Bulletin of the American Physical Society
APS March Meeting 2018
Volume 63, Number 1
Monday–Friday, March 5–9, 2018; Los Angeles, California
Session L08: Two-dimensional Topological Insulator: Theory |
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Sponsoring Units: DCMP Chair: Xiao Li, Univ of Maryland-College Park Room: LACC 153C |
Wednesday, March 7, 2018 11:15AM - 11:27AM |
L08.00001: Fingerprints of Topology in a Bulk Exciton Spectrum Andrew Allocca, Dmitry Efimkin, Victor Galitski The nontrivial topology of an insulator is widely considered to be nearly synonymous with the existence of Dirac surface states at its boundary. While these surface states have attracted a lot of attention, the properties of the bulk of these materials are usually considered to be conventional. Here we argue that nontrivial topology has fingerprints in the spectrum of excitons formed in their bulk. We consider the Bernevig-Hughes-Zhang model, which can be tuned between topological and trivial regimes, and show that the hierarchy of levels drastically changes as one crosses through the topological phase transition. In particular, the nontrivial Berry physics of an electron-hole pair in the topological regime generically splits excitonic states with different angular momenta and reorganizes the entire spectrum. |
Wednesday, March 7, 2018 11:27AM - 11:39AM |
L08.00002: Numerical Study on Fractionally Charged Zero-Modes in Quantum Hall Systems Yijia Wu, Hua Jiang, Jie Liu, Haiwen Liu, Xincheng Xie Fractionally charged fermions possessing non-Abelian statistics have been attracting wide attention for its potential application on topological quantum computation. Recently, experimental evidence of 3/2 fractional quantum Hall plateau has been observed in a single layer two-dimensional electron gas with confinement. We propose that the novel 3/2 plateau can be formed through tunneling-induced topological phase transition. Such topological phase transition, accompanied with Jackiw-Rebbi type zero-modes possessing non-Abelian statistics, has also been proposed in quantum spin Hall system. We present numerical evidence for the existence and transport properties of these fractionally charged zero-modes in quantum Hall systems. |
Wednesday, March 7, 2018 11:39AM - 11:51AM |
L08.00003: Unified Bulk-boundary Correspondence for Band Insulators Jun-Won Rhim, Jens Bardarson, Robert-jan slager The bulk-boundary correspondence provides for one of the most quintessential ideas in the topological classification of matter. However, the bulk-boundary correspondence has never been proven generally and has in certain scenarios been shown to fail to hold, depending on boundary profiles. In this regard we develop bulk numbers describing the exact number of in-gap modes without any of such subtleties in 1D. Based on this, we find a new 2D winding number, the pole winding number, that specifies the amount of robust metallic surface bands in the gap and their topological character. The underlying general methodology relies on a simple continuous extrapolation from the bulk to the boundary, while tracking the evolution of Green's function's poles in the vicinity of the bulk band edges. All the obtained numbers can be applied to the known insulating phases in a unified manner regardless of the specific symmetries. We directly apply our construction to various systems, including counterexamples for the conventional bulk-boundary correspondence in 1D, and predict the existence of boundary modes on various kinds of experimentally studied graphene edges. Finally, we sketch the 3D generalization of the pole winding number. |
Wednesday, March 7, 2018 11:51AM - 12:03PM |
L08.00004: Chern-Simons theory in the Varma phase Natalia Menezes, Cristiane Morais Smith, Giandomenico Palumbo In this talk, we analyze the topological response of a fermionic model defined on the Lieb lattice in presence of an electromagnetic field. The tight-binding model is built in terms of three species of spinless fermions and supports a topological Varma phase due to the spontaneous breaking of time-reversal symmetry. In the low-energy regime, the emergent effective Hamiltonian coincides with the so-called Duffin-Kemmer-Petiau (DKP) Hamiltonian, which describes relativistic pseudospin-0 quasiparticles. By considering a minimal coupling between the DKP quasiparticles and an external Abelian gauge field, we calculate both the Landau-level spectrum and the emergent Chern-Simons theory. The corresponding Hall conductivity reveals an atypical quantum Hall effect, which can be simulated in an artificial Lieb lattice. |
Wednesday, March 7, 2018 12:03PM - 12:15PM |
L08.00005: Confined Electronic States on Grain Boundaries in Topologically Gapped Graphene Madeleine Phillips, E. J. Mele Propagating edge modes are a signature of the topological order of the bulk spectrum. In this work, we consider a grain boundary embedded in a topologically ordered bulk as an interface between topologically identical mismatched domains. At such interfaces, the edge modes of the individual domains can hybridize to form an electronic state confined to the grain boundary. These states are not topologically protected, but for ordered grain boundaries backscattering can be suppressed by specific momentum selection rules. We study grain boundary modes in two models on the honeycomb lattice: the Haldane model and the Kane-Mele model, where the bulk is characterized by nontrivial Chern and Z_{2} invariants, respectively. We discuss the possibility of using grain boundary modes as transport channels and highlight the effects of grain boundary symmetry on band structure and spin degeneracies. Finally, we sketch out an extension of the spin orbit coupled model to the transition metal dichalcogenide quantum spin Hall insulators (TMD QSHIs), which suggests similarities between grain boundary modes in TMD QSHIs and those in topologically ordered graphene models. |
Wednesday, March 7, 2018 12:15PM - 12:27PM |
L08.00006: Characterizing topological band structures with space-group symmetric entanglement cuts Barry Bradlyn, Jennifer Cano, Zhijun Wang, Maia Vergniory, Luis Elcoro, Mois Aroyo, Claudia Felser, Andrei Bernevig The interplay of topology and geometry has been -- and continues to be -- a rich area of study for condensed matter physics. Recently, it has been realized that spatial symmetries allow for the stabilization of topological phases much more exotic than those that can be found with time-reversal symmetry alone. However, given an unknown symmetry-protected topological band structure, it is unclear in general how to experimentally diagnose its nontrivial topology. In this talk, we argue that the entanglement spectrum for certain symmetry-preserving subregions provides an approach for addressing this issue. We show that by choosing an entanglement subregion which respects a subgroup — either finite in the case of point subgroups, or infinite in the case of space subgroups — of the spatial symmetries of the Hamiltonian, we can extract information about the topological character of the occupied bands. |
Wednesday, March 7, 2018 12:27PM - 12:39PM |
L08.00007: The fate of interaction-driven topological insulators under disorder. Dmitri Efremov, Jing Wang, Carmine Ortix, Jeroen Van den Brink We analyze the effect of disorder on the weak-coupling instabilities of quadratic band crossing point (QBCP) in two-dimensional Fermi systems, which, in the clean limit, display interaction-driven topological insulating phases. In the framework of a renormalization group procedure, which treats fermionic interactions and disorder on the same footing, we test all possible instabilities and identify the corresponding ordered phases in the presence of disorder for both single-valley and two-valley QBCP systems. We find that disorder generally \co{suppresses the critical temperature at which the interaction-driven topologically non-trivial order sets in. Strong disorder can also cause a topological phase transition into a topologically trivial insulating state. |
Wednesday, March 7, 2018 12:39PM - 12:51PM |
L08.00008: What kind of topological states can be found in fractals? Adhip Agarwala, Shriya Pai, Vijay Shenoy The periodic table of topological insulators and superconductors classifies various topological phases by identifying their underlying symmetries and the spatial dimension d, where d is an integer. All topological phases show some form of bulk-boundary correspondence, where a nontrivially gapped bulk leads to robust edge states on the boundary. Can a topological phase exist in a nonintegral spatial dimension? What is "bulk-boundary correspondence" in a system where the bulk and boundary are not immediately identifiable? Motivated by these questions we construct topologically nontrivial Hamiltonian on Sierpinksi gasket, a fractal, which has a nonintegral Hausdorff dimension. Restricting to “translationally invariant” deterministic fractals, where each site is equivalently coordinated as any other, we find that such systems are always metals. Interestingly, such a metal is chiral in nature and has two terminal conductance close to unit value, even while the topological index is zero. We also demonstrate “surface states” in yet another fractal, the Sierpinksi tetrahedron, which interestingly has surfaces made of fractals. We describe and discuss various aspects of this physics. |
Wednesday, March 7, 2018 12:51PM - 1:03PM |
L08.00009: A formula for Z_2 invariant of topological insulators Zhi Li, Roger Mong We propose a new formula for the Z_2 topological invariant for topological insulators with time reversal (TR) symmetry. Compared to most formulas that use geometry in momentum space, our result is a local formula that works in real space, with or without translational invariance. In the latter case, our formula only requires a mobility gap instead of spectral gap. |
Wednesday, March 7, 2018 1:03PM - 1:15PM |
L08.00010: From Shockley Surface States to Topological Insulators Richard Martin The 1939 paper of Shockley [1] showed that for a 1D crystal a transition in the bulk band structure, where bands "cross" and exchange eigenvectors at the high symmetry points k=0 and k=pi/2, leads to emergence of a surface state in the gap. In a model with s and p states, the transition marks the change from atomic-like to bonding sp character, leaving a dangling bond, i.e., a half-filled surface state. In higher dimensions this becomes a surface band where the states at each k|| parallel to the surface are determined by a 1D problem with parameters that vary with k||. As Shockley pointed out, the mid-gap states should occur on metals but for insulators surface conditions can eliminate states in the gap, e.g, by passivation. Presumably for that reason this work is largely ignored in the literature of insulators. The purpose of this talk is to point out the prescience aspects of Shockley's work and a way to understand the bands of topological insulators by replacing the p state by a spin-orbit coupled p+ or p- state. The result is the model used to describe HgCdTe quantum wells and graphene can be described by a transformation to a two-site model. |
Wednesday, March 7, 2018 1:15PM - 1:27PM |
L08.00011: Hall Viscosity and Crystalline Gauge Field in Lattice Byungmin Kang, Joel Moore The Hall viscosity is a non-dissipative transport coefficient, which becomes non-zero in time-reversal symmetry broken systems such as quantum Hall systems. In the original formulation [Avron et. al., Phys. Rev. Lett. 75, 697 (1995)], the Hall viscosity is expressed in terms of a Berry curvature associated with the change in the metric of the background manifold on which the quantum state lives. Equivalently, the Hall viscosity is given by the Kubo formula involving the stress-energy tensor. However in the lattice setting, both the background metric and the stress-energy tensor may not be well-defined, which results in the main difficulty in properly defining the Hall viscosity in the lattice. In this talk, I will discuss a way to define the Hall viscosity of a lattice model using the idea of twisting the boundary conditions. In particular, I will provide the role of the crystalline gauge field in the Hall viscosity, which in fact plays a role similar to that of the electro-magnetic gauge field in the Hall conductivity. |
Wednesday, March 7, 2018 1:27PM - 1:39PM |
L08.00012: Nontrivial Topological Phase in the Absence of Berry Curvature Feng Liu, Katsunori Wakabayashi In conventional topological materials, the existence of topological states is characterized by the topological quantity such as nonzero Berry curvature, which corresponds to the magnetic field in momentum space. In this talk, we discuss a new type of nontrivial topological phase in two-dimensional systems in the absence of Berry curvature, but by the presence of nonzero Berry connection, which corresponds to the vector potential in momentum space. This is an application of the analogue of Aharanov-Bohm effect in momentum space. This nontrivial topological phase is demonstrated in a tight-binding model with alternated hopping both for square^{1} and honeycomb lattices^{2}. A corresponded realization made by the all-dielectric photonic crystal is also proposed^{3}. |
Wednesday, March 7, 2018 1:39PM - 1:51PM |
L08.00013: Steady states and edge state transport in topological Floquet-Bloch systems Iliya Esin, Mark Rudner, Gil Refael, Netanel Lindner We study the open system dynamics and steady states of two dimensional Floquet topological insulators: systems in which a topological Floquet-Bloch spectrum is induced by an external periodic drive. We solve for the bulk and edge state carrier distributions, taking into account energy and momentum relaxation through radiative recombination and electron-phonon interactions, as well as coupling to an external lead. We show that the resulting steady state resembles a topological insulator in the Floquet basis. The particle distribution in the Floquet edge modes exhibits a sharp feature akin to the Fermi level in equilibrium systems, while the bulk hosts a small density of excitations. We discuss two-terminal transport and describe the regimes where edge-state transport can be observed. Our results show that signatures of the non-trivial topology persist in the nonequilibrium steady state. |
Wednesday, March 7, 2018 1:51PM - 2:03PM |
L08.00014: Optical properties of Floquet Topological Insulators Steven McClendon, Tami Pereg-Barnea Irradiated graphene may become a Floquet topological insulator - a time dependent topological system with a topological quasi energy spectrum and states. We derive an approximate expression for the optical conductivity of the system at zero temperature. We treat the probe field using linear response while taking care of the pump field via Floquet theory. An analytic expression is possible to obtain when the pump field is turned on suddenly (quench) and the quasi-energy states are approximated near avoided crossing points. We estimate the amplitude of various optical transitions which govern the optical response. |
Wednesday, March 7, 2018 2:03PM - 2:15PM |
L08.00015: Topological Phase Transitions in the Photonic Spin Hall Effect Wilton De Melo Kort-Kamp The recent synthesis of two-dimensional staggered materials opens up burgeoning opportunities to study optical spin-orbit interactions in semiconducting Dirac-like systems. We take advantage of the crossroads between topology, phase transitions, spin-orbit interactions, and Dirac physics in the graphene family materials to unveil topological phase transitions in the photonic spin Hall effect. It is shown that an external static electric field and a high frequency circularly polarized laser allow for active on-demand manipulation of electromagnetic beam shifts. The spin Hall effect of light presents a rich dependence with radiation degrees of freedom, and material properties, and features nontrivial topological properties. We discover that photonic Hall shifts are sensitive to spin and valley properties of the charge carriers, providing an unprecedented pathway to investigate emergent spintronics and valleytronics in the graphene family. |
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