limit.
Charged topological entanglement entropy
NASA Astrophysics Data System (ADS)
Matsuura, Shunji; Wen, Xueda; Hung, Ling-Yan; Ryu, Shinsei
2016-05-01
A charged entanglement entropy is a new measure which probes quantum entanglement between different charge sectors. We study symmetry-protected topological (SPT) phases in (2+1)-dimensional space-time by using this charged entanglement entropy. SPT phases are short-range entangled states without topological order and hence cannot be detected by the topological entanglement entropy. We demonstrate that the universal part of the charged entanglement entropy is nonzero for nontrivial SPT phases and therefore it is a useful measure to detect short-range entangled topological phases. We also discuss that the classification of SPT phases based on the charged topological entanglement entropy is related to that of the braiding statistics of quasiparticles.
Topological nonsymmorphic crystalline superconductors
NASA Astrophysics Data System (ADS)
Wang, Qing-Ze; Liu, Chao-Xing
2016-01-01
Topological superconductors possess a nodeless superconducting gap in the bulk and gapless zero energy modes, known as "Majorana zero modes," at the boundary of a finite system. In this work, we introduce a new class of topological superconductors, which are protected by nonsymmorphic crystalline symmetry and thus dubbed "topological nonsymmorphic crystalline superconductors." We construct an explicit Bogoliubov-de Gennes type of model for this superconducting phase in the D class and show how Majorana zero modes in this model are protected by glide plane symmetry. Furthermore, we generalize the classification of topological nonsymmorphic crystalline superconductors to the classes with time reversal symmetry, including the DIII and BDI classes, in two dimensions. Our theory provides guidance to search for new topological superconducting materials with nonsymmorphic crystal structures.
Topological Nonsymmorphic Crystalline Superconductors
NASA Astrophysics Data System (ADS)
Wang, Qing-Ze; Liu, Chao-Xing
Topological superconductors possess a nodeless superconducting gap in the bulk and gapless zero energy modes, known as ``Majorana zero modes'', at the boundary of a finite system. In this work, we introduce a new class of topological superconductors, which are protected by nonsymmorphic crystalline symmetry and thus dubbed ``topological nonsymmorphic crystalline superconductors''. We construct an explicit Bogoliubov-de Gennes type of model for this superconducting phase in the D class and show how Majorana zero modes in this model are protected by glide symmetry. Furthermore, we generalize the classification of topological nonsymmorphic crystalline superconductors to the classes with time reversal symmetry, including the DIII and BDI classes, in two dimensions. Our theory provides a guidance to search for new topological superconducting materials with nonsymmorphic crystal structures.
Selected topics on the topology of ideal fluid flows
NASA Astrophysics Data System (ADS)
Peralta-Salas, Daniel
2016-08-01
This is a survey of certain geometric aspects of inviscid and incompressible fluid flows, which are described by the solutions to the Euler equations. We will review Arnold’s theorem on the topological structure of stationary fluids in compact manifolds, and Moffatt’s theorem on the topological interpretation of helicity in terms of knot invariants. The recent realization theorem by Enciso and Peralta-Salas of vortex lines of arbitrarily complicated topology for stationary solutions to the Euler equations will also be introduced. The aim of this paper is not to provide detailed proofs of all the stated results but to introduce the main ideas and methods behind certain selected topics of the subject known as Topological Fluid Mechanics. This is the set of lecture notes, the author gave at the XXIV International Fall Workshop on Geometry and Physics held in Zaragoza (Spain) during September 2015.
Tailoring exchange couplings in magnetic topological-insulator/antiferromagnet heterostructures
NASA Astrophysics Data System (ADS)
He, Qing Lin; Kou, Xufeng; Grutter, Alexander J.; Yin, Gen; Pan, Lei; Che, Xiaoyu; Liu, Yuxiang; Nie, Tianxiao; Zhang, Bin; Disseler, Steven M.; Kirby, Brian J.; Ratcliff, William, II; Shao, Qiming; Murata, Koichi; Zhu, Xiaodan; Yu, Guoqiang; Fan, Yabin; Montazeri, Mohammad; Han, Xiaodong; Borchers, Julie A.; Wang, Kang L.
2017-01-01
Magnetic topological insulators such as Cr-doped (Bi,Sb)2Te3 provide a platform for the realization of versatile time-reversal symmetry-breaking physics. By constructing heterostructures exhibiting Néel order in an antiferromagnetic CrSb and ferromagnetic order in Cr-doped (Bi,Sb)2Te3, we realize emergent interfacial magnetic phenomena which can be tailored through artificial structural engineering. Through deliberate geometrical design of heterostructures and superlattices, we demonstrate the use of antiferromagnetic exchange coupling in manipulating the magnetic properties of magnetic topological insulators. Proximity effects are shown to induce an interfacial spin texture modulation and establish an effective long-range exchange coupling mediated by antiferromagnetism, which significantly enhances the magnetic ordering temperature in the superlattice. This work provides a new framework on integrating topological insulators with antiferromagnetic materials and unveils new avenues towards dissipationless topological antiferromagnetic spintronics.
Geometric aspects of ordering phenomena
NASA Astrophysics Data System (ADS)
Cugliandolo, Leticia F.
2017-01-01
A macroscopic system prepared in a disordered phase and quenched across a second-order phase transition into an ordered phase undergoes a coarsening process whereby it orders locally in one of the equilibrium states. The study of the evolution of the morphology of the ordered structures in two dimensions has recently unveiled two interesting and generic features. On the one hand, the dynamics first approach a critical percolating state via the growth of a new lengthscale and satisfying scaling properties with respect to it. The time needed to reach the critical percolating state diverges with the system size, though more weakly than the equilibration time. On the other hand, once the critical percolating structures established, the geometrical and statistical properties at larger scales than the one established by the usual dynamic growing length remain the ones of critical percolation. These observations are common to different microscopic dynamics (single spin flip, local and non-local spin exchange, voter) in pure or weakly disordered systems. We discuss these results and we refer to the relevant publications for details. xml:lang="fr"
Geometric Observers for Dynamically Evolving Curves
Niethammer, Marc; Vela, Patricio A.; Tannenbaum, Allen
2009-01-01
This paper proposes a deterministic observer design for visual tracking based on nonparametric implicit (level-set) curve descriptions. The observer is continuous discrete with continuous-time system dynamics and discrete-time measurements. Its state-space consists of an estimated curve position augmented by additional states (e.g., velocities) associated with every point on the estimated curve. Multiple simulation models are proposed for state prediction. Measurements are performed through standard static segmentation algorithms and optical-flow computations. Special emphasis is given to the geometric formulation of the overall dynamical system. The discrete-time measurements lead to the problem of geometric curve interpolation and the discrete-time filtering of quantities propagated along with the estimated curve. Interpolation and filtering are intimately linked to the correspondence problem between curves. Correspondences are established by a Laplace-equation approach. The proposed scheme is implemented completely implicitly (by Eulerian numerical solutions of transport equations) and thus naturally allows for topological changes and subpixel accuracy on the computational grid. PMID:18421113
Geometric defects in quantum Hall states
NASA Astrophysics Data System (ADS)
Gromov, Andrey
2016-08-01
We describe a geometric (or gravitational) analog of the Laughlin quasiholes in fractional quantum Hall states. Analogously to the quasiholes, these defects can be constructed by an insertion of an appropriate vertex operator into the conformal block representation of a trial wave function; however, unlike the quasiholes these defects are extrinsic and do not correspond to true excitations of the quantum fluid. We construct a wave function in the presence of such defects and explain how to assign an electric charge and a spin to each defect and calculate the adiabatic, non-Abelian statistics of the defects. The defects turn out to be equivalent to the genons in that their adiabatic exchange statistics can be described in terms of representations of the mapping class group of an appropriate higher genus Riemann surface. We present a general construction that, in principle, makes it possible to calculate the statistics of Zn genons for any "parent" topological phase. We illustrate the construction on the example of the Laughlin state and perform an explicit calculation of the braiding matrices. In addition to non-Abelian statistics, geometric defects possess a universal Abelian overall phase, determined by the gravitational anomaly.
NASA Technical Reports Server (NTRS)
Kamhawi, Hilmi N.
2012-01-01
This report documents the work performed from March 2010 to March 2012. The Integrated Design and Engineering Analysis (IDEA) environment is a collaborative environment based on an object-oriented, multidisciplinary, distributed framework using the Adaptive Modeling Language (AML) as a framework and supporting the configuration design and parametric CFD grid generation. This report will focus on describing the work in the area of parametric CFD grid generation using novel concepts for defining the interaction between the mesh topology and the geometry in such a way as to separate the mesh topology from the geometric topology while maintaining the link between the mesh topology and the actual geometry.
Beam shaping using topological axicons (Conference Presentation)
NASA Astrophysics Data System (ADS)
Aleksanyan, Artur; Žukauskas, Albertas; Sanchez-Padilla, Benjamin; Malinauskas, Mangirdas; Brasselet, Etienne
2016-09-01
Controlling the angular spectrum content of light fields is a basic beam shaping strategy implying the control of the wavevector distribution. Here we propose a novel class of refractive optical elements generated by folding the conical surface of a usual (conical) axicon. In particular, we explore folding processes where the continuous deformation of the circular cross-section of an axicon lead to the appearance of geometrical singularities (cusps). This is illustrated considering two prototypical families derived from hypocycloidal and epicycloidal geometries. Such topological axicons have been fabricated at the micron scale by using photopolymerization technique and characterized both experimentally and theoretically.
The Data Transfer Kit: A geometric rendezvous-based tool for multiphysics data transfer
Slattery, S. R.; Wilson, P. P. H.; Pawlowski, R. P.
2013-07-01
The Data Transfer Kit (DTK) is a software library designed to provide parallel data transfer services for arbitrary physics components based on the concept of geometric rendezvous. The rendezvous algorithm provides a means to geometrically correlate two geometric domains that may be arbitrarily decomposed in a parallel simulation. By repartitioning both domains such that they have the same geometric domain on each parallel process, efficient and load balanced search operations and data transfer can be performed at a desirable algorithmic time complexity with low communication overhead relative to other types of mapping algorithms. With the increased development efforts in multiphysics simulation and other multiple mesh and geometry problems, generating parallel topology maps for transferring fields and other data between geometric domains is a common operation. The algorithms used to generate parallel topology maps based on the concept of geometric rendezvous as implemented in DTK are described with an example using a conjugate heat transfer calculation and thermal coupling with a neutronics code. In addition, we provide the results of initial scaling studies performed on the Jaguar Cray XK6 system at Oak Ridge National Laboratory for a worse-case-scenario problem in terms of algorithmic complexity that shows good scaling on 0(1 x 104) cores for topology map generation and excellent scaling on 0(1 x 105) cores for the data transfer operation with meshes of O(1 x 109) elements. (authors)
Disorder effects in correlated topological insulators
NASA Astrophysics Data System (ADS)
Hung, Hsiang-Hsuan; Barr, Aaron; Prodan, Emil; Fiete, Gregory A.
2016-12-01
Using exact diagonalization and quantum Monte Carlo calculations we investigate the effects of disorder on the phase diagram of both noninteracting and interacting models of two-dimensional topological insulators. In the fermion sign problem-free interacting models we study, electron-electron interactions are described by an on-site repulsive Hubbard interaction and disorder is included via the one-body hopping operators. In both the noninteracting and interacting models we make use of recent advances in highly accurate real-space numerical evaluation of topological invariants to compute phase boundaries and in the noninteracting models determine critical exponents of the transitions. We find different models exhibit distinct stability conditions of the topological phase with respect to interactions and disorder. We provide a general analytical theory that accurately predicts these trends.
Goldberg, P.W.
1993-04-01
In this paper we consider the problem of learning the positions of spheres in metric spaces, given as data randomly drawn points classified according to whether they are internal or external to an unknown sphere. The particular metrics under consideration are geometrical shape metrics, and the results are intended to be applicable to the problem of learning to identify a shape from related shapes classified according to whether they resemble it visually. While it is typically NP-hard to locate a central point for a hypothesis sphere, we find that it is however often possible to obtain a non-spherical hypothesis which can accurately predict whether further random points lie within the unknown sphere. We exhibit algorithms which achieve this, and in the process indicate useful general techniques for computational learning. Finally we exhibit a natural shape metric and show that it defines a class of spheres not predictable in this sense, subject to standard cryptographic assumptions.
Magnetic topology and current channels in plasmas with toroidal current density inversions
Ciro, D.; Caldas, I. L.
2013-10-15
The equilibrium magnetic field inside axisymmetric plasmas with inversions on the toroidal current density is considered. Previous works have shown that internal regions with negative current density lead to non-nested magnetic surfaces inside the plasma. Following these results, we derive a general expression relating the positive and negative currents inside the non-nested surfaces. This is done in terms of an anisotropy parameter that is model-independent and is based in very general properties of the magnetic field. We demonstrate that the positive currents in axisymmetric islands screen the negative one in the plasma center by reaching about twice its magnitude. Further, we illustrate these results by developing a family of analytical local solutions for the poloidal magnetic field in a region of interest that contains the inverted current. These local solutions exhibit non-nested magnetic surfaces with a combined current of at least twice the magnitude of the negative one, as prescribed from the topological arguments, and allow to study topological transitions driven by geometrical changes in the current profile. To conclude, we discuss the signatures of internal current density inversions in a confinement device and show that magnetic pitch measurements may be inappropriate to differentiate current reversals and small current holes in plasmas.
NASA Astrophysics Data System (ADS)
Knitter, Sebastian; Fatt Liew, Seng; Xiong, Wen; Guy, Mikhael I.; Solomon, Glenn S.; Cao, Hui
2016-01-01
We introduce a topological defect to a regular photonic crystal defect cavity with anisotropic unit cell. Spatially localized resonances are formed and have high quality factor. Unlike the regular photonic crystal defect states, the localized resonances in the topological defect structures support powerflow vortices. Experimentally we realize lasing in the topological defect cavities with optical pumping. This work shows that the spatially inhomogeneous variation of the unit cell orientation adds another degree of freedom to the control of lasing modes, enabling the manipulation of the field pattern and energy flow landscape.
Notes on topological insulators
NASA Astrophysics Data System (ADS)
Kaufmann, Ralph M.; Li, Dan; Wehefritz-Kaufmann, Birgit
2016-11-01
This paper is a survey of the ℤ2-valued invariant of topological insulators used in condensed matter physics. The ℤ-valued topological invariant, which was originally called the TKNN invariant in physics, has now been fully understood as the first Chern number. The ℤ2 invariant is more mysterious; we will explain its equivalent descriptions from different points of view and provide the relations between them. These invariants provide the classification of topological insulators with different symmetries in which K-theory plays an important role. Moreover, we establish that both invariants are realizations of index theorems which can also be understood in terms of condensed matter physics.
Switchable topological phonon channels
NASA Astrophysics Data System (ADS)
Süsstrunk, Roman; Zimmermann, Philipp; Huber, Sebastian D.
2017-01-01
Guiding energy deliberately is one of the central elements in engineering and information processing. It is often achieved by designing specific transport channels in a suitable material. Topological metamaterials offer a way to construct stable and efficient channels of unprecedented versatility. However, due to their stability it can be tricky to terminate them or to temporarily shut them off without changing the material properties massively. While a lot of effort was put into realizing mechanical topological metamaterials, almost no works deal with manipulating their edge channels in sight of applications. Here, we take a step in this direction, by taking advantage of local symmetry breaking potentials to build a switchable topological phonon channel.
Conductance spectroscopy of topological superconductor wire junctions
NASA Astrophysics Data System (ADS)
Setiawan, F.; Brydon, Philip; Sau, Jay
We study the zero-temperature transport properties of one-dimensional normal metal-superconductor (NS) junctions with topological superconductors across their topological transitions. Working within the Blonder-Tinkham-Klapwijk (BTK) formalism generalized for topological NS junctions, we analytically calculate the differential conductance for tunneling into two models of a topological superconductor: a spinless intrinsic p-wave superconductor and a spin-orbit-coupled s-wave superconductor in a Zeeman field. The zero-bias conductance takes nonuniversal values in the nontopological phase while it is robustly quantized at 2e2 / h in the topological regime. Despite this quantization at zero voltage, the zero-bias conductance only develops a peak (or a local maximum) as a function of voltage for sufficiently large interfacial barrier strength, or certain parameter regimes of spin-orbit coupling strength. Our calculated BTK conductance also shows that the conductance is finite inside the superconducting gap region because of the finite barrier transparency, providing a possible mechanism for the observed ``soft gap'' feature in the experimental studies. Work is done in collaboration with Sankar Das Sarma and supported by Microsoft Q, LPS-CMTC, and JQI-NSF-PFC.
Patterns of electromagnetic response in topological semimetals
NASA Astrophysics Data System (ADS)
Ramamurthy, Srinidhi T.; Hughes, Taylor L.
2015-08-01
Topological semimetals are gapless states of matter which have robust and unique electromagnetic responses and surface states. In this paper, we consider semimetals which have pointlike Fermi surfaces in various spatial dimensions D =1 ,2 ,3 which naturally occur in the transition between a weak topological insulator and a trivial insulating phase. These semimetals include those of Dirac and Weyl types. We construct these phases by layering strong topological insulator phases in one dimension lower. This perspective helps us understand their effective response field theory that is generally characterized by a 1-form b which represents a source of Lorentz violation and can be read off from the location of the nodes in momentum space and the helicities/chiralities of the nodes. We derive effective response actions for the two-dimensional (2D) and 3D Dirac semimetals and extensively discuss the response of the Weyl semimetal. We also show how our work can be used to describe semimetals with Fermi surfaces with lower codimension as well as to describe the topological response of 3D topological crystalline insulators.
Bulk entanglement spectrum reveals quantum criticality within a topological state.
Hsieh, Timothy H; Fu, Liang
2014-09-05
A quantum phase transition is usually achieved by tuning physical parameters in a Hamiltonian at zero temperature. Here, we show that the ground state of a topological phase itself encodes critical properties of its transition to a trivial phase. To extract this information, we introduce an extensive partition of the system into two subsystems both of which extend throughout the bulk in all directions. The resulting bulk entanglement spectrum has a low-lying part that resembles the excitation spectrum of a bulk Hamiltonian, which allows us to probe a topological phase transition from a single wave function by tuning either the geometry of the partition or the entanglement temperature. As an example, this remarkable correspondence between the topological phase transition and the entanglement criticality is rigorously established for integer quantum Hall states.
Topological principles of borosilicate glass chemistry.
Smedskjaer, Morten M; Mauro, John C; Youngman, Randall E; Hogue, Carrie L; Potuzak, Marcel; Yue, Yuanzheng
2011-11-10
Borosilicate glasses display a rich complexity of chemical behavior depending on the details of their composition and thermal history. Noted for their high chemical durability and thermal shock resistance, borosilicate glasses have found a variety of important uses from common household and laboratory glassware to high-tech applications such as liquid crystal displays. In this paper, we investigate the topological principles of borosilicate glass chemistry covering the extremes from pure borate to pure silicate end members. Based on NMR measurements, we present a two-state statistical mechanical model of boron speciation in which addition of network modifiers leads to a competition between the formation of nonbridging oxygen and the conversion of boron from trigonal to tetrahedral configuration. Using this model, we derive a detailed topological representation of alkali-alkaline earth-borosilicate glasses that enables the accurate prediction of properties such as glass transition temperature, liquid fragility, and hardness. The modeling approach enables an understanding of the microscopic mechanisms governing macroscopic properties. The implications of the glass topology are discussed in terms of both the temperature and thermal history dependence of the atomic bond constraints and the influence on relaxation behavior. We also observe a nonlinear evolution of the jump in isobaric heat capacity at the glass transition when substituting SiO(2) for B(2)O(3), which can be accurately predicted using a combined topological and thermodynamic modeling approach.
Topological susceptibility from slabs
NASA Astrophysics Data System (ADS)
Bietenholz, Wolfgang; de Forcrand, Philippe; Gerber, Urs
2015-12-01
In quantum field theories with topological sectors, a non-perturbative quantity of interest is the topological susceptibility χ t. In principle it seems straightforward to measure χ t by means of Monte Carlo simulations. However, for local update algorithms and fine lattice spacings, this tends to be difficult, since the Monte Carlo history rarely changes the topological sector. Here we test a method to measure χ t even if data from only one sector are available. It is based on the topological charges in sub-volumes, which we denote as slabs. Assuming a Gaussian distribution of these charges, this method enables the evaluation of χ t, as we demonstrate with numerical results for non-linear σ-models.
Real topological string amplitudes
NASA Astrophysics Data System (ADS)
Narain, K. S.; Piazzalunga, N.; Tanzini, A.
2017-03-01
We discuss the physical superstring correlation functions in type I theory (or equivalently type II with orientifold) that compute real topological string amplitudes. We consider the correlator corresponding to holomorphic derivative of the real topological amplitude G_{χ } , at fixed worldsheet Euler characteristic χ. This corresponds in the low-energy effective action to N=2 Weyl multiplet, appropriately reduced to the orientifold invariant part, and raised to the power g' = -χ + 1. We show that the physical string correlator gives precisely the holomorphic derivative of topological amplitude. Finally, we apply this method to the standard closed oriented case as well, and prove a similar statement for the topological amplitude F_g.
Topological Solitons in Physics.
ERIC Educational Resources Information Center
Parsa, Zohreh
1979-01-01
A broad definition of solitons and a discussion of their role in physics is given. Vortices and magnetic monopoles which are examples of topological solitons in two and three spatial dimensions are described in some detail. (BB)
Knot Theory and Topologically Massive Yang-Mills Theory
NASA Astrophysics Data System (ADS)
Yildirim, Tuna; Rodgers, Vincent; Nair, Parameswaran; Carter, Suzanne
2013-04-01
In 2+1 dimensions, we study Yang-Mills(YM) + Chern-Simons(CS) theory also known as topologically massive Yang-Mills(TMYM) theory. Using geometric quantization method we calculate the Wilson Loop expectation values of TMYM theory. At large distances, where only the topological theory survives, we obtain a condition that makes skein relations of knot theory useful to calculate Wilson loop expectation values of TMYM theory. These link invariants may lead to a better understanding of mass gap in 2+1 dimensions.
Physical implementation of topologically decoherence-protected superconducting qubits
Xue Zhengyuan; Wang, Z. D.; Zhu Shiliang
2008-02-15
We propose a scenario to physically implement a kind of topologically decoherence-protected qubit using superconducting devices coupled to a microwave cavity mode with unconventional geometric operations. It is shown that the two needed interactions for selective devices, which are required for implementing such protected qubits, as well as single-qubit gates, can be achieved by using the external magnetic flux. The easy combination of individual addressing with the many-device setup proposed in the system presents a distinct merit in comparison with the implementation of topologically protected qubits in a trapped-ion system.
Topological nodal line semimetals
NASA Astrophysics Data System (ADS)
Fang, Chen; Weng, Hongming; Dai, Xi; Fang, Zhong
2016-11-01
We review the recent, mainly theoretical, progress in the study of topological nodal line semimetals in three dimensions. In these semimetals, the conduction and the valence bands cross each other along a one-dimensional curve in the three-dimensional Brillouin zone, and any perturbation that preserves a certain symmetry group (generated by either spatial symmetries or time-reversal symmetry) cannot remove this crossing line and open a full direct gap between the two bands. The nodal line(s) is hence topologically protected by the symmetry group, and can be associated with a topological invariant. In this review, (i) we enumerate the symmetry groups that may protect a topological nodal line; (ii) we write down the explicit form of the topological invariant for each of these symmetry groups in terms of the wave functions on the Fermi surface, establishing a topological classification; (iii) for certain classes, we review the proposals for the realization of these semimetals in real materials; (iv) we discuss different scenarios that when the protecting symmetry is broken, how a topological nodal line semimetal becomes Weyl semimetals, Dirac semimetals, and other topological phases; and (v) we discuss the possible physical effects accessible to experimental probes in these materials. Project partially supported by the National Key Research and Development Program of China (Grant Nos. 2016YFA0302400 and 2016YFA0300604), partially by the National Natural Science Foundation of China (Grant Nos. 11274359 and 11422428), the National Basic Research Program of China (Grant No. 2013CB921700), and the “Strategic Priority Research Program (B)” of the Chinese Academy of Sciences (Grant No. XDB07020100).
Topological Dirac line nodes in centrosymmetric semimetals
NASA Astrophysics Data System (ADS)
Kim, Youngkuk; Wieder, Benjamin; Kane, Charles; Rappe, Andrew; TI seed Team
Dirac line nodes (DLNs) are one-dimensional lines of Dirac band-touching points, characterized by linear dispersion in only a single direction in momentum space. In the presence of inversion symmetry and time-reversal symmetry, crystals with vanishing spin-orbit coupling can host topologically protected DLNs. Recently, we have proposed and characterized a novel Z2 class of DLN semimetals [1]. We present Z2 topological invariants, dictating the presence of DLNs, based on the parity eigenvalues at the time-reversal invariant crystal momenta. Our first-principles calculations show that DLNs can be realized in Cu3N in an anti-ReO3 structure via a metal-insulator electronic transition, driven by transition metal doping. We also discuss the resultant surface states and the effects of spin-orbit coupling.