Bulletin of the American Physical Society
APS March Meeting 2019
Volume 64, Number 2
Monday–Friday, March 4–8, 2019; Boston, Massachusetts
Session P02: Topological Materials -- New Theoretical ApproachesFocus
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Sponsoring Units: DMP Chair: Ying Ran, Boston Coll Room: BCEC 107A |
Wednesday, March 6, 2019 2:30PM - 2:42PM |
P02.00001: Topological band structures in electric circuits Tobias Helbig, Tobias Hofmann, Ching Hua Lee, Martin Greiter, Ronny Thomale Topolectrical circuits [C.H. Lee at al., Comm. Phys. 1,39] present themselves as a platform to investigate fundamental topological states of matter realized in classical synthetic crystals. The manifold degrees of freedom unfolding as lattice connectivity and parameter choice in electric networks enable the implementation of arbitrary tight-binding models. We report on the design, measurement and engineering of admittance band structures in periodic circuits [T. Helbig, T. Hofmann et al., arXiv:1807.09555v1] providing an extensive symmetry classification. Furthermore, we review the effect of individual constituents on the presence of global symmetries. We employ our approach on explicating several examples reaching from the Su-Schrieffer-Heeger and the graphene model over the implementation of a Chern state [T. Hofmann, T. Helbig et al., arXiv:1809.08687v2] up to the realization of non-Hermitian physics in this classical environment. |
Wednesday, March 6, 2019 2:42PM - 2:54PM |
P02.00002: Topological Superconductivity in Honeycomb Dirac Systems Tamaghna Hazra, Kyungmin Lee, Mohit Randeria, Nandini Trivedi There has been a surge of recent interest in superconductivity (SC) in 2D Dirac materials ranging from transition metal dichalcogenides to twisted bilayer graphene. It is important to understand the precise conditions under which one obtains a topological SC state in such systems. We address this question in the simplest honeycomb lattice models that hosts both topological and trivial insulating states in 2D: the Kane-Mele (KM) model for spin-1/2 fermions and the Haldane model for spinless fermions. We describe the results of our extensive self-consistent Bogoliubov-deGennes calculations [1] for these models with a variety of pairing interactions, and show that topological SC states arise only for nearest-neighbor attraction. In the KM model, we find four distinct SC phases, all with finite center-of-mass momentum pairing. Two of these are topological SCs: one a helical spin-triplet SC which is time-reversal invariant and another a chiral spin-triplet SC with Chern number ±1 with equal-spin pairing in one valley and opposite-spin triplet pairing in the other valley. We also discuss possible experimental signatures of these phases. |
Wednesday, March 6, 2019 2:54PM - 3:06PM |
P02.00003: Haldane Circuit Tobias Hofmann, Tobias Helbig, Ching Hua Lee, Martin Greiter, Ronny Thomale We propose an implementation of the Chern state in a topolectrical circuit network, featuring topologically protected, unidirectional propagation of voltage packages at its boundary [T. Hofmann, T. Helbig, et al., arxiv:1809.08687]. Recently, electric circuit arrays have been established as an easily accessible and tunable environment to host synthetic topological states of matter [C. H. Lee, et al., Comm. Phys. 1, 39; T. Helbig, T. Hofmann, et al., arxiv:1807.09555]. The breaking of reciprocity and time-reversal symmetry as well as minimizing dissipation effects constitute the central challenges arising in a circuit realization of the Chern state. In this talk, we present operational amplifiers in a negative-impedance converter configuration as the key component to master these challenges. We report on our results of a dissipation-corrected circuit implementation of the Haldane model. |
Wednesday, March 6, 2019 3:06PM - 3:18PM |
P02.00004: Theory of Topological Phases and Topological Band Engineering of Graphene Nanoribbons Ting Cao, Fangzhou Zhao, Steven G. Louie Using first-principles and model Hamiltonian calculations, we show that 1D symmetry-protected topological phases exist in graphene nanoribbons (GNRs). Semiconducting GNRs of different width, edge shape, and terminating unit cells can belong to electronic topological classes characterized by different values of a Z2 invariant. Interfaces between topologically distinct GNRs characterized by different Z2 are predicted to support robust in-gap topological interface states which can be utilized as a tool for material engineering. The experimental realizations of these predictions and rational design of topologically-engineered GNR superlattices synthesized from molecular precursors have been achieved. We present here the theoretical basis and calculations for these states, showing novel robust electronic bands with desirable properties. We discuss how this manifestation of 1D topological phases may be used in future studies of 1D quantum spin physics. |
Wednesday, March 6, 2019 3:18PM - 3:30PM |
P02.00005: Spin-orbit torques in topological superconducting hybrid structures Cecilia Holmqvist, Adam Szewczyk, Carlo Canali Dirac materials with strong spin-orbit interaction have been shown to generate large surface spin accumulations in response to applied currents. Such materials have, in addition, been demonstrated to exert spin-orbit torques on adjacent ferromagnetic structures. This magnetoelectric effect in these materials is strong due to the efficient spin-momentum locking. In heterostructures consisting of superconductors and three-dimensional superconductors, this spin-momentum locking leads to an induced unconventional superconductivity that may be useful for superconducting spintronics. Here, we investigate theoretically the quantum transport properties of a ballistic junction consisting of two topological superconductors coupled over a quantum dot that is coupled to a ferromagnet. The spin-orbit torques acting on the ferromagnet are examined and are shown to depend strongly on the magnetization direction relative to the current direction. |
Wednesday, March 6, 2019 3:30PM - 3:42PM |
P02.00006: Topological Mechanics from Supersymmetry Michael Lawler, Jan Attig, Krishanu Roychowdhury, Simon Trebst In topological mechanics, the identification of a mechanical system's rigidity matrix with an electronic tight-binding model allows inferring topological properties of the mechanical system, such as the occurrence of `floppy' boundary modes, from the associated electronic band structure. Here we introduce an approach to systematically construct topological mechanical systems by an exact supersymmetry (SUSY) that relates the bosonic (mechanical) and fermionic (e.g. electronic) degrees of freedom. As examples, we discuss mechanical analogs of the Kitaev honeycomb model and of a second-order topological insulator with floppy corner modes. Our SUSY construction naturally defines hitherto unexplored topological invariants for bosonic (mechanical) systems, such as bosonic Wilson loop operators that are formulated in terms of a SUSY-related fermionic Berry curvature. |
Wednesday, March 6, 2019 3:42PM - 3:54PM |
P02.00007: Effects of electric field on topological phases in graphene nanoribbons Fangzhou Zhao, Ting Cao, Steven G. Louie We have recently shown that graphene nanoribbons (GNRs) host distinct topological phases. By first-principles calculations and tight-binding methods, we demonstrated that GNRs of different width, edge shape and end terminations can belong to different topological classes characterized by a Z2 invariant. Electric field, on the other hand, is also an essential external element that can be used to tune the electronic properties of nanomaterials such as their band gaps. We thus carry out studies on the effects of electric field on the topological phases in various graphene nanoribbons by first-principles calculations. |
Wednesday, March 6, 2019 3:54PM - 4:06PM |
P02.00008: Engineering of Chern insulators through defects Emma Minarelli, Kim Pöyhönen, Gerwin Van Dalum, Teemu Ojanen, Lars Fritz Impurities embedded in electronic systems induce bound states which can hybridize and lead to impurity bands. Recently, doping of insulators with impurities has been identified as a promising route towards engineering electronic topological states of matter. We illustrate how to engineer Chern insulators starting from a three-dimensional topological insulator with a gapped surface that is intentionally doped with magnetic impurities. The main advantage of the protocol is that it is robust and independent of details, always leading to a Chern insulator supporting a topological phase with Chern number one. |
Wednesday, March 6, 2019 4:06PM - 4:42PM |
P02.00009: Symmetry Indicators of Band Topology Invited Speaker: Hoi Chun Po Topological invariants of band structures are generally defined using the Bloch wave functions, which make them challenging to compute in realistic first-principles calculations. Spatial symmetries, however, can provide very powerful shortcuts for diagnosing certain classes of topological materials, as is epitomized by the Fu-Kane criterion for inversion-symmetric topological insulators. I will describe our theory of symmetry indicators1, which utilizes symmetry data in a maximal manner to diagnose band topology in any symmetry setting, including magnetic materials2. Aside from serving as an anchor for a more unified theoretical treatment of topological crystalline insulators3, the simplicity of the theory allows us to perform a comprehensive database search and uncovers thousands of topological materials4. |
Wednesday, March 6, 2019 4:42PM - 4:54PM |
P02.00010: Anomalous Hall Effect in Symmetry Protected Toplogical Metals Xuzhe Ying, Alex Kamenev Anomalous Hall effect is known to have several major contributions, including the intrinsic contribution from the Berry phase of Bloch electrons and skew scattering from impurities. Previously we showed that there exists a class of materials dubbed as symmetry protected topological (SPT) metals. In SPT metals, the intrinsic part of the Hall conductivity shows a discontinuity over the topological phase transition. Such a discontinuity is protected by a certain symmetry, like the particle-hole symmetry. |
Wednesday, March 6, 2019 4:54PM - 5:06PM |
P02.00011: Classification of flat bands from irremovable discontinuities of Bloch wave functions Jun-Won Rhim, Bohm-Jung Yang We show that flat bands can be categorized into two distinct classes, that is, singular and nonsingular flat bands. In the case of a singular flat band, its Bloch wave function possesses irremovable discontinuities generated by the band crossing with other bands. This singularity precludes the compact localized states from forming a complete set spanning the flat band. Once the degeneracy at the band crossing point is lifted, the singular flat band becomes dispersive and can acquire a finite Chern number in general, suggesting a new route for obtaining a nearly flat Chern band. On the other hand, the Bloch wave function of a non-singular flat band has no singularity, and thus it can be completely isolated from other bands while preserving the perfect flatness. We show that a singular flat band displays a novel bulk-boundary correspondence such that the presence of the robust boundary mode is guaranteed by the singularity of the Bloch wave function. Moreover, we develop a general scheme to construct a flat band model Hamiltonian in which one can freely design its singular or non-singular nature. Finally, we propose a general formula for the compact localized state spanning the flat band. |
Wednesday, March 6, 2019 5:06PM - 5:18PM |
P02.00012: A membrane-network model for (3+1)D topological phases Akin Morrison, Meng Hua, Alexander K Sirota, Chi Yan Jeffrey Teo Non-chiral topological phases in 2D can be understood using the Levin-Wen string-net model. Here, we construct a membrane-network model in 3D. The model has as input a generalized tensor category, which consists of a collection of modular tensor categories and equipped with a non-associative product structure, such as anyon pair condensation, that respects locality. The construction outputs an exactly soluble Hamiltonian in 3D. We speculate this model describes topological phases in 3D that dynamically generate (1+1)D stringy excitations that host low-energy conformal field theories |
Wednesday, March 6, 2019 5:18PM - 5:30PM |
P02.00013: Hierarchical Majoranas in a Programmable Nanowire Network Zhicheng Yang, Thomas Iadecola, Claudio Chamon, Christopher M Mudry We propose a hierarchical architecture for building “logical” Majorana zero modes using “physical” Majorana zero modes at the Y-junctions of a hexagonal network of semiconductor nanowires. Each Y-junction contains three “physical” Majoranas, which hybridize when placed in close proximity, yielding a single effective Majorana mode near zero energy. The hybridization of effective Majorana modes on neighboring Y-junctions is controlled by applied gate voltages on the links of the honeycomb network. This gives rise to a tunable tight-binding model of effective Majorana modes. We show that selecting the gate voltages that generate a Kekule vortex pattern in the set of hybridization amplitudes yields an emergent “logical” Majorana zero mode bound to the vortex core. The position of a logical Majorana can be tuned adiabatically, without moving any of the “physical” Majoranas or closing any energy gaps, by programming the values of the gate voltages to change as functions of time. A nanowire network supporting multiple such “logical” Majorana zero modes provides a physical platform for performing adiabatic non-Abelian braiding operations in a fully controllable manner. |
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