Bulletin of the American Physical Society
APS March Meeting 2018
Monday–Friday, March 5–9, 2018; Los Angeles, California
Session A08: Topological Insulator: General Theory |
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Sponsoring Units: DCMP Chair: Daniel Bulmash, University of Maryland-College Park Room: LACC 153C |
Monday, March 5, 2018 8:00AM - 8:12AM |
A08.00001: Topological invariants of disconnected elementary band representations Jennifer Cano, Barry Bradlyn, Zhijun Wang, Luis Elcoro, Maia Vergniory, Claudia Felser, Mois Aroyo, Andrei Bernevig Elementary band representations transform according to a minimal set of symmetry-related orbitals. When there is a gap between two groups of bands that together transform as an elementary band representation, at least one of those groups of bands is topological, in the sense that it cannot be smoothly deformed to an atomic limit that preserves the crystal symmetry. These topological bands come in two varieties, depending on whether or not they have a stable topological index (for example, a Chern number). We show that in either case, we can construct a nontrivial topological invariant that is a physical observable. |
Monday, March 5, 2018 8:12AM - 8:24AM |
A08.00002: Topological Pumping Processes and Higher-Order Topological Insulators Wladimir Benalcazar, Andrei Bernevig, Taylor Hughes We expand the theory of topological insulators with quantized electric multipole moment to cover associated topological pumping phenomena and a novel class of 3D insulator with chiral hinge states. Just as a varying dipole generates charge pumping, a varying quadrupole generates dipole pumping, and a varying octupole generates quadrupole pumping. For non-trivial adiabatic cycles, the transport of these moments is quantized. An analysis of these interconnected phenomena leads to the conclusion that a new kind of Chern-type insulator exists, which has chiral, hinge-localized modes in 3D. We provide the minimal models for the non-trivial pumping processes and the hinge Chern insulator. We also describe the topological invariants that protect them. |
Monday, March 5, 2018 8:24AM - 8:36AM |
A08.00003: New topological invariants in non-Hermitian systems Ananya Ghatak, Tanmoy Das Recently developed parity (P) and time-reversal (T) symmetric non-Hermitian (NH) systems govern a rich variety of new and characteristically distinct physical properties, which may or may not have a direct analog in their Hermitian counterparts. Owing to the PT-invariance as well as loss of hermiticity of the Hamiltonians, the usual topological invariants do not necessarily appear in this case. Recalling the fact that in PT-symmetric NH Hamiltonians, positive inner products of the eigenstates require the presence of a hidden symmetry, often termed as ‘C’-symmetry. We show that with the help of the C-symmetry, new topological invariants can be constructed in the NH Hamiltonians. We will present variety of examples with characteristically distinct topological invariants. |
Monday, March 5, 2018 8:36AM - 8:48AM |
A08.00004: Topological Hofstadter problem in four dimensions with a quantized Hall response Canon Sun, Yi Li We generalize the Hofstadter problem of two-dimensional quantum Hall systems to a time-reversal invariant Hofstadter problem in four dimensions (4D) based on a 4D quantum Hall model, where spin-1/2 particles are coupled to a Landau-type SU(2) gauge field via spin-orbit coupling. The non-trivial topology is manifested through the spatial separation of (3+1)d surface Weyl modes with opposite chiralities. We further investigate the bulk-edge correspondence in this 4D Hofstadter problem and show the presence of a quantized Hall response under parallel E and B fields as a consequence of the (3+1)d chiral anomaly. A possible realization of the 4D Hofstadter system in ultra-cold atomic systems via synthetic dimension is also proposed. |
Monday, March 5, 2018 8:48AM - 9:00AM |
A08.00005: Fractons and Gapped Boundaries Daniel Bulmash, Thomas Iadecola We investigate gapped boundaries of fracton systems. Fracton phases of matter are 3+1D systems which are fully gapped and translationally invariant but have point-like excitations which are immobile, that is, no local operator moves a single excitation without creating additional particles. Using known exactly solvable models (both “type-I” and “type-II”), we show that particles can be more mobile at surfaces than in the bulk. This change in mobility is well-described by a picture in which excitations condense at the surface; this is similar to gapped boundaries of 2+1D topological order, but our picture applies even to models which are not known to be related to any 2+1D topological order. We then use our condensation picture to investigate what gapped boundaries are possible and discuss a generalization of the Lagrangian subgroup criterion used in standard 2+1D Abelian topological order. |
Monday, March 5, 2018 9:00AM - 9:12AM |
A08.00006: Modeling Axion Insulators Nicodemos Varnava, David Vanderbilt The Chern-Simons magnetoelectric coupling can be used to provide a Z_{2} topological classification of 3D insulators having either time-reversal or inversion symmetry. When time-reversal is present, the invariant distinguishes trivial from strong topological insulators; when inversion is present, the topological phase is called an axion insulator. Here we describe two tight-binding models that provide insight into the topological properties of axion insulators and their surfaces. The first one starts from a simple k-space Hamiltonian that is transformed to real space and manipulated to obtain an axion insulator. The second model is more physically motivated, being based on previous work intended to model the topological properties of pyrochlore iridates, a class of materials that have been of considerable interest due to an interplay between electronic and spin-orbit interactions. We use these models to clarify the conditions under which the surface can be gapped and, when it is gapped, how the sign of the half-integer quantum Hall effect at the surface is determined. |
Monday, March 5, 2018 9:12AM - 9:24AM |
A08.00007: A time-reversal symmetric topological magnetoelectric effect in 3D topological insulators Bernd Rosenow, Heinrich-Gregor Zirnstein One of the hallmarks of time-reversal symmetric topological insulators in 3D is the topological magnetoelectric effect (TME). So far, a time-reversal breaking variant of this effect has attracted much attention, in the sense that the induced electric charge changes sign when the direction of an externally applied magnetic field is reversed. Theoretically, this effect is described by the so-called axion term. Here, we discuss a time-reversal symmetric TME, where the electric charge depends only on the magnitude of the magnetic field but is independent of its sign. We obtain this non-perturbative result both analytically and numerically, and suggest a mesoscopic setup to demonstrate it experimentally. |
Monday, March 5, 2018 9:24AM - 9:36AM |
A08.00008: Magnetic Proximity Effect in the Surface of 3D Topological Insulators Timothy Philip, Matthew Gilbert Recent experiments have focused on proximity-coupling ferromagnets with 3D topological insulators (TIs) to open a time-reversal-breaking mass gap in the surface state dispersion and generate a quantum anomalous Hall (QAH) effect. Little, however, is theoretically understood about the magnetic proximity effect in this system. In this talk, we investigate this proximity effect by modeling the aforementioned heterostructure within a tight-binding framework. We analytically derive a contact self-energy for the ferromagnet that, when added to the surface state Hamiltonian, breaks time-reversal symmetry. By examining the spectral function, we see that the resultant surface state gap depends non-linearly on both the hopping parameters and exchange interaction strength within the ferromagnet. For large exchange interaction strength in the ferromagnet, we find that the surface state mass gap, and thus the QAH conductivity, has the opposite sign as the exchange field in the ferromagnet, contrary to naïve expectations. Based on these results, we propose a simple experimental setup by which a topological phase transition can be realized in this heterostructure by varying the angle of a small external magnetic field. |
Monday, March 5, 2018 9:36AM - 9:48AM |
A08.00009: Topological magnetoelectric effect: Coulomb interaction and staggered magnetization Stefan Rex, Flavio Nogueira, Asle Sudbo We present theoretical results on the topological magnetoelectric effect (TME) in 3D topological insulators (TIs) with induced magnetization at the surface. We examine the effect of (i) Coulomb interaction among the topological surface states and (ii) a staggered magnetization. |
Monday, March 5, 2018 9:48AM - 10:00AM |
A08.00010: Magnetoconductance signatures of chiral domain-wall bound states in magnetic topological insulators Kunal Tiwari, William Coish, Tami Pereg-Barnea Recent magnetoconductance measurements performed on magnetic topological insulator candidates have revealed butterfly-shaped hysteresis. This hysteresis has been attributed to the formation of gapless chiral domain-wall bound states during a magnetic field sweep. We treat this phenomenon theoretically, providing a link between microscopic magnetization dynamics and butterfly hysteresis in magnetoconductance. Further, we illustrate how a spatially resolved conductance measurement can probe the most striking feature of the domain-wall bound states: their chirality. This work establishes a regime where a definitive link between butterfly hysteresis in longitudinal magnetoconductance and domain-wall bound states can be made. This analysis provides an important tool for the identification of magnetic topological insulators. |
Monday, March 5, 2018 10:00AM - 10:12AM |
A08.00011: A coupled wire model of a symmetry-preserving massive surface state of a fractional topological insulator Alexander Sirota, Sharmistha Sahoo, Gil Young Cho, Jeffrey Teo The surface Dirac fermion of a topological insulator cannot turn massive in the single-body setting without breaking charge conservation or time-reversal symmetry. Under many-body interactions, the surface state can acquire an excitation energy gap while preserving the symmetries and support fractional anyonic surface excitations. Example includes the T-Pfaffian and Pfaffian-antisemion surface topological order. The built-in many-body interacting nature of a fractional topological insulator (FTI) -- a topological insulator of fractionally charged partons -- renders the generalization of the single-body Dirac surface state somewhat irrelevant. In fact, it was shown in our previous analysis that a symmertry-preserving massive surface state exists. Here, using an exactly-solvable coupled wire model, we construct an explicit microscopic theory of the fractional surface state and discuss a particle-vortex duality. |
Monday, March 5, 2018 10:12AM - 10:24AM |
A08.00012: (d - 2)-dimensional edge states of rotation symmetry protected topological states Zhida Song, Zhong Fang, Chen Fang We study fourfold rotation invariant gapped topological systems with time-reversal symmetry in two and three dimensions (d = 2; 3). We show that in both cases nontrivial topology is manifested by the presence of the (d - 2)-dimensional edge states, existing at a point in 2D or along a line in 3D. For fermion systems without interaction, the bulk topological invariants are given in terms of the Wannier centers of filled bands, and can be readily calculated using a Fu-Kane-like formula when inversion symmetry is also present. The theory is extended to strongly interacting systems through explicit construction of microscopic models having robust (d - 2)-dimensional edge states. |
Monday, March 5, 2018 10:24AM - 10:36AM |
A08.00013: Diagnosing topological crystalline insulators using surface theories Eslam Khalaf, Hoi Chun Po, HARUKI WATANABE, Ashvin Vishwanath We investigate the possible surface modes in the three-dimensional |
Monday, March 5, 2018 10:36AM - 10:48AM |
A08.00014: Topological crystalline insulators on nonprimitive lattice Heejae Kim, Shuichi Murakami In this presentation, we focus on the topological crystalline insulators (TCIs) protected by mirror symmetry and those by glide symmetry. Such a mirror-symmetric TCI is characterized by an integer topological number known as mirror Chern number (MCN) and a glide-symmetric TCI is characterized by a Z2 topological number. Meanwhile, in nonprimitive lattices, a half of the reciprocal vectors may not be invariant under the mirror and glide operations, and the formulae of the topological numbers should be altered. In our previous work, we derived a new formula of the Z2 topological number for glide-symmetric TCI on the nonprimitive lattices. In the present work, we give a new formula of the MCN on the nonprimitive lattices. We then describe how the topological numbers for mirror- and glide-symmetric systems change in the nonprimitive lattices, in terms of the trajectory of the Weyl nodes within the intermediate Weyl semimetal phase between two bulk-insulating phases. We also show how the expressions of these topological numbers are reduced by adding additional symmetries. |
Monday, March 5, 2018 10:48AM - 11:00AM |
A08.00015: Stacking disorder in Topological Insulators and Dirac/Weyl (semi)metals Syed Raza, Meng Hua, Ching-Kai Chiu, Jeffrey Teo The recent vast developments of newly discovered and revisited spin-orbit coupled materials are largely fueled by their potential as topological insulators or (semi)metals. These topological states were first understood using band theories, where lattice momenta are conserved. Subsequently, there were also theoretical studies on disordered topological states. However, applications to materials has been relatively limited. We theoretically investigate the phase-change material family (GeTe)_{m}(Sb_{2}Te_{3})_{n}, which is known to undergo temperature/disorder-driven amorphous-crystalline as well as metal-insulator phase transitions. More recently, under certain distinct crystalline stacking layer configurations, the materials were proposed to be topological insulating and Dirac/Weyl (semi)metallic. Using an effective electronic model, we study the effects of stacking disorder on the topological phase transitions. |
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