Bulletin of the American Physical Society
APS March Meeting 2013
Volume 58, Number 1
Monday–Friday, March 18–22, 2013; Baltimore, Maryland
Session W8: Topological Insulators: Theory III |
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Sponsoring Units: DCMP Chair: Maxim Dzero, Kent State University Room: 307 |
Thursday, March 21, 2013 2:30PM - 2:42PM |
W8.00001: Modifying properties of Chern insulators by time dependent perturbations Benjamin M. Fregoso, Victor Galitski We study the quantum dynamics of topological Chern insulators in the presence a time dependent perturbation. We show that and under proper drive conditions they can be turned in to trivial insulators or insulators with a higher Chern number. We discuss signatures of such states in the context of non-adiabatic Thouless pumping. We argue that this provides a way to tune the properties of topological systems. [Preview Abstract] |
Thursday, March 21, 2013 2:42PM - 2:54PM |
W8.00002: Band Splitting by Period Potential and Resultant Topological Quantum Numbers Liang Sun, Kun Yang When a Chern band is split into two subbands by breaking lattice translation symmetry that results in a doubled unit cell, the subbands have a set of Chern numbers whose sum has to be the same as the origin band. This, however, does not uniquely determine the Chern numbers of individual subbands. We show how the subbands Chern numbers are related to the structure of the original band, as well as the details of the periodic perturbation. We also generalize this one-to-two band splitting case to one-to-many splitting, as well as the case with time-reversal symmetry, where the Chern number is zero but the bands can carry Z2 topological quantum numbers. [Preview Abstract] |
Thursday, March 21, 2013 2:54PM - 3:06PM |
W8.00003: Using topological entanglement entropy to identify low energy effective field theories of fractional Chern Insulators Bryan Clark, Andrei Bernevig The physics of quantum interacting many-body systems allow for a wide variety of phases, whose properties are governed by low energy field theories. In this talk, we write down prototypical parton Chern insulating wave-functions with chern numbers 1,2,3, and 5 and determine their corresponding low energy effective field theory by computing their topological entanglement entropy. We also discuss non-universal aspects of the entanglement entropy including the effect of changing the mass on the corner terms and the slope of the area law. [Preview Abstract] |
Thursday, March 21, 2013 3:06PM - 3:18PM |
W8.00004: Adiabatic continuity between Hofstadter and Chern insulator states Yinghai Wu, Jainendra Jain, Kai Sun We show that the topologically nontrivial bands of Chern insulators are adiabatic cousins of the Landau bands of Hofstadter lattices. We demonstrate adiabatic connection also between several familiar fractional quantum Hall states on Hofstadter lattices and the fractional Chern insulator states in partially filled Chern bands, which implies that they are in fact different manifestations of the same phase. This adiabatic path provides a way of generating many more fractional Chern insulator states and helps clarify that nonuniformity in the distribution of the Berry curvature is responsible for weakening or altogether destroying fractional topological states. [Preview Abstract] |
Thursday, March 21, 2013 3:18PM - 3:30PM |
W8.00005: Entanglement Entropy at Generalized RK Points of Quantum Dimer Models Alexander Selem, Christopher Herdman, K. Birgitta Whaley We study the $n=2$ R\' enyi entanglement entropy of the triangular quantum dimer model via Monte Carlo sampling of Rokhsar-Kivelson(RK)-like ground state wavefunctions. Using the construction proposed by Kitaev and Preskill [Phys. Rev. Lett. 96, 110404 (2006)] and an adaptation of the Monte Carlo algorithm described in [Phys. Rev. Lett. 104, 157201 (2010)], we compute the topological entanglement entropy (TEE) at the RK point $\gamma = (1.001 \pm .003) \ln 2$ confirming earlier results. Additionally, we compute the TEE of the ground state of a generalized RK-like Hamiltonian and demonstrate the universality of TEE over a wide range of parameter values within a topologically ordered phase approaching a quantum phase transition. For systems sizes that are accessible numerically, we find that the quantization of TEE depends sensitively on correlations. We characterize corner contributions to the entanglement entropy and show that these are well described by shifts proportional to the number and types of corners in the bipartition. [Preview Abstract] |
Thursday, March 21, 2013 3:30PM - 3:42PM |
W8.00006: Thermal Instability of Edge States in a 1D Topological Insulator Oscar Viyuela, Angel Rivas, Miguel Angel Martin-Delgado The stability of topological phases of matter, also known as topological orders, against thermal noise has provided several surprising results in the context of topological codes used in topological quantum information. However, very little is known about the behavior of a topological insulator (TI) subjected to the disturbing thermal effect of its surrounding environment. This is of great relevance if we want to address key questions such as the robustness of TIs to thermal noise, existence of thermalization processes, use of TIs as platforms for quantum computation, etc. In this work, we have studied the dynamical thermal effects on the protected edge states of a TI when it is considered as an open quantum system in interaction with a noisy environment at a certain temperature $T$. Let us recall that stable edge states are a defining signature of topological insulators. Outstandingly, we find that the usual protection of edge states against quantum perturbations and randomness is lost in the case of thermal effects, despite the fermion-boson interaction with the thermal environment respects chiral symmetry, which is the symmetry responsible for the protection (robustness) of the edge states in this TI. We are able to compute decay rates for practical implementations. PRB (2012) [Preview Abstract] |
Thursday, March 21, 2013 3:42PM - 3:54PM |
W8.00007: Torsional Response, bulk-boundary correspondence, and Viscosity in Topological Insulators Taylor Hughes, Robert Leigh, Onkar Parrikar We discuss the relationship between torsion and visco-elastic response of 2D time-reversal breaking topological insulators. We connect the bulk topological response to a new anomalies in the momentum current of the chiral edge theory that we have determined. We also discuss the implications for spectral flow and the emergence of a chiral-gravity type response theory. [Preview Abstract] |
Thursday, March 21, 2013 3:54PM - 4:06PM |
W8.00008: Effect of static charge fluctuations on the conduction along the edge of two-dimensional topological insulator Jukka Vayrynen, Moshe Goldstein, Leonid Glazman Static charge disorder may create electron puddles in the bulk of a material which nominally is in the insulating state. A single puddle -- quantum dot -- coupled to the helical edge of a two-dimensional topological insulator enhances the electron backscattering within the edge. The backscattering rate increases with the electron dwelling time in the dot. While remaining inelastic, the backscattering off a dot may be far more effective than the proposed earlier inelastic processes involving a local scatterer with no internal structure. We find the temperature dependence of the dot-induced correction to the universal conductance of the edge. In addition to the single-dot effect, we calculate the classical temperature-independent conductance correction caused by a weakly conducting bulk. We use our theory to assess the effect of static charge fluctuations in a heterostructure on the edge electron transport in a two-dimensional topological insulator. [Preview Abstract] |
Thursday, March 21, 2013 4:06PM - 4:18PM |
W8.00009: Backscattering Between Helical Edge States via Dynamic Nuclear Polarization Adrian Del Maestro, Timo Hyart, Bernd Rosenow We describe how the non-equilibrium spin polarization of one dimensional helical edge states at the boundary of a two dimensional topological insulator can dynamically induce a polarization of nuclei via the hyperfine interaction. When combined with a spatially inhomogeneous Rashba coupling, the resulting steady state polarization of the nuclei produces backscattering between the topologically protected edge states leading to a reduction in the conductance which persists to zero temperature. We study these effects in both short and long edges, uncovering deviations from Ohmic transport at finite temperature and a current noise spectrum which may hold the fingerprints for experimental verification of the backscattering mechanism. [Preview Abstract] |
Thursday, March 21, 2013 4:18PM - 4:30PM |
W8.00010: Symmetries in the entanglement spectrum and topological phases protected by spatial discrete symmetries Po-Yao Chang, Shinsei Ryu We study topological phases protected by spacial (non-local) symmetries using the entanglement spectrum. Exploiting the structure of the entanglement Hamiltonian that can be formulated as the supersymmetric quantum mechanics, we study how a spacial symmetry constrains the entanglement spectrum when the bipartitioning is consistent with the spatial symmetry. Specific examples we took a look at include a reflection symmetric topological insulator composed of two Chern insulators with opposite chiralities in one and two spacial dimensions. For both topological insulators, the edge states in the physical energy spectrum can be gapped while the entangling boundary remains gapless. [Preview Abstract] |
Thursday, March 21, 2013 4:30PM - 4:42PM |
W8.00011: Interfacial Protection of Topological Surface States in Ultrathin Sb Films Guang Bian, Xiaoxiong Wang, Yang Liu, Thomas Miller, Tai-Chang Chiang Spin-polarized gapless surface states in topological insulators form chiral Dirac cones. When such materials are reduced to thin films, the Dirac states on the two faces of the film can overlap and couple by quantum tunneling, resulting in a thickness-dependent insulating gap at the Dirac point. Calculations for a freestanding Sb film with a thickness of four atomic bilayers yield a gap of 36 meV, yet angle-resolved photoemission measurements of a film grown on Si(111) reveal no gap formation. The surprisingly robust Dirac cone is explained by calculations in terms of interfacial interaction. Our work suggests that quantum tunneling, an intrinsic property dependent on the film thickness, and substrate bonding, an extrinsic factor amenable to interfacial engineering, can be effectively manipulated to achieve desired electronic and spintronic properties of topological thin films. [Preview Abstract] |
Thursday, March 21, 2013 4:42PM - 4:54PM |
W8.00012: ABSTRACT WITHDRAWN |
Thursday, March 21, 2013 4:54PM - 5:06PM |
W8.00013: Controlling topological insulating phases by tuning the coupling strength of Dirac fermions in chalcogenide ternary compounds Jeongwoo Kim, Jinwoong Kim, Seung-Hoon Jhi Chalcogenide ternary compounds such as Ge$_{2}$Sb$_{2}$Te$_{5}$ are considered as superlattice of topological insulating layers and band insulating layers. Using first-principles methods and a model Hamiltonian, we study the topological phases of the chalcogen compounds arising from the interactions of Dirac fermionic states existing at the interfaces between the topological insulating and band insulating layers. We particularly investigate the interactions of Dirac fermions upon varying the thickness of band insulating layers or upon introducing magnetic impurities in the layers. We observe a jump of Dirac cones from one time-reversal invariant momentum to another when the thickness is changed. We also discuss the degree of freedom in the spin helicity of the Dirac fermions and how it limits the topological phases. [Preview Abstract] |
Thursday, March 21, 2013 5:06PM - 5:18PM |
W8.00014: The space group classification of topological band insulators Vladimir Juricic, Robert-Jan Slager, Andrej Mesaros, Jan Zaanen The existing classification of topological band insulators(TBIs) departs from time-reversal symmetry, but the role of the crystal symmetries in the physics of these topological states remained elusive. I will discuss the classification of TBIs protected not only by time-reversal, but also by space group symmetries [1]. I find three broad classes of topological states: (a) $\Gamma$-states robust against general time-reversal invariant perturbations; (b) Translationally-active states protected from elastic scattering, but susceptible to topological crystalline disorder; (c) Valley topological insulators sensitive to the effects of non-topological and crystalline disorder. These three classes give rise to 18 different two-dimensional, and, at least 70 three-dimensional TBIs. I will show how some of these topological states can be realized in two dimensions when tight-binding M-B model, originally introduced for HgTe quantum wells, is generalized to include longer-range hoppings. Finally, experimental implications of our classification scheme with an emphasis on topological states in Sn-based materials will be discussed. \\[4pt] [1] R.-J. Slager, A. Mesaros, V. Juricic, and J. Zaanen, arXiv:1209.2610. [Preview Abstract] |
Thursday, March 21, 2013 5:18PM - 5:30PM |
W8.00015: Why is the bulk resistivity of topological insulators so small? Tianran Chen, Brian Skinner, Boris Shklovskii As-grown topological insulators (TIs) are typically heavily-doped $n$-type crystals. Compensation by acceptors is used to move the Fermi level to the middle of the band gap, but even then TIs have a frustratingly small bulk resistivity. We show that this small resistivity is the result of band bending by poorly screened fluctuations in the random Coulomb potential. Using numerical simulations of a completely compensated TI, we find that the bulk resistivity has an activation energy of just $0.15$ times the band gap, in good agreement with experimental data. At lower temperatures activated transport crosses over to variable range hopping with a relatively large localization length. \textbf{Reference:} B. Skinner, T. Chen, B. I. Shklovskii, \textit{Phys. Rev. Lett.} \textbf{109}, 176801 (2012). [Preview Abstract] |
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