Bulletin of the American Physical Society
APS March Meeting 2017
Volume 62, Number 4
Monday–Friday, March 13–17, 2017; New Orleans, Louisiana
Session F3: Topological Phases in Three Dimensions |
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Sponsoring Units: DCMP Chair: Ching-Kai Chiu, University of Maryland Room: 262 |
Tuesday, March 14, 2017 11:15AM - 11:27AM |
F3.00001: Polarization induced $Z_{2}$ and Chern topological phases in a periodically driving field Shu-Ting Pi, Sergey Savrasov $Z_{2}$ and Chern topological phases such as newly discovered quantum spin Hall and original quantum Hall states hardly both co--exist in a single material due to their contradictory requirement on the time--reversal symmetry (TRS). We show that although the TRS is broken in systems with a periodically driving field, an effective TRS can still be defined provided the ac--field is linearly polarized or certain other conditions are satisfied. The controllable TRS provides us a route to manipulate contradictory phases by tuning the polarization. To demonstrate the idea, we consider a tight-binding model that is relevant to several monolayered materials as a benchmark system. Our calculation shows not only topological $% Z_{2}$ to Chern phase transition occurs but rich Chern phases are also observed. In addition, we also discussed the realization of our proposal in real materials, such as spin-orbit coupled graphene and crystal Bismuth. This opens the possibility of manipulating various topological phases in a single material and can be a promising approach to engineer new electronic states of matter. [Preview Abstract] |
Tuesday, March 14, 2017 11:27AM - 11:39AM |
F3.00002: Topological Phases of a Su-Schrieffer-Heeger ladder system Suraj Hegde, Karmela Padavic, Wade DeGottardi, Smitha Vishveshwara We study a ladder system whose legs are comprised of two Su-Schrieffer-Heeger (SSH) dimer chains. The parameters are chosen so that the system exhibits particle-hole symmetry and has a Z x Z topological invariant . In the parameter space of the ladder system, we employ a transfer matrix approach to chart out the topological phase diagram identifying two distinct topological phases and a trivial phase. Each topological phase is marked by the existence of two zero energy edge-modes on either the top or bottom legs of the ladder. We consider the effect of disorder and (quasi-)periodicity on the system; in the latter case, we show that the phase diagram is reminiscent of Hofstadter's butterfly diagram. In addition, we consider the effect of finite size on the edge-mode wave functions, the lifting of degeneracy of the zero modes and the phase boundaries. We briefly discuss the realization of the SSH ladder system in cold atomic systems and its connections to Majorana wires. [Preview Abstract] |
Tuesday, March 14, 2017 11:39AM - 11:51AM |
F3.00003: Knot cycles in (3$+$1)D topological phases Syed Raza, Sharmistha Sahoo, Jeffrey C. Y. Teo Multi-component knots in 3D can be tangled with trivial mutual linking number, for example the Borromean ring, Whitehead link, Brunnian link and chain. In topological phases, topological strings such as vortices and line defects can carry low energy quasi-(1$+$1)D electronic degrees of freedom. Moreover, they can exhibit non-trivial mutual statistics with other quasi-particles and quasi-strings. We consider the non-trivial knot cycles of these topological strings in (3$+$1)D topological phases, moving one of the strings cyclically in time around the rest of the knot configuration, and study their quantum statistical behaviors. In particular, we focus on their non-abelian statistics and non-local adiabatic pumping. [Preview Abstract] |
(Author Not Attending)
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F3.00004: Decorated defect condensate, a window to topological phase of matter Yizhi You We investigate the unconventional quantum phases in 3d Weyl metals. The emergent boson fields, coupling with the Weyl fermion bilinears, contain a Wess-Zumino-Witten term or topological $\Theta$ term inherited from the momentum space monopoles carried by Weyl points. Three types of unconventional quantum critical points will be studied in order: (1) The transition between two distinct symmetry breaking phases whose criticality is beyond Landau's paradigm. (2) The transition between a symmetry breaking state to a topological ordered state. (3) The transition between $3d$ topological order phase to trivial disordered phase whose criticality could be traced back to a $Z_2$ symmetry breaking transition on the surface of $4d$. The essence of these unconventional critical points lies in the fact that the topological defect of an order parameter carries either a nontrivial quantum number or a topological term so the condensation of the defects would either break some symmetry or give rise to a topological order phase with nontrivial braiding statistics. [Preview Abstract] |
Tuesday, March 14, 2017 12:03PM - 12:15PM |
F3.00005: Axionic instability near topological quantum phase transition Tatsushi Imaeda, Yuki Kawaguchi, Yukio Tanaka, Masatoshi Sato Recently, axion electrodynamics in topological materials is one of the hot topics in condensed matter physics[1-3]. In~particular,~it has been pointed out that axion electrodynamics exhibits instability with~exotic electromagnetic response in~the presence of background~electric fields [2].~~In the presentation, we discuss~the instability due to dynamical axion field near a topological phase transition, where~the axion~field may have a large fluctuation decreasing the critical~electric field of the instability.~We report the electro-magnetic~response of the axion field~using two different model Hamiltonians.\\ \\ $[1]$ X.-L. Qi $\backslash $textit\textbraceleft et al.\textbraceright , Phys. Rev. B $\backslash $textbf\textbraceleft 78\textbraceright , 195424 (2008). \newline [2] R. Li $\backslash $textit\textbraceleft et al.\textbraceright , Nat. Phys. $\backslash $textbf\textbraceleft 6\textbraceright , 284 (2010). \newline [3] H. Ooguri $\backslash $textit\textbraceleft et al.\textbraceright , Phys. Rev. Lett. $\backslash $textbf\textbraceleft 108\textbraceright , 161803 (2012). [Preview Abstract] |
Tuesday, March 14, 2017 12:15PM - 12:27PM |
F3.00006: Axion electrodynamics, $S$-duality, and monoid of fractional topological insulators in three dimensions Peng Ye, Meng Cheng, Eduardo Fradkin Fractional topological insulators in three dimensions admit fractional axion angles and fractionalized bulk excitations. Most of previous studies on fractional topological insulators are based on parton (Gutzwiller projective) constructions of various types (e.g., Ye, Hughes, Maciejko, Fradkin 2016). In this talk, we report new results on fractional topological insulators. First, on a general ground, we study the $S$-duality transformations of QED$_4$ coupled to fractionalized matter. When time-reversal symmetry is imposed, the duality transformations directly apply to gauged fractional topological insulators, leading to a sequence of quantized axion angles that are allowed by time-reversal symmetry. Second, we consider stacking (monoid) operation among topological insulators and fractional topological insulators. The stacking operations generate all fractional topological insulators. Third, we present a topological quantum field theory with symmetry, from which we may systematically derive fractional axion angles. [Preview Abstract] |
Tuesday, March 14, 2017 12:27PM - 12:39PM |
F3.00007: Higher-order Topological Insulators and Superconductors Frank Schindler, Ashley Cook, Maia Garcia Vergniory, Titus Neupert Symmetry-protected topological bulk insulators in $d$ dimensions are typically characterized by the presence of gapless modes localized on $(d-1)$-dimensional symmetry-preserving boundary segments. Here, we introduce a class of three-dimensional topological insulators which calls for a generalization of this bulk-boundary correspondence: while these systems host no gapless surface states for a generic symmetry-preserving termination, they feature topologically protected gapless edge states. They are topologically protected by spatio-temporal symmetries and classified by a three-dimensional bulk $\mathbb{Z}_2$ invariant based on Wilson loop spectroscopy. We give both time-reversal breaking and time-reversal invariant examples, with chiral and Kramers paired edge states, respectively. Possible realizations, including topological insulators with triple-Q $(\pi, \pi, \pi)$ magnetic order, are discussed. Furthermore, the equivalent concept for topological superconductors is explored: We show that a three-dimensional superconductor with $p+\mathrm{i}d_{x^2-y^2}$ pairing symmetry hosts chiral Majorana edge states. As well as being of great fundamental interest, these phases may be important for a variety of lossless transport applications. [Preview Abstract] |
Tuesday, March 14, 2017 12:39PM - 12:51PM |
F3.00008: Geometric Model of Topological Insulators from the Maxwell Algebra Giandomenico Palumbo I propose a novel geometric model of time-reversal-invariant topological insulators in three dimensions in presence of an external electromagnetic field. Their gapped boundary supports relativistic quantum Hall states and is described by a Chern-Simons theory, where the gauge connection takes values in the Maxwell algebra. This represents a non-central extension of the Poincare' algebra and takes into account both the Lorentz and magnetic-translation symmetries of the surface states. In this way, I derive a relativistic version of the Wen-Zee term and I show that the non-minimal coupling between the background geometry and the electromagnetic field in the model is in agreement with the main properties of the relativistic quantum Hall states in the flat space. [Preview Abstract] |
Tuesday, March 14, 2017 12:51PM - 1:03PM |
F3.00009: Non-Abelian fractional topological insulators in three spatial dimensions from coupled wires Thomas Iadecola, Titus Neupert, Claudio Chamon, Christopher Mudry The study of topological order in three spatial dimensions constitutes a major frontier in theoretical condensed matter physics. Recently, substantial progress has been made in constructing (3+1)-dimensional Abelian topological states of matter from arrays of coupled quantum wires. In this talk, I will illustrate how wire constructions based on non-Abelian bosonization can be used to build and characterize non-Abelian symmetry-enriched topological phases in three dimensions. In particular, I will describe a family of states of matter, constructed in this way, that constitute a natural non-Abelian generalization of strongly correlated three dimensional fractional topological insulators. These states of matter support strongly interacting symmetry-protected gapless surface states, and host non-Abelian pointlike and linelike excitations in the bulk. [Preview Abstract] |
Tuesday, March 14, 2017 1:03PM - 1:15PM |
F3.00010: Anyon structure of fractional topological insulating slabs with gapped surfaces Alexander Sirota, Sharmistha Sahoo, Jeffrey C.Y. Teo, Gil Young Cho We consider fractional topological insulators (FTI) in three dimensions whose bulk quasiparticle excitations consist of partons coupled with a $Z_{2n+1}$ gauge theory. Their surface states can acquire an excitation energy gap by either breaking time reversal symmetry, charge $U(1)$ symmetry, or preserving both symmetries while introducing additional T-Pfaffian-like surface topological order. We theoretically study the anyon and symmetry structures of these gapped surface states as well as quasi-$(2+1)$D slabs of FTI with distinct opposite gapped surfaces. [Preview Abstract] |
Tuesday, March 14, 2017 1:15PM - 1:27PM |
F3.00011: Band geometry and electrical response of Chern insulators Albert Brown, Fenner Harper, Rahul Roy Band geometry plays an important role in the stability of fractionalized topological phases in partially filled Chern bands. In Landau levels, the response to non-uniform electric fields is related to a geometric quantity, the Hall viscosity. Here we study the connection between quantum band geometry and response to spatially varying electric fields and show that these responses may be used to probe band geometric quantities. [Preview Abstract] |
Tuesday, March 14, 2017 1:27PM - 1:39PM |
F3.00012: Entanglement Chern Number in Tree Dimensions Hiromu Araki, Takahiro Fukui, Yasuhiro Hatsugai We have characterized some of topological phases by the entanglement Chern number (e-Ch), which is defined as the Chern number of the entanglement Hamiltonian.\footnote{ T. Fukui and Y. Hatsugai, JPSJ, {\bf 83}, 113705 (2014)} The partition of the system is not necessarily spatial but can be spin partition, which is the extensive partition. If a system respects the time reversal symmetry, the Chern number is trivial but the e-Ch can be non-zero. For instance, the e-Ch characterizes the quantum spin Hall phase of the Kane--Mele model and its phase diagram by the $Z_2$ topological number is successfully reproduced by the e-Ch.\footnote{H. Araki, T. Kariyado, T. Fukui and Y. Hatsugai, JPSJ, {\bf 85}, 043706 (2016)} For the Fu--Kane--Mele model,\footnote{L. Fu, C. L. Kane and E. J. Mele, PRL, {\bf 98}, 106803 (2007)} its weak phases are well described by the non trivial section e-Ch and the strong phase is characterized by the existence of the Weyl points of the entanglement Hamiltonian.\footnote{ H. Araki, T. Fukui and Y. Hatsugai, in preparation.} [Preview Abstract] |
Tuesday, March 14, 2017 1:39PM - 1:51PM |
F3.00013: Wilson operator algebras and ground states for coupled BF theories Apoorv Tiwari, Xiao Chen, Shinsei Ryu The multi-flavor $BF$ theories in (3+1) dimensions with cubic or quartic coupling are the simplest topological quantum field theories that can describe fractional braiding statistics between loop-like topological excitations (three-loop or four-loop braiding statistics). In this paper, by canonically quantizing these theories, we study the algebra of Wilson loop and Wilson surface operators, and multiplets of ground states on three torus. In particular, by quantizing these coupled $BF$ theories on the three-torus, we explicitly calculate the $\mathcal{S}$- and $\mathcal{T}$-matrices, which encode fractional braiding statistics and topological spin of loop-like excitations, respectively. In the coupled $BF$ theories with cubic and quartic coupling, the Hopf link and Borromean ring of loop excitations, together with point-like excitations, form composite particles. [Preview Abstract] |
Tuesday, March 14, 2017 1:51PM - 2:03PM |
F3.00014: Glide-symmetric topological crystalline insulators with nonprimitive lattices Heejae Kim, Shuichi Murakami Topological crystalline insulators (TCIs) with glide symmetry have been theoretically proposed recently. Such glide-symmetric TCIs are characterized by a Z2 topological number. In our previous work, we studied a phase transition between the TCI phase and a normal insulator (NI) phase, and show that the Weyl semimetal phase intervenes between the TCI and the NI phases. In this presentation, we consider this glide-symmetric TCI in nonprimitive lattices. In this case, the previous formula of the Z2 topological number does not apply. We give a new formula of the Z2 topological number for glide-symmetric TCI on nonprimitive lattices, and describe how TCI-NI phase transitions occur via emergence of Weyl nodes. We also apply the results to magnon systems and photonic crystals with glide symmetries. [Preview Abstract] |
Tuesday, March 14, 2017 2:03PM - 2:15PM |
F3.00015: The quantitative relationship between polarization differences and the zone-averaged shift photocurrent Benjamin Fregoso, Takahiro Morimoto, Joel E. Moore A relationship is derived between differences in electric polarization between bands and the ``shift vector'' that controls part of a material's bulk photocurrent, then demonstrated in several models. Electric polarization has a quantized gauge ambiguity and is normally observed at surfaces via the surface charge density, while shift current is a bulk property and gauge-invariant at each point in momentum space. They are connected because the same optical transitions that are described in shift currents pick out a relative gauge between valence and conduction bands. We treat subtleties arising when there are degenerate bands or points at the Brillouin zone where optical transitions are absent. This relationship means that materials with significant interband polarization differences must have high bulk photocurrent, meaning that the modern theory of polarization can be used as an efficiently calculable means to search for bulk photovoltaic material candidates. [Preview Abstract] |
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