Bulletin of the American Physical Society
APS March Meeting 2011
Volume 56, Number 1
Monday–Friday, March 21–25, 2011; Dallas, Texas
Session B35: Topological Insulators: Theory I |
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Sponsoring Units: DCMP Chair: Kai Sun, University of Maryland Room: C140 |
Monday, March 21, 2011 11:15AM - 11:27AM |
B35.00001: Classification of Gapped Topological Phases in 1D Interacting System Xie Chen, Zheng-Cheng Gu, Xiao-Gang Wen Topological phases exist in quantum many-body systems beyond the usual symmetry breaking understanding of phase and phase transition. While a full classification of topological insulators and superconductors has been given for non-interacting fermions, the question of what phases exist for strongly interacting systems and how to identify them seems hard. Here we give a full classification of 1D gapped phases with possible topological and symmetry breaking order in both spin and fermion systems, based on the local unitary equivalence relation between short-range correlated matrix product states, which represent well the class of 1D gapped ground states. We find that in certain symmetry classes, the classification result for non- interacting systems is changed when strong interaction is allowed. Understanding about 1D system also allows us to obtain some simple results for topological phases in higher dimensions when certain symmetries are present. [Preview Abstract] |
Monday, March 21, 2011 11:27AM - 11:39AM |
B35.00002: Classification of topological insulators and superconductors using KR theory Abhishek Roy Kitaev's periodic table\footnote{A. Kitaev, Proceedings of the L.D.Landau Memorial Conference Advances in Theoretical Physics, June 22-26, 2008} provided a classification of topological insulators and superconductors. The classes are indexed by dimension and symmetries. We present a method of arriving at the table using KR theory. This gives a unified and systematic method of constructing model Hamiltonians for each class, as well as those for boundaries and defects. We motivate the formulae for the topological invariants and explain the diagonal periodicity in the invariants. [Preview Abstract] |
Monday, March 21, 2011 11:39AM - 11:51AM |
B35.00003: The classification of topological insulators and superconductors Ching-Kai Chiu, Michael Stone, Taylor Hughes We use the process of band crossings during quantum phase transitions to explain the periodic table of topological insulators and superconductors. This is achieved by showing how irreducible representations of the real and complex Clifford algebras are related to the 10 Altland-Zirnbauer symmetry classes of Hamiltonian matrices which are associated with time reversal, particle-hole, and chiral symmetries. The representation theory not only reveals why a unique topological invariant ($0, Z_2, Z$) exists for each specific symmetry class and dimension, but also shows the interplay between quantum phase transitions, topologically protected boundary modes, and topological invariants. [Preview Abstract] |
Monday, March 21, 2011 11:51AM - 12:03PM |
B35.00004: Chern Numbers Hiding in Time of Flight Images Indubala Satija, Erhai Zhao, Parag Ghosh, Noah Bray-Ali Since the experimental realization of synthetic magnetic fields in neural ultracold atoms, transport measurement such as quantized Hall conductivity remains an open challenge. Here we propose a novel and feasible scheme to measure the topological invariants, namely the chern numbers, in the time of flight images. We study both the commensurate and the incommensurate flux, with the later being the main focus here. The central concept underlying our proposal is the mapping between the chern numbers and the size of the dimerized states that emerge when the two-dimensional hopping is tuned to the highly anisotropic limit. In a uncoupled double quantum Hall system exhibiting time reversal invariance, only odd-sized dimer correlation functions are non-zero and hence encode quantized spin current. Finally, we illustrate that inspite of highly fragmented spectrum, a finite set of chern numbers are meaningful. Our results are supported by direct numerical computation of transverse conductivity. [Preview Abstract] |
Monday, March 21, 2011 12:03PM - 12:15PM |
B35.00005: Topological Nature of Phonon Hall Effect Lifa Zhang, Jie Ren, Jian-Sheng Wang, Baowen Li We provide a topological understanding on phonon Hall effect in dielectrics with Raman spin-phonon coupling. A general expression for phonon Hall conductivity is obtained in terms of the Berry curvature of band structures. We find a nonmonotonic behavior of phonon Hall conductivity as a function of magnetic field. Moreover, we observe a phase transition in phonon Hall effect, which corresponds to the sudden change of band topology, characterized by the altering of integer Chern numbers. This can be explained by touching and splitting of phonon bands. [Preview Abstract] |
Monday, March 21, 2011 12:15PM - 12:27PM |
B35.00006: Effects of Metallic Contacts on Topological Insulator Surface States Jimmy Hutasoit, Tudor Stanescu We study the effect of the coupling between a time-reversal invariant topological insulator and a metal. The coupling of the surface states to the metal is studied both numerically, using a tight-binding model, and analytically within a two-dimensional effective theory. The original surface state described by a massless Dirac fermion acquires a non-trivial spectral profile upon interaction with the metal. This results in the broadening of the surface modes and a shift in the position of the $\Gamma$- point, which may sink into the valence band at strong coupling. [Preview Abstract] |
Monday, March 21, 2011 12:27PM - 12:39PM |
B35.00007: Spin active scattering at the interface between a metal and a topological insulator Erhai Zhao, Chun Zhang, Mahmoud Lababidi We present theoretical results for the spin-active scattering and local spectrum at the interface between a metal and a three-dimensional topological band insulator. We show that there exists a critical incident angle at which complete (100\%) spin flip reflection occurs and the spin rotation angle jumps by $\pi$. We discuss the origin of this phenomena, and systematically study the dependence of spin-flip and spin-conserving scattering amplitudes on the interface transparency and metal Fermi surface parameters. The interface spectrum contains a well-defined Dirac cone in the tunneling limit, and smoothly evolves into a continuum of metal induced gap states for good contacts. We also investigate the complex band structure of Bi$_2$Se$_3$. [Preview Abstract] |
Monday, March 21, 2011 12:39PM - 12:51PM |
B35.00008: Floquet Topological Insulator in Semiconductor Quantum Wells Netanel Lindner, Gil Refael, Victor Galitski Topological phase transitions between a conventional insulator and a state of matter with topological properties have been proposed and observed in mercury telluride - cadmium telluride quantum wells. We show that a topological state can be induced in such a device, initially in the trivial phase, by irradiation with microwave frequencies, without closing the gap and crossing the phase transition. We show that the quasi-energy spectrum exhibits a single pair of helical edge states. The velocity of the edge states can be tuned by adjusting the intensity of the microwave radiation. We discuss the necessary experimental parameters for our proposal. This proposal provides an example and a proof of principle of a new non-equilibrium topological state, Floquet topological insulator, introduced in this paper. arXiv:1008.1792 [Preview Abstract] |
Monday, March 21, 2011 12:51PM - 1:03PM |
B35.00009: A study of localized states in topological insulators Kun Woo Kim, Tamar Pereg-Barnea, Gil Refael Perturbative and Semiclasscial approaches are employed to find the localized state of the toplogical insulators both on sample edges and defects in the bulk. The models used are massive Dirac with either one or two valleys. The topology is provided by the mass term which has either a momentum dependence or a different sign on the two Dirac points. A semiclasscial Hamiltonian is deduced by following a certain classical path and the Hamilton-Jacobi equation determines the dynamics. Our semiclassical results reproduce the lattice model's chiral edge modes and allow us to investigate impurity bound states. These bound states also appear in a T-matrix calculation. [Preview Abstract] |
Monday, March 21, 2011 1:03PM - 1:15PM |
B35.00010: Zero modes in the bulk of the Topological Insulators induced by disorder or dislocations David Schmeltzer The enigma of the finite conductivity which comes from the bulk of the Topological Insulators (T.I.) is solved by showing that domain walls in the T.I. bind protected zero modes. We consider two scenarios: a)-Dislocations: -We solve the massive Dirac equation (which corresponds to the T.I. in four and two dimensions) in a curved space generated by the coordinates transformation induced by a single dislocation or a single disclination. We examine the condition for the protected zero modes caused by Torsion and Curvature. b) Disorder:-We use the Keldish formalism to study the effect of disorder and interaction of the T.I. We identify an effective Non-Linear Sigma model with a Maxweell and Chern-Simon term which correspond to the different phases: regular metal, regular insulator, topological insulator and protected metals. [Preview Abstract] |
Monday, March 21, 2011 1:15PM - 1:27PM |
B35.00011: Zero energy modes in heterostructures Tudor Petrescu, Stephan Rachel, Karyn Le Hur Zero energy gapless modes have been realized in 1-dimensional domain walls of 2-dimensional systems. In the case of single- or bi-layer graphene, such a quantum wire can be realized by inverting the sign of the gap across a one dimensional interface, without time-reversal symmetry breaking. With the experimental realization of artificial graphene, previously unrealistic additional terms in the Hamiltonian such as staggered potential or artificial gauge fields can be exploited towards the same goal. We classify these terms and study the interplay of disorder effects and boundary conditions. [Preview Abstract] |
Monday, March 21, 2011 1:27PM - 1:39PM |
B35.00012: Protected Entanglement Spectrum in Disordered Topological Insulators Emil Prodan, Taylor Hughes, Andrei Bernevig The topological insulating phase is robust against disorder. However, the phase diagram of a topological insulator, more precisely the boundary between the trivial and topological phases, can be strongly reshaped by the disorder. It is therefore important to devise methods that can efficiently map the extent of the topological phase in the presence of disorder. This talk will describe two such methods and presents several applications. First, it is shown that, in the topological phase, the entanglement spectrum remains extended while in the trivial phase it becomes localized, in the presence of disorder. The localized/delocalized character of the entanglement spectrum has a clear signature in the level statistics, which can be used to efficiently map the boundary between topological and trivial phase. The second method is based on efficient real space calculations of the bulk invariants that do not involve twisted boundary conditions. In fact, it is shown that both methods involve only data encoded in the ground states of the systems. [Preview Abstract] |
Monday, March 21, 2011 1:39PM - 1:51PM |
B35.00013: Theory of Inversion Symmetric Topological Insulators Taylor Hughes, Emil Prodan, B. Andrei Bernevig We analyze translationally-invariant insulators with inversion symmetry that fall outside the current established classification of topological insulators. These insulators exhibit no edge or surface modes in the energy spectrum and hence they are not edge metals when the Fermi level is in the bulk gap. However, they do exhibit protected modes in the entanglement spectrum localized on the cut between two entangled regions. There is a direct connection between the inversion eigenvalues of the Hamiltonian band structure and the mid-gap states in the entanglement spectrum. We also analyze the linear response of these insulators and provide examples of when the inversion eigenvalues determine a non-trivial charge polarization, a quantum Hall effect, an anisotropic 3D quantum Hall effect, or a magneto-electric polarization. [Preview Abstract] |
Monday, March 21, 2011 1:51PM - 2:03PM |
B35.00014: Topological Properties of Insulators with Inversion Symmetry Ari Turner, Yi Zhang, Roger Mong, Ashvin Vishwanath There are many phases of insulators with inversion symmetry (with no other symmetry required). In particular, certain inversion parities cannot change unless there is a phase transition. I will show how to use these parities to classify phases of topological insulators and explain which combinations of these parities have physical consequences (e.g. for the magnetoelectric effect). Many of these results can be derived by pictorial arguments using the entanglement spectrum. [Preview Abstract] |
Monday, March 21, 2011 2:03PM - 2:15PM |
B35.00015: Computing topological invariants without inversion symmetry Alexey Soluyanov, David Vanderbilt We consider the problem of calculating the weak and strong topological indices in noncentrosymmetric time-reversal ($T$) invariant insulators. In 2D we use a gauge corresponding to hybrid Wannier functions that are maximally localized in one dimension. Although this gauge is not smoothly defined on the two-torus,\footnote{A. A. Soluyanov and D. Vanderbilt, arXiv:1009.1415} it respects the $T$ symmetry of the system and allows for a definition of the ${Z}_2$ invariant in terms of time-reversal polarization.\footnote{L. Fu and C. L. Kane, Phys. Rev. B {\bf 74}, 195312 (2006)} In 3D we apply the 2D approach to $T$-invariant planes. We illustrate the method with first-principles calculations on GeTe and HgTe under $[100]$ and $[111]$ strain. Our approach is different from the one suggested previously by Fukui and Hatsugai\footnote{T. Fukui and Y. Hatsugai, J. Phys. Soc. Jpn. {\bf 76}, 053702 (2007)} and should be easier to implement in {\it ab initio} code packages. Time permitting, we will also discuss methods for decomposing the band space into $T$-paired Chern subspaces, and for carrying out a general construction of a Wannier representation for ${Z}_2$ insulators. [Preview Abstract] |
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