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: Non-Compact 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 two-band 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 2pi-quantized change in the Berry-Zak phase between a pair of rotation-invariant lines in the Brillouin zone, henceforth referred to as a returning Thouless pump (RTP). We show that the RTP is associated with metallic in-gap states under open boundary conditions with sharply-terminated hoppings; more generally, the RTP is associated to anomalous fractional Berry-Zak 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 two-band Hamiltonians in Wigner-Dyson 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 two-band Hamiltonians to arbitrarily many bands; such generalization is a hallmark of symmetry-protected 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 two-band 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 2π-quantized change in the Berry-Zak phase between a pair of rotation-invariant lines in the Brillouin zone, henceforth referred to as a returning Thouless pump (RTP). We show that the RTP is associated with metallic in-gap states under open boundary conditions with sharply-terminated hoppings; more generally, the RTP is associated to anomalous fractional Berry-Zak 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 two-band Hamiltonians in Wigner-Dyson 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 two-band Hamiltonians to arbitrarily many bands; such generalization is a hallmark of symmetry-protected delicate topology. |
Monday, March 14, 2022 8:36AM - 8:48AM |
A59.00004: Quantized helicity of Berry connection and band topology of magneto-electric 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 three-dimensional topological materials. The non-degenerate bands of time-reversal-symmetry breaking Chern insulators are known to support quantized flux of Abelian Berry connections or Chern numbers. Can generic three-dimensional insulators support quantized helicity of Berry connections? To answer this question, we discuss the general principles for constructing tight-binding Hamiltonians of N-band systems, which can exhibit quantized helicity as bulk topological invariants. Based on such model Hamiltoians, we address various physical properties of magneto-electric 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 non-trivial 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 finite-size scaling of the localization of the bulk modes. We also simulate time-domain 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 Second-order Topological Insulators in Three Dimensions Jionghao Wang Higher-order topological insulators are established as topological crystalline insulators with crystalline symmetries. One celebrated example is the second-order 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 second-order topological insulator can exist in an amorphous system without any spatial order. Here we predict the existence of a second-order 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 higher-order topological phase, we remarkably find that structural disorder can induce a second-order topological insulator from a topologically trivial phase in a regular geometry. We finally demonstrate the existence of a second-order topological phase in amorphous systems with time-reversal 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 two-dimensional 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 spin-orbit 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 K-theoretical classification that is concerned with stable topological phases, like Chern insulators. In this talk, we present theoretical models of three-dimensional rotation-symmetric fragile topological insulators in class AI, which have n surface Dirac cones that are protected by time-reversal and n-fold rotation (Cn) 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 Z2 topological insulator having gapless surface states with either a quadratic band touching or four (six) Dirac cones, which are protected by time-reversal and C4 (C6) symmetries. Furthermore, we demonstrate that the surface states are gapped out through hybridization with an s-orbital 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 half-quantized 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 electron-phonon interactions, we predict a magnetic-field-induced 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 glide-symmetric 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 first-principles 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 loss-fluence spectroscopy is further proposed to measure the quantum metric in a pump-probe 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 one-dimensional Aubry-André-Harper models Kiryl Piasotski Using a Dirac model in 1+1 dimensions, a reliable model describing the low-energy behavior of a wide class of tight-binding models, a field-theoretical version of Wannier functions, the Zak-Berry 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 low-energy 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, non-Abelian 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 non-Abelian transformation, we establish a bulk-boundary 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 bulk-boundary 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 bulk-boundary correspondence. Unlike the electronic systems, in the electric circuit systems, a proper definition of the norm has not been known, and therefore, the bulk-boundary 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 bulk-boundary 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: Non-Hermitian waves in a continuous periodic medium Kazuki Yokomizo, Taiki Yoda, Shuichi Murakami The non-Hermitian skin effect induces the localization of bulk eigenstates at boundaries in non-Hermitian systems [1]. Although the non-Hermitian skin effect plays a crucial role, it has been studied mostly in tight-binding systems. In this work, we study waves in a non-Hermitian 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 non-Bloch 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 non-Hermitian 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: Non-Hermitian topological band structures with generalized inversion symmetry Ryo Okugawa, Ryo Takahashi, Kazuki Yokomizo Non-Hermitian 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 non-Hermitian skin effects and exceptional points by using inversion symmetry. We show that parities of the winding numbers can be determined from eigenvalues on the inversion-invariant momenta. The simple expressions for the winding numbers allow us to easily detect skin effects and exceptional points in non-Hermitian band structures. |
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