Bulletin of the American Physical Society
APS March Meeting 2014
Volume 59, Number 1
Monday–Friday, March 3–7, 2014; Denver, Colorado
Session A43: Defects in Topological Insulators |
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Sponsoring Units: DCMP Chair: Ruihua He, Boston College Room: Mile High Ballroom 4B |
Monday, March 3, 2014 8:00AM - 8:12AM |
A43.00001: ``Holographic'' treatment of surface disorder in topological insulators Kun Woo Kim, Roger Mong, Marcel Franz, Gil Refael What is the effect of surface-only disorder on the electronic states of a 3d TI? The layers in the clean bulk parallel to surface probe the surface impurities as they hop in and out of the surface layer. A recursive treatment of the impurity effects is made possible through successive elimination of the lattice layer by layer. This leads to non-linear renormalization group flow of an effective surface impurity potential. We found an exact mapping between the recursion relation and Schrodinger equation along the layers, therefore the modified self energy due to surface impurity could be simply obtained from the transfer matrix method. As a concrete example of 2d topological insulator, we found the exact expression of on-layer self energy for a clean system and an asymptotic expression that captures a general behavior of layers deep in the bulk. [Preview Abstract] |
Monday, March 3, 2014 8:12AM - 8:24AM |
A43.00002: Absence of levitation and annihilation at the topological phase transition of a disordered one-dimensional model in class AIII Ian Mondragon-Shem, Juntao Song, Taylor L Hughes, Emil Prodan We study the disorder-induced topological phase transition of a one-dimensional model belonging to class AIII of the Altland-Zirnbauer classification of fermions. To characterize the topological state, we derive a covariant real-space representation of the integer invariant. Using this invariant, we show that the system remains topological even after all the single particle states of the system become localized and the energy spectrum becomes gapless. For a critical disorder strength which we compute analytically, there emerges a delocalized state at zero energy where the topological invariant changes value and the nontrivial ground state transforms into a trivial one. This type of topological phase transition is fundamentally different from the levitation and annihilation paradigm that is found in higher-dimensional systems e.g. the quantum Hall state. In order to understand this type of phase transition, we map the system to a spin-1/2 model which provides an insightful real-space picture of the underlying physics near the critical point. EP and JTS were supported by U.S. NSF grants DMS 1066045, DMR-1056168, NSFC grant 11204065 and RFDPHEC grant. A2013205168. TLH and IM-S were supported by ONR Grant No. N0014-12-1-0935. [Preview Abstract] |
Monday, March 3, 2014 8:24AM - 8:36AM |
A43.00003: Bulk-Defect Correspondence in Particle-Hole Symmetric Insulators and Semimetals Andreas Ruegg, Fernando de Juan, Dung-Hai Lee Lattices with a basis can host crystallographic defects which share the same topological charge (e.g. the Burgers vector $\vec b$ of a dislocation) but differ in their microscopic structure of the core. We demonstrate that in insulators with particle-hole symmetry and an odd number of orbitals per site, the microscopic details drastically affect the electronic structure: modifications can create or annihilate non-trivial bound states with an associated fractional charge. We show that this observation is related to the behavior of end modes of a dimerized chain and discuss how the end or defect states are predicted from topological invariants in these more complicated cases. Furthermore, using explicit examples on the honeycomb lattice, we explain how bound states in vacancies, dislocations and disclinations are related to each other and to edge modes and how similar features arise in nodal semimetals such as graphene. [Preview Abstract] |
Monday, March 3, 2014 8:36AM - 8:48AM |
A43.00004: Topological Invariants for Disordered Systems: Analysis and Computation Juntao Song, Emil Prodan Non-Commutative Geometry enables one to formulate topological invariants for aperiodic systems, in particular, for Disordered Topological Insulator from different symmetry classes with or without magnetic fields. Examples of such invariants, to be discussed in this talk, are the non-commutative Chern numbers, non-commutative winding numbers, electric polarization of systems from certain symmetry classes and the magneto-electric response of strong topological insulators. We show that these non-commutative formulas provide the basis for some of the most efficient and accurate algorithms for computing topological invariants in the presence of strong disorder. Using explicit calculations, we demonstrated that, in many instances, we obtain quantization of the invariants with machine precision, even when the Fermi level is in dense localized spectrum (i.e. not in spectral gap). Phase diagrams computed with these algorithms will be presented, for models from various symmetry classes. Acknowledgement: This research was supported from U.S. NSF grants DMS-1066045, DMR-1056168 and DMS-1160962 and NSFC grant 11204065 and RFDPHEC grant. A2013205168. [Preview Abstract] |
Monday, March 3, 2014 8:48AM - 9:00AM |
A43.00005: Disorder induced Floquet Topological Insulators Paraj Bhattacharjee, Netanel Lindner, Mikael Rechtsman, Gil Refael We investigate the possibility of realizing a disorder induced topological state in two dimensional periodically driven systems. This phenomenon is akin to the topological Anderson insulator (TAI) in equilibrium systems. We focus on graphene band structures, where in the presence of the driving electromagnetic field, but in the absence of disorder, the system starts off in a trivial state due to the presence of a sublattice potential. We show that by adding on-site disorder a topological state is induced in this system. We numerically compute the average Bott index (the analog of the Chern number for disordered systems) to show that starting from a trivial phase, topological behavior can be observed at finite disorder strength. In the topological phase, we detect chiral edge states by a numerical time evolution of wavepackets at the edge of the system. We propose an experimental set-up in photonic lattices to observe this phenomenon. [Preview Abstract] |
Monday, March 3, 2014 9:00AM - 9:12AM |
A43.00006: Soliton Defects in One-dimensional Topological Three-band Hamiltonian Gyungchoon Go, Kyeong Tae Kang, Jung Hoon Han Defect formation in the one-dimensional topological three-band model is examined within both lattice and continuum models. Classic results of Jackiw-Rebbi and Rice-Mele for the soliton charge is generalized to the three-band model. The presence of the central flat band in the three-band model makes the soliton charge as a function of energy behave in a qualitatively different way from the two-band Dirac model case. Quantum field-theoretical calculation of Goldstone and Wilczek is also generalized to the three-band model to obtain the soliton charge. Diamond-chain lattice is shown to be an ideal structure to host a topological three-band structure. [Preview Abstract] |
Monday, March 3, 2014 9:12AM - 9:24AM |
A43.00007: Phases of a one dimensional chain of topological twist defects Abhishek Roy, Jeffrey Teo, Xiao Chen A topological twist defect acts on a system containing abelian anyons by permuting anyon labels in a manner that preserves their braiding properties. We investigate a one dimensional chain of twist defects. The Hamiltonian consists of Wilson loop operators, each enclosing a pair of neighbouring defects. We explore both gapped and gapless phases. For the former, we use anyon pumping to classify the ground states. For the latter, we present numerical evidence for the central charge for various values of the coupling constants. We extend the above results from twofold defects (which are similar to $Z_k$ parafermions) to threefold defects introduced by us earlier in an exactly solvable lattice model [1]. \\[4pt] [1] Unconventional Fusion and Braiding of Topological Defects in a Lattice Model. Jeffrey C.Y. Teo, Abhishek Roy, Xiao Chen arXiv:1306.1538 [Preview Abstract] |
Monday, March 3, 2014 9:24AM - 9:36AM |
A43.00008: Quantum dot as a magnetic impurity in a helical edge: a source of resistance weakly dependent on temperature Jukka Vayrynen, Moshe Goldstein, Yuval Gefen, Leonid Glazman The bulk of a doped two-dimensional topological insulator may accommodate spontaneously-formed quantum dots (charge puddles). We show that a Coulomb blockaded quantum dot hosting an odd number of electrons acts as a magnetic impurity effective in backscattering of electron moving along the helical edge. The exchange interaction between the dot and the edge, derived from a microscopic Hamiltonian, is anisotropic in general. The exchange anisotropy makes the dot spin an efficient backscatterer. The resulting negative correction to the helical edge conductance may exhibit a broad plateau in its temperature dependence. Being averaged over the Fermi level position, the correction to the ideal conductance becomes logarithmic in temperature. The effect of external magnetic field on transport is also discussed, and a connection to recent experiments is made. [Preview Abstract] |
Monday, March 3, 2014 9:36AM - 9:48AM |
A43.00009: Weak antilocalisation in topological insulators Xintao Bi, Ewelina Hankiewicz, Dimitrie Culcer Topological insulators (TI) have changed our understanding of insulating behaviour. They are insulators in the bulk but conducting along their surfaces due to spin-orbit interaction. Much of the recent research focuses on overcoming the \textit{transport bottleneck}, the fact that surface state transport is overwhelmed by bulk transport stemming from unintentional doping. The key to overcoming this bottleneck is identifying unambiguous signatures of surface state transport. This talk will discuss one such signature, which is manifest in the coherent backscattering of electrons. Due to strong spin-orbit coupling in TI one expects to observe weak antilocalisation rather than weak localisation, meaning that coherent backscattering increases the electrical conductivity. The features of this effect, however, are rather subtle, because in TI the impurities have strong spin-orbit coupling as well. I will show that spin-orbit coupled impurities introduce an additional time scale, which is expected to be shorter than the dephasing time, and the resulting conductivity has a \textit{logarithmic dependence} on the carrier density, a behaviour hitherto unknown in 2D electron systems. The result we predict is observable experimentally and would provide a smoking gun test of surface transport. [Preview Abstract] |
Monday, March 3, 2014 9:48AM - 10:00AM |
A43.00010: Anderson Localization in Disordered Systems with Competing Channels Hongyi Xie In a variety of physical contexts, for example, exciton-polaritons and field-effect transistors based on bi- or trilayer graphene, the situation arises that two or more propagating channels with different transport properties are coupled together and modifying each other's properties. One could ask what happens to the localization properties when a less localized lattice is coupled to a more localized one? Will the less localized one dominate the localization of the system or the more localized? The qualitative answer to this question depends on the dimensionality of the system. Correspondingly, we exactly solved the Anderson models on a two-leg ladder and on a two-layer Bethe lattice. In one dimension, the localization lengths of two coupled chains are of the order of the localization length of the more localized chain under resonance conditions. On the Bethe lattices, the less disordered lattice is not affected much by the more disordered lattice in the presence of coupling. These trends are believed to be persistent in high dimensions. [Preview Abstract] |
Monday, March 3, 2014 10:00AM - 10:12AM |
A43.00011: The Even and Odd Chern Numbers for Disordered Topological Insulators Emil Prodan The $K^0(M)$ group classifies the projectors and the $K^{-1}(M)$ classifies the unitaries defined over a manifold $M$. The even and the odd Chern numbers assign integers to the topological classes from $K^0(M)$ and $K^{-1}(M)$, respectively. If $M$ is the Brillouin torus in various dimensions, the even and the odd Chern numbers become the classifying invariants for the A and AIII symmetry classes of Topological Insulators, respectively. For arbitrary (even/odd) dimension, we recently showed that these two invariants can be defined in the presence of strong disorder. Inspired by the Non-Commutative Geometry program, we were able to demonstrate that both invariants remain quantized and non-fluctuating as long as the Fermi level resides in a region of localized spectrum. The most direct consequence of this result is that {\it all} topological phases from A and AIII symmetry classes are surrounded by phase-boundaries harboring extended states. Summary of these results and phase diagrams of various disordered models from the A and AIII symmetry classes will be presented. [Preview Abstract] |
Monday, March 3, 2014 10:12AM - 10:24AM |
A43.00012: Quantum dot in Topological Insulator Nanofilm: energy spectra and optical transitions Thakshila Herath, Prabath Hewageegana, Vadym Apalkov We introduce a quantum dot in topological insulator nanofilm as a bump at a surface of nanofilm. Such 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 two types of states, corresponding to ``conduction'' and ``valence'' bands of topological insulator nanofilm. We study the energy and optical (intraband and interband) spectra of such defined quantum dots and their dependence on the dot parameters. Both intraband and interband optical transitions have the same selection rules. While the interband absorption spectra have multi-peak structure, the intraband spectra has one strong peak and a few weak high frequency satellites. [Preview Abstract] |
Monday, March 3, 2014 10:24AM - 10:36AM |
A43.00013: Dephasing effect on backscattering of helical surface states in 3D topological insulators Haiwen Liu, Hua Jiang, Qing-feng Sun, X.C. Xie We analyze the dephasing effect on the backscattering behavior of the helical surface states in 3D topological insulators. Considering the dilute non-magnetic impurities condition, we calculate the second-order scattering amplitude and the backscattering cross-section for both short-range and long-range scattering potentials. Our results indicate the combination effect of dephasing and scattering can cause backscattering in the helical SS, although one of them can not alone. In specific, the long-range Coulomb potential can cause extremely large backscattering when energy is close to the Dirac point. This large backscattering can lead to the anomalous ``gap-like'' features observed in recent experiments [$Nat. Phys. {\bf7}, 840 (2011)$]. [Preview Abstract] |
Monday, March 3, 2014 10:36AM - 10:48AM |
A43.00014: ABSTRACT WITHDRAWN |
Monday, March 3, 2014 10:48AM - 11:00AM |
A43.00015: Magnetic interaction and magnetic fluctuations in topological insulators with ordered and disordered magnetic adatoms Maia G. Vergniory, Levan Chotorlishvili, Arthur Ernst, Vitali Dugaev, Andreas Komnik, Mijail Otrokov, Evgueni Chulkov, Jamal Beradkar Using a first-principles Green's function approach we study magnetic properties of the magnetic binary topological insulators Bi$_2$Se$_3$, Bi$_2$Te$_23$ and Sb$_2$Te$_3$ doped with 3d transition metals. We analyze the magnetic phase for each dopant, the exchange interaction, the Curie temperature and the Bloch spectral function. Furthermore, we observe that the interaction of magnons with surface electrons essentially renormalizes the electron energy spectrum. The renormalized spectrum is nonlinear and can be characterized by a negative effective mass of electrons and holes for any k point different from 0. The electron velocity near the Dirac point depends on the electron-magnon coupling. [Preview Abstract] |
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