Bulletin of the American Physical Society
APS March Meeting 2022
Volume 67, Number 3
Monday–Friday, March 14–18, 2022; Chicago
Session A59: New Forms and Phenomenology of Topological MatterRecordings Available

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Sponsoring Units: DCMP Chair: Sayed Ali Akbar Ghorashi, Stonybrook University Room: Hyatt Regency Hotel DuSable AB 
Monday, March 14, 2022 8:00AM  8:12AM 
A59.00001: NonCompact Atomic Insulators Frank Schindler, Andrei B Bernevig We study the conditions for Bloch bands to be spanned by symmetric and strictly compact Wannier states that have zero overlap with all lattice sites beyond a certain range. Similar to the characterization of topological insulators in terms of an algebraic (rather than exponential) localization of Wannier states, we find that there may be impediments to the compact localization even of topologically ``trivial" obstructed atomic insulators. These insulators admit exponentially localized Wannier states centered at unoccupied orbitals of the crystalline lattice. First, we establish a sufficient condition for an insulator to have a compact representative. Second, for $\mathcal{C}_2$ rotational symmetry, we prove that the complement of fragile topological bands cannot be compact, even if it is an atomic insulator. Third, for $\mathcal{C}_4$ symmetry, our findings imply that there exist fragile bands with zero correlation length. Fourth, for a $\mathcal{C}_3$symmetric atomic insulator, we explicitly derive that there are no compact Wannier states overlapping with less than $18$ lattice sites. We conjecture that this obstruction generalizes to all finite Wannier sizes. Our results can be regarded as the stepping stone to a generalized theory of Wannier states beyond dipole or quadrupole polarization. 
Monday, March 14, 2022 8:12AM  8:24AM 
A59.00002: Delicate Topology, Part I Aleksandra Nelson, Aris Alexandradinata, Tomas Bzdusek, Titus Neupert Pontrjagin's seminal topological classification of twoband Hamiltonians in three momentum dimensions is hereby enriched with the inclusion of a crystallographic rotational symmetry. The enrichment is attributed to a new topological invariant which quantifies a 2piquantized change in the BerryZak phase between a pair of rotationinvariant lines in the Brillouin zone, henceforth referred to as a returning Thouless pump (RTP). We show that the RTP is associated with metallic ingap states under open boundary conditions with sharplyterminated hoppings; more generally, the RTP is associated to anomalous fractional BerryZak phases of surface states, no matter how the hoppings are terminated. The RTP adds to the family of topological invariants (the Hopf and Chern numbers) that are known to classify twoband Hamiltonians in WignerDyson symmetry class A. Of these, the RTP and Hopf invariants are delicate, meaning that they can be trivialized by adding a particular trivial band to either the valence or the conduction subspace. Not all trivial band additions will nullify the RTP invariant, which allows its generalization beyond twoband Hamiltonians to arbitrarily many bands; such generalization is a hallmark of symmetryprotected delicate topology. 
Monday, March 14, 2022 8:24AM  8:36AM 
A59.00003: Delicate Topology, Part II Aris Alexandradinata, Tomas Bzdusek, Aleksandra Nelson, Titus Neupert Pontrjagin's seminal topological classification of twoband Hamiltonians in three momentum dimensions is hereby enriched with the inclusion of a crystallographic rotational symmetry. The enrichment is attributed to a new topological invariant which quantifies a 2πquantized change in the BerryZak phase between a pair of rotationinvariant lines in the Brillouin zone, henceforth referred to as a returning Thouless pump (RTP). We show that the RTP is associated with metallic ingap states under open boundary conditions with sharplyterminated hoppings; more generally, the RTP is associated to anomalous fractional BerryZak phases of surface states, no matter how the hoppings are terminated. The RTP adds to the family of topological invariants (the Hopf and Chern numbers) that are known to classify twoband Hamiltonians in WignerDyson symmetry class A. Of these, the RTP and Hopf invariants are delicate, meaning that they can be trivialized by adding a particular trivial band to either the valence or the conduction subspace. Not all trivial band additions will nullify the RTP invariant, which allows its generalization beyond twoband Hamiltonians to arbitrarily many bands; such generalization is a hallmark of symmetryprotected delicate topology. 
Monday, March 14, 2022 8:36AM  8:48AM 
A59.00004: Quantized helicity of Berry connection and band topology of magnetoelectric systems Yuxin Wang, Shouvik Sur, Alexander C Tyner, Pallab Goswami In classical electrodynamics, the flux and the helicity are two important physical quantities, which can be used to characterize topological properties of electromagnetic fields. They can also play important roles for defining bulk invariants of threedimensional topological materials. The nondegenerate bands of timereversalsymmetry breaking Chern insulators are known to support quantized flux of Abelian Berry connections or Chern numbers. Can generic threedimensional insulators support quantized helicity of Berry connections? To answer this question, we discuss the general principles for constructing tightbinding Hamiltonians of Nband systems, which can exhibit quantized helicity as bulk topological invariants. Based on such model Hamiltoians, we address various physical properties of magnetoelectric topological insulators, including those of topological Hopf insulators. 
Monday, March 14, 2022 8:48AM  9:00AM Withdrawn 
A59.00005: Robustness of topological edge states in amorphous systems Zhetao Jia, Aleksandr Avdoshkin, Elizabeth Dresselhaus, Yertay Zhiyenbayev, Joel E Moore, Boubacar Kante Since their discovery in crystalline materials, topological insulators have also been realized in amorphous solids, where nontrivial topology is captured by the real space version of the Chern number. Unlike the periodic lattice, disorder in amorphous structure induces Anderson localization of the bulk modes. Working with a model of an amorphous topological insulator with geometric disorder that preserves local coordination number, we study how the interplay of localization and nonlinearity improves the stability of edge states. The analytical investigation is based on the extracted finitesize scaling of the localization of the bulk modes. We also simulate timedomain evolution numerically, verifying suppressed dissipation in edge state propagation for the amorphous lattice compared with its periodic counterpart. 
Monday, March 14, 2022 9:00AM  9:12AM 
A59.00006: Structural Disorder Induced Secondorder Topological Insulators in Three Dimensions Jionghao Wang Higherorder topological insulators are established as topological crystalline insulators with crystalline symmetries. One celebrated example is the secondorder topological insulator in three dimensions that hosts chiral hinge modes protected by crystalline symmetries. Since amorphous solids are ubiquitous, it is important to ask whether such a secondorder topological insulator can exist in an amorphous system without any spatial order. Here we predict the existence of a secondorder topological insulating phase in an amorphous system without any crystalline symmetry. Such a topological phase manifests in the winding number of the quadrupole moment, the quantized longitudinal conductance and the hinge states. Furthermore, in stark contrast to the viewpoint that structural disorder should be detrimental to the higherorder topological phase, we remarkably find that structural disorder can induce a secondorder topological insulator from a topologically trivial phase in a regular geometry. We finally demonstrate the existence of a secondorder topological phase in amorphous systems with timereversal symmetry. 
Monday, March 14, 2022 9:12AM  9:24AM 
A59.00007: Obstructed atomic limits and boundary states in a mikado of SSH chains Quentin Marsal, Daniel Varjas, Adolfo G Grushin In this presentation, I consider a twodimensional amorphous system made of randomly distributed intertwined SSH chains coupled to each other. We show that, similarly to isolated SSH chains, it has two topologically distinct electronic configurations, that when interfaced with each other, result in edge modes at the interface. By using our recently developed local symmetry indicators for amorphous systems we determine which symmetries protect the boundary states. 
Monday, March 14, 2022 9:24AM  9:36AM 
A59.00008: Fragile topological insulators protected by rotation symmetry without spinorbit coupling Shingo Kobayashi, Akira Furusaki Recent theoretical studies have introduced the concept of fragile topological insulators, whose nontrivial band structure can be trivialized by addition of a trivial band. Fragile topological insulators fall outside the scope of the Ktheoretical classification that is concerned with stable topological phases, like Chern insulators. In this talk, we present theoretical models of threedimensional rotationsymmetric fragile topological insulators in class AI, which have n surface Dirac cones that are protected by timereversal and nfold rotation (C_{n}) symmetries (n = 2, 4, 6). We clarify that the topological insulators are classified into two kinds of fragile topological insulators. One is a fragile Z topological insulator whose only nontrivial topological index is the Euler class that specifies the number of surface Dirac cones. The other is a fragile Z_{2} topological insulator having gapless surface states with either a quadratic band touching or four (six) Dirac cones, which are protected by timereversal and C_{4} (C_{6}) symmetries. Furthermore, we demonstrate that the surface states are gapped out through hybridization with an sorbital band localized at the surface. 
Monday, March 14, 2022 9:36AM  9:48AM 
A59.00009: Interplay between the axion field and the lattice vibrations in insulators Mohamed Nabil Y Lhachemi, Ion Garate Axion electrodynamics describes the magnetoelectric phenomena that follow from a θE·B term in the electromagnetic Lagrangian, where θ is the axion field and E and B are the electric and magnetic fields (respectively). In topological materials, axion electrodynamics has been predicted to produce remarkable phenomena such as the halfquantized Hall effect, the quantized topological magnetoelectric effect and the chiral magnetic effect. In this talk, we concentrate on phononic manifestations of axion electrodynamics in insulators, which have remained unexplored. By evaluating the change in the theta field due to electronphonon interactions, we predict a magneticfieldinduced Born effective charge and show that it displays a maximum across a topological phase transition. We comment on the application of our theory to the MnBiTe family of materials. 
Monday, March 14, 2022 9:48AM  10:00AM 
A59.00010: Theory of surface energies and crystal shapes of topological crystalline insulators Yutaro Tanaka, Tiantian Zhang, Makio Uwaha, Shuichi Murakami Understanding equilibrium crystal shapes makes a substantial contribution to controlling the properties of materials. Relationships between topology and crystal shapes are important for applications of topological materials to dissipationless electronics, spintronics, and quantum computers. However, very little is known about the crystal shapes of the topological materials. Here we show that the surface energy of glidesymmetric topological crystalline insulators (TCI) depends on the parity of the Miller index of the surface in a singular way. This singular surface energy of the TCI affects the equilibrium crystal shapes, resulting in emergence of the unique crystal facets of the TCI. This singular dependence of the topological surface states is unique to the TCI protected by the glide symmetry in contrast to a TCI protected by a mirror symmetry. In addition, we show that such singular surface states of the TCI protected by the glide symmetries can be realized in KHgSb by performing firstprinciples calculations. Our results provide the basis for designs and manipulations of crystal facets by utilizing symmetry and topology. 
Monday, March 14, 2022 10:00AM  10:12AM 
A59.00011: Unification and measurement of topological order Wei Chen, Shahram Panahiyan, Gero von Gersdorff Topological order manifests as different physical quantities according to the dimensions and symmetries of the materials, such as Majorana fermions and quantized Hall conductance, just to list a few. We elaborate that all these phenomena in any dimension and symmetry class can be described by a unified topological invariant called wrapping number, which is analogous to the Gauss map in differential geometry. The wrapping number takes the form of integration of a certain curvature function over the momentum space, and the curvature function is further shown to be equivalent to an important quantity that generally characterizes all quantum phase transitions called fidelity susceptibility, also known as the quantum metric. A lossfluence spectroscopy is further proposed to measure the quantum metric in a pumpprobe experiment, through which the topological order in any noninteracting system can be directly measured, as demonstrated explicitly for graphene. 
Monday, March 14, 2022 10:12AM  10:24AM Withdrawn 
A59.00012: Universality of Wannier functions in generalized onedimensional AubryAndréHarper models Kiryl Piasotski Using a Dirac model in 1+1 dimensions, a reliable model describing the lowenergy behavior of a wide class of tightbinding models, a fieldtheoretical version of Wannier functions, the ZakBerry connection, and the geometric tensor is presented. Two fundamental Abelian gauges of Wannier functions are identified and universal scaling of the Dirac Wannier functions in terms of four fundamental scaling functions that depend only on the phase γ of the gap parameter and the charge correlation length ξ in an insulator is studied. The two gauges allow for a universal lowenergy formulation of the surface charge and surface fluctuation theorems, relating the boundary charge and its fluctuations to the bulk properties of the system. In the regime of small gaps, the universal scaling of all lattice Wannier functions and their moments in the corresponding gauges is studied. Finally, nonAbelian lattice gauges are discussed. It is found that lattice Wannier functions of maximal localization show universal scaling and are uniquely related to the Dirac Wannier function of the lower band. In addition, via the winding number of the determinant of the nonAbelian transformation, we establish a bulkboundary correspondence for the number of edge states up to the bottom of a certain band, which requires no additional symmetry constraints. 
Monday, March 14, 2022 10:24AM  10:36AM 
A59.00013: New formalism for studying topological phases of electric circuits Ryo Takahashi, Yosuke Nakata, Shuichi Murakami In recent years, topological phases have been realized not only in electronic systems but also in artificial systems such as electric circuits [1]. In order to investigate the bulkboundary correspondence, which is one of the important properties of the topological phases, it is necessary to correctly define the norm of the eigenstates, and conservation of the norm is crucial in establishing bulkboundary correspondence. Unlike the electronic systems, in the electric circuit systems, a proper definition of the norm has not been known, and therefore, the bulkboundary correspondence has not been shown so far. In this presentation, we propose a new formalism in which a conserved norm is defined for certain general classes of electric circuits, and discuss its consequences in bulkboundary correspondence. Our new formalism is expected to be useful for the comprehensive study of topological properties of electric circuits. 
Monday, March 14, 2022 10:36AM  10:48AM 
A59.00014: NonHermitian waves in a continuous periodic medium Kazuki Yokomizo, Taiki Yoda, Shuichi Murakami The nonHermitian skin effect induces the localization of bulk eigenstates at boundaries in nonHermitian systems [1]. Although the nonHermitian skin effect plays a crucial role, it has been studied mostly in tightbinding systems. In this work, we study waves in a nonHermitian continuous periodic medium. Then, we find that the localization length of all the skin modes is common. In this talk, we show that this remarkable behavior can be explained in terms of the nonBloch band theory proposed in our previous work [2]. Namely, the constant localization length reflects the circular shape of the generalized Brillouin zone. We also show that same behavior of bulk eigenstates is found in a nonHermitian photonic crystal. [1] S. Yao and Z. Wang, Phys. Rev. Lett. 121, 086803 (2018). [2] K. Yokomizo and S. Murakami, Phys. Rev. Lett. 123, 066404 (2019). 
Monday, March 14, 2022 10:48AM  11:00AM 
A59.00015: NonHermitian topological band structures with generalized inversion symmetry Ryo Okugawa, Ryo Takahashi, Kazuki Yokomizo NonHermitian skin effects and exceptional points can be topologically characterized by integer winding numbers. In this study, we simplify the topological analysis using the winding numbers for nonHermitian skin effects and exceptional points by using inversion symmetry. We show that parities of the winding numbers can be determined from eigenvalues on the inversioninvariant momenta. The simple expressions for the winding numbers allow us to easily detect skin effects and exceptional points in nonHermitian band structures. 
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