Bulletin of the American Physical Society
APS March Meeting 2021
Volume 66, Number 1
Monday–Friday, March 15–19, 2021; Virtual; Time Zone: Central Daylight Time, USA
Session M45: Higher-Order Topological InsulatorsLive
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Sponsoring Units: DCMP Chair: Frank Schindler, Princeton University |
Wednesday, March 17, 2021 11:30AM - 11:42AM Live |
M45.00001: Higher-order topology of Bismuth Pallab Goswami, Alexander Tyner Recently, several theoretical and experimental works have proposed bismuth as a solid-state realization of higher-order topological insulators. However, the topological classification of bismuth has been performed based on various symmetry indicators. We show the symmetry indicators are insufficient for defining the bulk topological invariants of sixteen-band, Liu-Allen model. In this work, we perform homotopy classification of non-Abelian Berry’s connections for the Liu-Allen model of bismuth, and compute bulk invariants from the windings of gauge-invariant eigenvalues of straight Wilson lines and planar Wilson loops. We identify a set of topological invariants for the hexagonal planes of bismuth and antimony from the quantized non-Abelian flux, which are crucial for addressing the higher-order topology of such materials. |
Wednesday, March 17, 2021 11:42AM - 11:54AM Live |
M45.00002: Quasi-One-Dimensional Higher-Order Topological Insulators Chiho Yoon, Cheng-Cheng Liu, Hongki Min, Fan Zhang Quasi-1D β-Bi4X4 (X=Br, I) are prototype weak topological insulators (TI). For the α phases, recent high-throughput database screening suggests that Bi4Br4 is a rare higher-order TI (HOTI) whereas Bi4I4 has trivial symmetry indicators. We show that in fact the two α phases are both pristine HOTIs yet with distinct hinge state patterns. The location of inversion center dictates Bi4Br4 (Bi4I4) to feature opposite (the same) dimerizations of a surface or intrinsic (bulk or extrinsic) origin at two side surfaces. Our results imply the possible existence of many topological materials beyond the scope of symmetry indicators and establish a new TI paradigm in a unique material platform. [arXiv:2005.14710] |
Wednesday, March 17, 2021 11:54AM - 12:06PM Live |
M45.00003: Filling anomaly in 2D and 3D C4 symmetric lattices Yuan Fang, Jennifer Cano We derive the symmetry indicator formulas for the filling anomaly on the 2D square lattice with spinful atoms occupying multiple Wyckoff positions. We consider two sets of symmetries: C4, T, I or C4, TI. Our symmetry indicators generalize previous work where only one atom in the unit cell is considered. The formulas are valid for atomic insulators and fragile topological insulators and can be used to determine the corner charge. They can also be used to analyze the second order topology in C4 symmetric 3D insulators and semimetals with time-reversal symmetry and spin-orbit coupling, by studying their two dimensional kz slices. As an example, we build an explicit tight-binding model on a body-centered tetragonal lattice and numerically calculate the energy spectrum on a rod that is finite in two dimensions and infinite in the third. Our symmetry indicators correctly describe the higher-order hinge states and Fermi arcs in cases where the existing indicators do not apply. |
Wednesday, March 17, 2021 12:06PM - 12:18PM Live |
M45.00004: Quadrupole moments, edge polarizations, and corner charges in the Wannier representation Shang Ren, Ivo Souza, David Vanderbilt The modern theory of polarization determines the macroscopic end charge of a truncated 1D insulator, modulo e, from a knowledge of bulk properties alone. A more subtle problem is the determination of the corner charge of a 2D insulator from a knowledge of bulk and edge properties. While previous works mainly considered symmetry constraints, here we focus on the case that the only bulk symmetry is inversion, so that the corner charge can take arbitrary values. We develop a Wannier-based formalism that allows the corner charge to be predicted, modulo e, only from calculations on ribbon geometries of two different orientations. We find that the interior quadrupole and edge dipole contributions depend upon the gauge used to construct the Wannier functions, although their sum is gauge-independent. From this we conclude that any Wannier-based method for computing the corner charge requires the use of a common gauge throughout the calculation. We satisfy this constraint by using a projection-based Wannier construction, thereby successfully predicting the corner charge for several tight-binding models. |
Wednesday, March 17, 2021 12:18PM - 12:30PM Live |
M45.00005: Bound states in the continuum of higher-order topological phases Wladimir Benalcazar, Alexander Cerjan In this talk, we connect the study of bound states in the continuum (BICs) with the field of topological band theory. Specifically, we show that lattices with higher-order topology can support corner-localized BICs: topological, symmetry-protected states that remain localized to corners even though they are not spectrally isolated within an energy gap. We propose a method for the direct identification of BICs in condensed matter settings and use it to demonstrate the existence of BICs in a concrete lattice model. Although symmetry-protected, corner-induced filling anomalies give rise to these states, additional symmetries protect them from hybridizing with their degenerate bulk states. We demonstrate the protection mechanism for BICs in this model as arising from the simultaneous presence of chiral and C4v symmetries. We further show how breaking this mechanism transforms the BICs into higher-order topological resonances. |
Wednesday, March 17, 2021 12:30PM - 12:42PM Live |
M45.00006: Observation of a higher-order topological bound state in the continuum Alexander Cerjan, Marius Jürgensen, Wladimir Benalcazar, Sebabrata Mukherjee, Mikael C Rechtsman It is commonly thought that spectral isolation is required to identify boundary-localized topological states, as without a bulk bandgap at the same energy as the boundary states, it is not obvious whether these boundary-localized states can remain exponentially localized despite being degenerate with the bulk bands, or if they instead hybridize and lose their localization. Recently, it was predicted that the corner states can still remain localized if additional symmetries are present. |
Wednesday, March 17, 2021 12:42PM - 12:54PM Live |
M45.00007: Simulating Higher-Order Topological Insulators in Density Wave Insulators Kuan-Sen Lin, Barry Bradlyn Since the discovery of the Harper-Hofstadter model, it has been known that condensed matter systems with periodic modulations can be promoted to non-trivial topological states with emergent gauge fields in higher dimensions. In this talk, we present a general procedure to compute the gauge fields in higher dimensions associated to low-dimensional systems with periodic density wave modulations. We construct 2D models with modulations that can be promoted to higher-order topological phases with U(1) and SU(2) gauge fields in 3D. Corner modes in our 2D models can be pumped by adiabatic sliding of the phase of the modulation, yielding hinge modes in the promoted models. We also examine a 3D Weyl semimetal (WSM) gapped by charge-density wave (CDW) order, possessing quantum anomalous Hall (QAH) surface states. We show that this 3D system is equivalent to a 4D nodal line system gapped by a U(1) gauge field with a nonzero second Chern number. We explain the recently identified interpolation between QAH and obstructed QAH phases of a 3D WSM gapped by CDWs using the corresponding 4D theory. Our results can extend the search for (higher-order) topological states in higher dimensions to density wave systems. |
Wednesday, March 17, 2021 12:54PM - 1:06PM Live |
M45.00008: Glide Symmetry Protected Higher-Order Topological Insulators from Semimetals with butterfly-like Nodal Lines XIAOTING ZHOU, Chuang-Han Hsu, Hugo Aramberri, Cheng-Yi Huang, Mikel Iraola, Juan L. Mane, Maia Garcia Vergniory, Hsin Lin, Nicholas Kioussis We propose a new family of topological semimetals (TSMs) which harbors an unprecedented nodal line (NL) landscape consisting of a pair of concentric intersecting coplanar ellipses (CICE). We identify the generic criteria for the existence of the CICE in a time reversal invariant spinless fermion system with negligible spin-orbital coupling (SOC). Consequently, 9 out of 230 space groups (SGs) are feasible for hosting CICE whose location centers in the Brillouin zone (BZ) are identified. We provide a simplest model with SG Pbam which exhibits CICE, and the exotic intertwined drumhead surface states. Then, we unveil the intrinsic link between this exotic class of nodal-line semimetals (NLSMs) and a Z4 = 2 topological crystalline insulator (TCI), by including substantial SOC. This TCI supports in turn a double-hourglass fermion on the (001) surface protected by two glide mirror symmetries, which originates from the intertwined drumhead surface states (DSSs) of the CICE NLs. The higher order topology is further demonstrated for the first time by the emergence of one-dimensional (1D) helical hinge states protected by a glide symmetry. |
Wednesday, March 17, 2021 1:06PM - 1:18PM Live |
M45.00009: Square-root higher-order topological insulators and topological semimetals Tomonari Mizoguchi, Yoshihito Kuno, Tsuneya Yoshida, Yasuhiro Hatsugai Recently, square-root topological insulators, whose topological properties are inherited from the squared Hamiltonian, have attracted interests from both theoretical and experimental points of view. Most of the examples proposed or realized so far are 1D, first-order topological insulators. |
Wednesday, March 17, 2021 1:18PM - 1:30PM Live |
M45.00010: Pfaffian formalism for higher-order topological insulators Heqiu Li, Kai Sun We generalize the Pfaffian formalism, which has been playing an important role in the study of time-reversal invariant topological insulators (TIs), to 3D chiral higher-order topological insulators (HOTIs) protected by the product of four-fold rotational symmetry C4 and the time-reversal symmetry T. This Pfaffian description reveals a deep and fundamental link between TIs and HOTIs, and allows important conclusions about TIs to be generalized to HOTIs. As examples, we demonstrate how to generalize Fu-Kane's parity criterion for TIs to HOTIs, and also present a general method to efficiently compute the Z2 index of 3D chiral HOTIs without a global gauge. |
Wednesday, March 17, 2021 1:30PM - 1:42PM Live |
M45.00011: Principles of higher-order topology Shouvik Sur, Alexander Tyner, Pallab Goswami The higher-order topological insulators are crystalline-symmetry-protected phases of matter, which can support zero-energy states, localized at the sharp corners and hinges of a sample. Despite rapidly developing inter-disciplinary research on diverse aspects of higher-order topology, the fundamental organizing principles remain obscured by the absence of bulk topological invariants. In this work, we develop a unified theory of different orders of topological insulators, based on first and second homotopy classifications of non-Abelian, Berry's connections. The bulk invariants are computed from the windings of gauge-invariant eigenvalues of Wilson lines and planar Wilson loops. We show the various orders of topological insulators can be distinguished by the number of high-symmetry axes that can support non-trivial windings of Wannier centers. These high-symmetry directions determine the orientations of surfaces, which can host massless, Dirac fermions as gapless, surface states. |
Wednesday, March 17, 2021 1:42PM - 1:54PM Live |
M45.00012: Generalized corner-charge formula in higher-order topological insulators and its application to one-dimensional electrides Ryo Takahashi, Motoaki Hirayama, Tiantian Zhang, Satoru Matsuishi, Hideo Hosono, Shuichi Murakami In Cn-symmetric higher-order topological insulators, the corner charge is quantized to fractional values [1,2], calculated from irreducible representations at high-symmetry k points. Unlike previous works, which rely on assumptions that wavefunctions are periodic even close to boundaries [2], we obtain formulae for the corner charge for general cases with minimal assumptions. We also show that the corner charge quantization holds in more general cases, such as systems with edges gapped by surface reconstructions. As an application of these formulae, we show that the apatite A6B4(SiO4)6, one of the one-dimensional electrides, realizes a higher-order topological insulator with 2/3-filled one-dimensional hinge states [3,4], which is explained with our formula. [1] W. A. Benalcazar, T. Li, T. L. Hughes, Phys. Rev.B 99, 245151 (2019). [2] H. Watanabe, S. Ono, Phys. Rev. B 102, 165120 (2020). [3] M. Hirayama, R. Takahashi, S. Matsuishi, H. Hosono, and S. Murakami, Phys. Rev. Research 2, 043131 (2020). [4] M.Hirayama, S. Matsuishi, H. Hosono, and S. Murakami, Phys. Rev. X 8, 031067 (2018). |
Wednesday, March 17, 2021 1:54PM - 2:06PM Live |
M45.00013: Higher-Order Topology and Defect States in the Charge-Density-Wave Phase of (TaSe4)2I Meng Hua, Brian Khor, Yichen Hu, Benjamin J. Wieder, Jeffrey C. Y. Teo Recent theoretical and experimental investigations have identified the quasi-1D compound (TaSe4)2I as a Weyl semimetal phase that becomes gapped by an incommensurate charge-density wave (CDW) just below room temperature. Although dynamical excitations of the CDW phase angle φ have been shown to exhibit incipient experimental signatures of (valley-) axion electrodynamics, the bulk topology of the insulating CDW phase at static φ remains uncertain. We present a physically motivated, lattice-commensurate coupled-wire model based on Topological Quantum Chemistry and crystalline symmetry that approximates the CDW phase of (TaSe4)2I. Our model hosts several higher-order and weak topological phases, which depend on the values of several symmetry-allowed Dirac mass terms corresponding to distinct CDWs. We also present evidence for helical modes bound to line defects, including disclinations, boundary hinges, and Dirac mass(phase angle) vortices, in the CDW state. |
Wednesday, March 17, 2021 2:06PM - 2:18PM Live |
M45.00014: Discovery of Higher-Order Topological Insulators using the Spin Hall Conductivity as a Topology Signature Marcio Costa, Gabriel Ravanhani Schleder, Carlos Mera Acosta, Antonio M Padilha, Frank Cerasoli, Marco Buongiorno Nardelli, Adalberto Fazzio The discovery and realization of topological insulators, a phase of matter which hosts metallic boundary states when the d-dimension insulating bulk is confined to (d-1)-dimensions, led to several potential applications. Recently, it was shown that protected topological states can manifest in (d-2)-dimensions, such as hinge and corner states for three- and two-dimensional systems, respectively. These nontrivial materials are named higher-order topological insulators (HOTIs). Here we show a connection between spin Hall effect and HOTIs using a combination of ab initio calculations and tight-binding modeling. The model demonstrates how a non-zero bulk midgap spin Hall conductivity (SHC) emerges within the HOTI phase. Following this, we performed high-throughput density functional theory calculations to find unknown HOTIs, using the SHC as a criterion. We calculated the SHC of 693 insulators resulting in seven stable two-dimensional HOTIs. Our work guides novel experimental and theoretical advances towards higher-order topological insulators realization and applications. |
Wednesday, March 17, 2021 2:18PM - 2:30PM Live |
M45.00015: Quantized surface magnetism and higher-order topology: Application to the Hopf insulator Penghao Zhu, Taylor L Hughes, Aris Alexandradinata We identify topological aspects of the subextensive magnetic moment contributed by the surfaces of a three-dimensional crystallite – assumed to be insulating in the bulk as well as on all surface facets, with trivial Chern invariants in the bulk. The geometric component of this subextensive moment is given by its derivative with respect to the chemical potential, at zero temperature and zero field, per unit surface area, and hence corresponds to the surface magnetic compressibility. The sum of the surface compressibilities contributed by two opposite facets of a cube-shaped crystallite is quantized to an integer multiple of the fundamental constant e/hc; this integer is in one-to-one correspondence with the net chirality of hinge modes on the surface of the crystallite, manifesting a link with higher-order topology. The contribution by a single facet to the magnetic compressibility need not be quantized to integers; however, symmetry and/or Hilbert-space constraints can fix the single-facet compressibility to half-integer multiples of e/hc, as will be exemplified by the Hopf insulator. |
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