Bulletin of the American Physical Society
APS March Meeting 2017
Volume 62, Number 4
Monday–Friday, March 13–17, 2017; New Orleans, Louisiana
Session V37b: Focus Session Topological Materials: Theory and Modeling |
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Sponsoring Units: DMP Chair: Stephen Eltinge, Yale University Room: 384 |
Thursday, March 16, 2017 2:30PM - 2:42PM |
V37b.00001: First principles calculations of the two dimensional topological insulator stanene on substrates Stephen Eltinge, Minjung Kim, Stephen Albright, Rui Peng, Ke Zou, Fred Walker, Charles Ahn, Sohrab Ismail-Beigi Topological insulators are a class of materials under continued intense investigation due to their potentially robust current carrying surface or edge states. Stanene, the two dimensional form of tin, has been predicted to be a 2D topological insulator due to its large spin-orbit interaction. There exist a number of first principles calculations of stanene both as an isolated layer as well as on a substrate, but the only successful experimental report involves the growth of stanene on Bi$_2$Te$_3$, and does not show signatures of topological behavior.* In this work, we present first-principles density functional theory calculations of stanene on a Bi$_2$Te$_3$ substrate and report on the binding, interfacial structure, and role of various decorating groups ({\it i.e.}, atoms or molecules binding to stanene). In addition, we will describe the possible benefits of using wide gap insulators such as CdTe as substrates.\\ $^*$F. Zhu, W. Chen, Y. Xu, C. Gao, D. Guan, C. Liu, D. Qian, S.-C. Zhang, and J. Jia, {\it Nat.\ Mater.}\ (2015). [Preview Abstract] |
Thursday, March 16, 2017 2:42PM - 2:54PM |
V37b.00002: Topological Quantum Chemistry II: Predicting topological materials in layered systems Jennifer Cano, Barry Bradlyn, Zhijun Wang, M. G. Vergniory, Luis Elcoro, M. I. Aroyo, Claudia Felser, B. Andrei Bernevig We continue to develop a theory that describes the connectivity of a band structure based on the real space positions of atoms in the material and their relevant orbitals. We develop criteria to determine when a topological band structure is possible and identify several promising crystal structures to search for topological (or topological crystalline) materials. We then apply this result to layered systems, i.e., stacked layers of hexagonal (graphene) or square lattices and generalizations and show which orbitals need to be at the Fermi level to yield a topological insulator. Using this information, we predict candidate topological materials. [Preview Abstract] |
Thursday, March 16, 2017 2:54PM - 3:06PM |
V37b.00003: Topological Quantum Chemistry III: Topological data mining based on band connectivity Maia Vergniory, Barry Bradlyn, Jennifer Cano, Zhijun Wang, Luis Elcoro, Mois Aroyo, Claudia Felser, Bogdan Andrei Bernevig In this talk I will present the theory and implementation to calculate and tabulate the band connectivity for every orbital of all elements that can appear in materials database of the 230 space groups and that can sit at every Wyckoff position allowed by that group. Using this tables we can predict all the topological semimetals and topological insulators (including time reversal, symmorphic and non symmorphic) that we can find in any database. [Preview Abstract] |
Thursday, March 16, 2017 3:06PM - 3:18PM |
V37b.00004: Band structure engineering by disorder at a topological insulator surface Yishuai Xu, Janet Chiu, Lin Miao, Haowei He, Zhanybek Alpichshev, Aharon Kapitulnik, Rudro R. Biswas, L. Andrew Wray Three-dimensional topological insulators (TI) are bulk insulators with Z2 topological order that give rise to Dirac surface states. These states are well protected against localization from perturbations that do not break time reversal symmetry, such as lattice disorder. However, recent studies show that even without localization, lattice disorder can change electronic states near the Dirac point dramatically, making ring-shaped resonance states near defects. I will talk about new results in which we have compared the form of these defects seen by STM with modeling results for randomly distributed scalar potential defects at a TI surface. We find that at typical defect densities for M2X3 TIs, coherent propagation of electrons between defect related resonance states can give rise to an emergent electron gas that supports diffusive electrical transport in a narrow range of energies near the Dirac point. [Preview Abstract] |
Thursday, March 16, 2017 3:18PM - 3:30PM |
V37b.00005: Triangular Quantum Loop Topography for Machine Learning Yi Zhang, Eun-Ah Kim Despite rapidly growing interest in harnessing machine learning in the study of quantum many-body systems there has been little success in training neural networks to identify topological phases. The key challenge is in efficiently extracting essential information from the many-body Hamiltonian or wave function and turning the information into an image that can be fed into a neural network. When targeting topological phases, this task becomes particularly challenging as topological phases are defined in terms of non-local properties. Here we introduce triangular quantum loop (TQL) topography: a procedure of constructing a multi-dimensional image from the "sample" Hamiltonian or wave function using two-point functions that form triangles. Feeding the TQL topography to a fully-connected neural network with a single hidden layer, we demonstrate that the architecture can be effectively trained to distinguish Chern insulator and fractional Chern insulator from trivial insulators with high fidelity. Given the versatility of the TQL topography procedure that can handle different lattice geometries, disorder, interaction and even degeneracy our work paves the route towards powerful applications of machine learning in the study of topological quantum matters. Reference: arXiv:1611.01518. [Preview Abstract] |
Thursday, March 16, 2017 3:30PM - 3:42PM |
V37b.00006: Role of dissipation in realistic Majorana nanowires Chunxiao Liu We carry out a realistic simulation of Majorana nanowires in order to quantitatively (or at least semiquantitatively) understand the latest high quality experimental data, and in the process, develop a comprehensive picture for what physical mechanisms may be operational in realistic nanowires leading to the discrepancies between the minimal theory and the experimental observations (e.g. weakness of the Majorana conductance peak, breaking of particle-hole symmetry). Our focus is on understanding specific intriguing features in the data, and our goal is to establish matters of principle controlling the physics of the best possible nanowires available in current experiments. Based on our current work, we identify finite dissipation, finite temperature, multisubband effects, and the nature of the finite barrier at the tunnel junction as the four most important physical mechanisms leading to the discrepancies. Our theoretical results including these realistic effects agree well with the best available experimental data in ballistic nanowires. [Preview Abstract] |
Thursday, March 16, 2017 3:42PM - 3:54PM |
V37b.00007: Construction and classification of fermionic symmetry protected topological phases in 3D Zhengcheng Gu, Qingrui Wang Symmetry protected topological phases(SPT) become a fascinating subjects in recent condensed matter research. In this talk, I will discuss how to construct and classify SPT phases in interacting fermion systems. In particular, I will make use of a general group supercohomology theory to construct and classify fermionic SPT phases in 3D. [Preview Abstract] |
Thursday, March 16, 2017 3:54PM - 4:06PM |
V37b.00008: Model Hamiltonian and Time Reversal Breaking Topological Phases in Anti-Ferromagnetic half-Heusler Materials Jiabin Yu, Chao-Xing Liu, Binghai Yan We proposed 4-band and 6-band $\mathbf{k\cdot p}$ models for half-Heusler materials with anti-ferromagnetism propagated along $(\raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} \thinspace ,\thinspace \raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} ,\thinspace \raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} \thinspace )$. Dirac semimetal phase was found in 4-band model protected by inversion symmetry and the combination of half-translation and time reversal symmetry $\hat{S}$. 4-band model also gives rise to Weyl semimetal, Type-A triple point phase (if $C_{3v}$ symmetries exist) and topological mirror insulating phase (if mirror or glide symmetry exists). In 6-band model, we found anti-ferromagnetic topological insulating phase protected by $\hat{S}$ resulted from band inversion between $\mathrm{\Gamma }_{6}$ and $\mathrm{\Gamma }_{8}$ bands. [Preview Abstract] |
Thursday, March 16, 2017 4:06PM - 4:18PM |
V37b.00009: Transition of a three-dimensional $Z_N$ topologically ordered phase to a trivial phase Ching-Yu Huang, Tzu-Chieh Wei Topologically ordered quantum systems have robust physical properties, such as quasiparticle statistics and ground-state degeneracy, which do not depend on the microscopic details of the Hamiltonian. We consider a three-dimensional $Z_N$ topological phase under a string tension $g$. First we calculate the modular matrices S and T using tensor network methods and these matrices can serve as order parameters to determine the critical string tension $g_c$. The obtained transition agrees with results from a mapping to a three-dimensional classical N-state Potts model. [Preview Abstract] |
Thursday, March 16, 2017 4:18PM - 4:30PM |
V37b.00010: Anatomy of Topological Surface States: Exact Solutions from Destructive Interference on Frustrated Lattices Flore Kunst, Maximilian Trescher, Emil Bergholtz The hallmark of topological phases is their robust surface whose intriguing properties - such as the one-way transport on the chiral edge of a Chern insulator and the sudden disappearance of surface states forming open Fermi arcs on the surface of Weyl semimetals - are impossible to realize on the surface alone. Yet, despite the glaring simplicity of non-interacting topological bulk Hamiltonians and their concomitant energy spectrum, the detailed study of the corresponding surface states has essentially been restricted to numerical simulation. In this presentation, I will show that exact analytical solutions of both topological and trivial surface states can be obtained for generic tight-binding models on a large class of geometrically frustrated lattices in any dimension. I illustrate our findings by introducing two simple examples. Firstly, I will derive exact chiral Chern insulator edge states on the Kagom\'e lattice. Next, I expand the method by one dimension, which leads to the derivation of the Fermi arc solution for a Weyl semimetal model. [Preview Abstract] |
Thursday, March 16, 2017 4:30PM - 4:42PM |
V37b.00011: Topological phase transition in metallic single-wall carbon nanotube induced by magnetic field Rin Okuyama, Wataru Izumida, Mikio Eto The single-wall carbon nanotube (SWNT) can be regarded as a one-dimensional topological insulator owing to the sublattice symmetry for $A$ and $B$ lattice sites [1]. It is characterized by a $\mathbb{Z}$ topological invariant, winding number, in both the absence (class BDI) and presence (AIII) of magnetic field. We theoretically study the topological phase transition in a metallic SWNT, in which a small energy gap is opened by the mixing between $\sigma$ and $\pi$ orbitals owing to a finite curvature of the tube surface and closed by applying a magnetic field $B=B^*$ parallel to the tube axis [2]. We demonstrate discontinuous changes in the winding number at $B^*$, 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 length $\sim$ 1 $\mu$m, using a 1D lattice model to effectively describe the mixing between $\sigma$ and $\pi$ orbitals and spin-orbit interaction [3]. --- [1] W. Izumida, R. Okuyama et al., Phys. Rev. B 93, 195442 (2016). [2] R. Okuyama, W. Izumida, and M. Eto, arXiv:1610.05034. [3] W. Izumida et al., J. Phys. Soc. Jpn 78, 074707 (2009). [Preview Abstract] |
Thursday, March 16, 2017 4:42PM - 4:54PM |
V37b.00012: Rhombohedral Sb$_{\mathrm{2}}$Se$_{\mathrm{3}}$ as an intrinsic topological insulator due to strong van der Waals inter-layer coupling Guohua Cao, Huijun Liu, Zhenyu Zhang Topological insulators are a new class of quantum materials, which have insulating energy gaps in bulk form, but exhibit robust gapless surface states. It was theoretically predicted and experimentally confirmed that the binary tetradymites Bi$_{\mathrm{2}}$Te$_{\mathrm{3}}$, Bi$_{\mathrm{2}}$Se$_{\mathrm{3}}$, and Sb$_{\mathrm{2}}$Te$_{\mathrm{3}}$ are three-dimensional topological insulators. In this talk, we demonstrate by first-principles approach that the prevailingly believed trivial system of Sb$_{\mathrm{2}}$Se$_{\mathrm{3}}$ with relatively weaker spin-orbital coupling, is actually also a topological insulator, as characterized by its topologically protected surface states and the $Z_{\mathrm{2}}$ invariant. The underlying reason is the ubiquitous van der Waals interaction between quintuple layers. We also generalize our considerations to several related systems in an attempt to draw generic guiding principles. [Preview Abstract] |
Thursday, March 16, 2017 4:54PM - 5:06PM |
V37b.00013: Protected Zero Energy States in Quasicrystals Ezra Day-Roberts, Rafael Fernandes, Alex Kamenev Several two-dimensional bipartite quasicrystals display a macroscopically large number of zero-energy states (ZES) in their density of states. Although the existence and even the precise number of ZES are known, their origin remains debated. Here we argue that these ZES arise from the topology of the lattice -- in particular, from the intrinsic local mismatch between the two sublattices that form the bipartite quasicrystal. While in the kite-and-dart lattice there is no difference between local and global mismatch, the rhombus Penrose lattice self-organizes in local domains with different signs of the sublattice mismatch. We construct a theoretical framework that demonstrate the equivalence between the total local mismatch and the ZES, and discuss the robustness of ZES and their possible experimental manifestations. [Preview Abstract] |
Thursday, March 16, 2017 5:06PM - 5:18PM |
V37b.00014: Anderson Localization from the Berry-Curvature Interchange in Quantum Anomalous Hall Systems Yulei Han, Zhenhua Qiao In this talk, we theoretically investigate the localization mechanism of the quantum anomalous Hall effect (QAHE) in the presence of spin-flip disorders. We show that the QAHE stays quantized at weak disorders, then enters a Berry-curvature mediated metallic phase at moderate disorders, and finally goes into the Anderson insulating phase at strong disorders. From the phase diagram, we find that at the charge neutrality point although the QAHE is most robust against disorders, the corresponding metallic phase is much easier to be localized into the Anderson insulating phase due to the interchange of Berry curvatures carried, respectively, by the conduction and valence bands. In the end, we provide a phenomenological picture related to the topological charges to better understand the underlying physical origin of the QAHE Anderson localization. [Preview Abstract] |
Thursday, March 16, 2017 5:18PM - 5:30PM |
V37b.00015: Edge states of mechanical diamond Yuta Takahashi, Toshikaze Kariyado, Yasuhiro Hatsugai Bulk-edge correspondence, a basic principle in topological phases, emerges not only in quantum mechanics but also in classical mechanics. A typical example is mechanical graphene, a spring-mass model with the honeycomb lattice\footnote{T. Kariyado and Y. Hatsugai, Sci. Rep. {\bf 5}, 18107 (2015).}. Frequency dispersion of mechanical graphene shows creation and annihilation of Dirac cones with varying the uniform tension of the system. Localized edge modes arise with boundaries as in the case of graphene\footnote{S. Ryu and Y. Hatsugai, Phys. Rev. Lett. {\bf 89}, 077002 (2002).}.\\ We generalize its discussion to three-dimensional diamond lattice, dubbed as mechanical diamond. Instead of Dirac cones, line nodes appear due to the chiral symmetry. Moreover, explicit multiple localized zero modes exist with boundaries in some regions of projected two-dimensional Brillouin zone. We discuss the topological nature of localized modes in terms of Zak phase and winding number\footnote{Y. Takahashi, T. Kariyado and Y. Hatsugai, in preparation.}. [Preview Abstract] |
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