Bulletin of the American Physical Society
APS March Meeting 2022
Volume 67, Number 3
Monday–Friday, March 14–18, 2022; Chicago
Session B59: Progress Report on Higher-Order TopologyRecordings Available
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Sponsoring Units: DCMP Chair: Jennifer Cano, Stonybrook University Room: Hyatt Regency Hotel -DuSable AB |
Monday, March 14, 2022 11:30AM - 11:42AM Withdrawn |
B59.00001: Supercurrent interferometry of higher-order topological insulators Yanfeng Zhou, Fan Zhang A three-dimensional topological insulator (TI) can be uniquely characterized by its boundary modes localized at surfaces, hinges, or/and corners. However, the state-of-the-art experimental techniques often find it challenging to determine the presence and location of the boundary modes particularly if they only exist at selected surfaces and hinges. Here we propose a supercurrent interferometry to solve this problem by exploiting the critical current interference in a superconductor-HOTI-superconductor Josephson junction. We further demonstrate that the spatial information of the surface or hinge modes can be unambiguous determined by retrieving the quantum phase information lost in the critical current measurement, as exemplified by our calculations of the Bi4Br4 system. |
Monday, March 14, 2022 11:42AM - 11:54AM |
B59.00002: Observation of room-temperature quantum spin Hall edge state in a higher order topological insulator Bi4Br4 Md. Shafayat Hossain, Nana Shumiya, Jia-Xin Yin, Zhiwei Wang, Maksim Litskevich, Chiho Yoon, Yongkai Li, Ying Yang, Yuxiao Jiang, Guangming Cheng, Yen-Chuan Lin, Qi Zhang, Zijia Cheng, Tyler A Cochran, Xian Yang, Brian Casas, Tay-Rong Chang, Titus Neupert, Hsin Lin, Nan Yao, Fan Zhang, Luis Balicas, Yugui Yao, Zahid M Hasan Realizing macroscopic quantum phenomena at room temperature is a major pursuit in physics. The quantum spin Hall (QSH) state, a prototypical quantum phenomenon that features a two-dimensional insulating bulk and a topologically protected helical edge state at zero magnetic field, has not been realized at room temperature. Here, using scanning tunneling microscopy, we directly visualize a QSH edge state on the surface of the higher-order topological insulator Bi4Br4. We find that the atomically resolved lattice exhibits a large insulating gap of over 200meV while an atomically sharp monolayer step edge hosts an in-gap gapless state, which is the hallmark of topological bulk-boundary correspondence. An external magnetic field can gap the edge state, consistent with the time-reversal symmetry protection of the underlying topology. Furthermore, via directly identifying the geometrical hybridization of such edge states, we show the manifestation of the Z2 topology of the QSH state and visualize the building blocks of the higher-order topological insulator phase in Bi4Br4. Most notably, both the insulating gap and topological edge state persist up to 300K, pointing to the room temperature realization of the QSH state. |
Monday, March 14, 2022 11:54AM - 12:06PM |
B59.00003: Antiperovskite Highe- Order Topological Insulators for Quantum Sensing Applications Omar A Ashour, Sinead M Griffin A burgeoning area in quantum sensing is in exploring the correlated, entangled phases found in quantum materials as new pathways to low-threshold sensors. For example, quantum materials have been suggested as next-generation detectors of low-mass dark matter and for THz sensing applications. In this work, we propose a scheme for using symmetry-protected phases in topological materials as a low-threshold sensor. Through ab initio density functional theory calculations, we study antiperovskites, higher-order topological insulators characterized by a Z4 topological invariant whose surface states are protected by time-reversal and inversion symmetries. We examine how low-energy perturbations can cause topological changes in these materials, and discuss their potential in quantum sensing schemes. |
Monday, March 14, 2022 12:06PM - 12:18PM |
B59.00004: Beyond hinge states: bulk spin-based signatures of non-axionic higher-order topology Kuan-Sen Lin, Giandomenico Palumbo, Gregory A Fiete, Benjamin J Wieder, Barry Bradlyn Higher-order topological insulators (HOTIs) in 3D are characterized by a novel bulk-boundary correspondence, featuring protected modes on 1D boundary hinges in highly-symmetric model geometries. However, the ability to unambiguously detect these non-trivial hinge modes can be hampered by details of the surface and hinge termination, motivating the search for bulk observables characterizing HOTIs. For electronic materials, the existence of a spin degree of freedom can provide information on the non-trivial band topology. In this work, we introduce generalized Wilson loop numerical methods to derive quantized bulk indicators of non-axionic higher-order topology in the spin spectrum of 3D systems. In addition, we apply these techniques in position space to describe signatures of the gapped surfaces of HOTIs. We then relate these bulk and surface signatures to experimentally relevant observables beyond the axionic magnetoelectric effect. We also investigate the implications of non-trivial topology on the spin texture of the energy bands for strong TIs. We conclude with a discussion of potential applications for spintronic devices. |
Monday, March 14, 2022 12:18PM - 12:30PM |
B59.00005: Crystalline Responses for Rotation-Invariant Higher-Order Topological Insulators Julian May-Mann, Taylor L Hughes Two-dimensional higher-order topological insulators can display a number of exotic phenomena, such as half-integer charges localized at corners or disclination defects. In this presentation, we analyze these phenomena, focusing on the paradigmatic example of the quadrupole insulator with C4 rotation symmetry. We present a topological field theory description of the mixed geometry-charge responses. Our theory provides a unified description of the corner and disclination charges in terms of a physical geometry (which encodes disclinations), and an effective geometry (which encodes corners). |
Monday, March 14, 2022 12:30PM - 12:42PM |
B59.00006: Bulk-boundary correspondence in 2D chiral-symmetric higher-order topological insulators. Suman Aich, Babak Seradjeh Higher-order topological phases support states localized at boundaries of the system with co-dimension larger than one. Extensive work on the classification and the nature of bulk invariants characterizing such phases based on crystalline symmetries and Wilson loops has been performed. However, the question of how to find the bulk invariants of the generalized chiral-symmetric pi-flux model remains open. A classification in terms of quantized bulk quadrupole moment is insufficient since it gives a Z2 invariant and does not account for the number of zero-energy corner states known to be a Z invariant in simple cases. These models also cannot be classified based on crystalline symmetries due to the existence of anti-commuting mirror symmetries. In this work, we study the symmetry structure of partial Wilson loops for this class of models and define a set of bulk Z invariants that fully characterize their topology. We illustrate the connection between these invariants and the number of corner states in various models with extended hopping terms, thus establishing the bulk-boundary correspondence in these models. |
Monday, March 14, 2022 12:42PM - 12:54PM |
B59.00007: Chiral-symmetric higher-order topological phases protected by multipole winding number invariants Wladimir A Benalcazar We introduce novel higher-order topological phases in chiral-symmetric systems (class AIII of the ten-fold classification), most of which would be misidentified as trivial by current theories. These phases are protected by multipole winding numbers, bulk integer topological invariants that in 2D and 3D are built from sublattice multipole moment operators, as defined herein. The integer value of a multipole winding number indicates the number of degenerate zero-energy states localized at each corner of a crystal. These phases are generally boundary-obstructed and robust in the presence of disorder. |
Monday, March 14, 2022 12:54PM - 1:06PM |
B59.00008: Higher-order topological insulators with double band-inversions Shouvik Sur, Pallab Goswami Symmetry indicators and band-inversion play pivotal roles in determining the topology of bulk bandstructures. Here, we discuss a class of higher-order topological insulators that do not accommodate symmetry indicators, but continue to support a notion of band-inversion. We identify a general principle for constructing multi-band models of such insulators with an even number of band-inversions, and propose suitable topological invariants. We also discuss the surface states they support and establish a bulk-boundary correspondence. |
Monday, March 14, 2022 1:06PM - 1:18PM |
B59.00009: Beyond Axion Electrodynamics in Helical Higher-Order Topological Insulators Benjamin J Wieder, Giandomenico Palumbo, Kuan-Sen Lin, Frank Schindler, Stepan S Tsirkin, Titus Neupert, Andrei B Bernevig, Barry Bradlyn, Gregory A Fiete Solid-state materials including bismuth, MoTe2, and BiBr have been predicted to be higher-order topological insulators (HOTIs). In theoretical HOTI models, odd numbers of helical hinge modes encircle finite-sized samples, providing an indicator of the bulk HOTI phase in the presence of global crystal symmetries. However, the boundaries of real material samples lack the global symmetries of HOTI models, and there exist topologically trivial models with extrinsic hinge states. Furthermore, unlike chiral HOTIs (magnetic axion insulators), the bulk axion angle θ of helical HOTIs is trivial (modulo 2π). It is hence desirable to identify unambiguous bulk and surface experimental signatures of helical HOTI phases analogous to – but distinct from – the axionic magnetoelectric effects present in 3D TIs and chiral HOTIs with θ = π. In this talk, we use dimensional reduction, non-Abelian Berry phase, magnetic flux insertion, and field theory to demonstrate the existence of quantized bulk topological signatures of helical HOTI phases beyond θ, placing helical HOTIs on the same physical footing as well-understood axionic insulators. We conclude by discussing the experimental implications of our findings. |
Monday, March 14, 2022 1:18PM - 1:30PM |
B59.00010: Higher-order topological insulator phase in a modified Haldane model XIAOTING ZHOU, Baokai Wang, Hsin Lin, Arun Bansil We explore the topological properties of a modified Haldane model (MHM) in which the strength of the nearest-neighbor and next-nearest-neighbor hopping terms is made unequal and the threefold rotational symmetry C3 is broken by introducing a dimerization term (|t1w(2w)| < t1s(2s)) in the Hamiltonian. Using the parameter η = t1w/t1s = t2w/t2s, we show that this MHM supports a transition from the quantum anomalous Hall insulator to a higher-order topological insulator (HOTI) phase at η = ±0.5. It also hosts a zero-energy corner mode on a nanodisk that can transition to a trivial insulator without gap closing when the inversion symmetry is broken. The gap-closing critical states are found to be magnetic semimetals with a single Dirac node which, unlike the classic Haldane model, can move along the high-symmetry lines in the Brillouin zone. Our MHM offers a rich tapestry of HOTIs and other topological and nontopological phases. |
Monday, March 14, 2022 1:30PM - 1:42PM |
B59.00011: Multi-gap topology of the Wilson loop operator in mirror symmetric insulators Penghao Zhu We study the multi-gap topology of the periodic spectra of Wilson loop operators (WLOs) in mirror symmetric insulators. We develop two topological invariants each associated with a mirrorinvariant gap in the Wilson loop spectrum. We propose that both topological invariants in combination determine the general higher-order bulk-boundary correspondence in 2D mirror symmetric, boundary-obstructed topological insulators. Finally, we demonstrate that these new multi-gap topological invariants apply to anomalous cases beyond those captured by the nested Wilson loop, and we subsequently develop an understanding of the correlation between WLOs along two orthogonal directions |
Monday, March 14, 2022 1:42PM - 1:54PM |
B59.00012: Higher-Order Topological Phases on Quantum Fractals Bitan Roy, Sourav Manna, Snehasish Nandy Electronic materials harbor a plethora of exotic quantum phases, ranging from unconventional superconductors to non-Fermi liquids, and more recently topological phases of matter. While these quantum phases in integer dimensions are well characterized by now, their presence in fractional dimensions remain vastly unexplored. Here we theoretically show that a special class of crystalline, namely higher-order topological phases that via an extended bulk-boundary correspondence feature robust gapless modes on lower dimensional boundaries, such as corners and hinges, can be found on a representative family of fractional materials, \emph{quantum fractals}. To anchor this general proposal, we demonstrate realizations of second-order topological insulators and superconductors, respectively supporting charged and neutral Majorana corner modes, on planar Siperpenski carpet and triangle fractals. These predictions can be experimentally tested on designer electronic fractal materials, as well as on various highly tunable metamaterial platforms, such as photonic and acoustic lattices. |
Monday, March 14, 2022 1:54PM - 2:06PM |
B59.00013: Symmetry indicators vs. bulk winding numbers of topologically non-trivial bands Alexander C Tyner, Pallab Goswami The symmetry-indicators provide valuable information about the topological properties of band structures in real materials. For inversion-symmetric, non-magnetic materials, the pattern of parity eigenvalues of various Kramers-degenerate bands at the time-reversal-invariant momentum points are generally analyzed with the combination of strong Z4, and weak Z2 indices. Can the symmetry indicators identify the tunneling configurations of SU(2) Berry’s connections or the three-dimensional, winding numbers of topologically non-trivial bands? We perform detailed analytical and numerical calculations on various effective tight-binding models to answer this question. If the parity eigenvalues are regarded as fictitious Ising spins, located at the vertices of Miller hypercube, the strong Z4 index describes the net ferro-magnetic moment, which is shown to be inadequate for identifying non-trivial bands, supporting even integer winding numbers. We demonstrate that an ``anti-ferromagnetic” index, measuring the staggered magnetization can distinguish between bands possessing zero, odd, and even integer winding numbers. The coarse-grained analysis of symmetry-indicators is substantiated by computing the change in rotational-symmetry-protected, quantized Berry’s flux and Wilson loops along various high-symmetry axes. By simultaneously computing ferromagnetic and anti-ferromagnetic indices, we categorize various bands of bismuth, antimony, rhombohedral phosphorus, and Bi2Se3. |
Monday, March 14, 2022 2:06PM - 2:18PM |
B59.00014: Hinge solitons in three-dimensional second-order topological insulators Yu-Liang Tao Higher-order topological insulators have recently witnessed rapid progress in various fields ranging from condensed matter physics to electric circuits. A well-known higher-order state is the second-order topological insulator in three dimensions with gapless states localized on the hinges. A natural question in the context of nonlinearity is whether solitons can exist on the hinges in a second-order topological insulator. Here we theoretically demonstrate the existence of stable solitons localized on the hinges of a second-order topological insulator in three dimensions when nonlinearity is involved. By means of systematic numerical study, we find that the soliton has strong localization in real space and propagates along the hinge unidirectionally without changing its shape. We further construct an electric network to simulate the second-order topological insulator. When a nonlinear inductor is appropriately involved, we find that the system can support a bright soliton for the voltage distribution demonstrated by stable time evolution of a voltage pulse. |
Monday, March 14, 2022 2:18PM - 2:30PM |
B59.00015: Edge Charge Pumping in Insulators with Inversion Symmetry Xuzhe Ying Higher order topological insulators were first proposed to host half quantized corner charge associated with degenerate corner states. Such proposal has motivated wide interest in predicting the corner charge in various situations and its relation to the electric multipole moment. In this talk, we will discuss the change of the corner charge for noninteracting two dimensional insulators with inversion symmetry undergoing adiabatic evolution. We show that the change of the corner charge is accounted for by the adiabatic current flowing along the edges of the system. To derive the analytical expression for the adiabatic current, the study of systems with quasi-1D geometry is necessary, indicating that the change of the corner charge is neither a purely bulk nor edge effect, but rather a mixed one. The derived adiabatic current was examined and shows good agreement with the numerical calculation of Benalcazar-Bernevig-Hughes model. Our work suggests that the study of the change of corner charge and the associated adiabatic edge current may advance the understanding of electric multipole moment in crystalline insulators. |
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