Bulletin of the American Physical Society
APS March Meeting 2020
Volume 65, Number 1
Monday–Friday, March 2–6, 2020; Denver, Colorado
Session U54: Topological Crystalline Phases 
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Sponsoring Units: DCMP Room: Mile High Ballroom 2A 
Thursday, March 5, 2020 2:30PM  2:42PM 
U54.00001: Aperiodic Topological Crystalline Insulators Huaqing Huang, YongShi Wu, Feng Liu Topological crystalline insulators (TCIs) are usually described with topological protection imposed by the crystalline symmetry. In general, however, the existence of TCI states does not necessitate the periodicity of crystals as long as an essential lattice symmetry can be identified. Here we demonstrate the compatibility of TCIs with aperiodic systems, as exemplified by an octagonal quasicrystal. In contrast to most common topological insulators and TCIs, the proposed aperiodic TCIs are attributed to a different symmetryinvoked band inversion mechanism, which inverts states with the same parities but opposite eigenvalues of a specific symmetry (such as reflection). The nontrivial topology is characterized by a nonzero integer ``mirror Bott index''. Moreover, we demonstrate that the topological edge states and quantized conductance of the aperiodic TCI, which are robust against disorder, can be effectively manipulated by external electric fields. Our findings not only provide a better understanding of electronic topology in relation to symmetry but also extend the experimental realization of topological states to much broader material categories beyond crystals. 
Thursday, March 5, 2020 2:42PM  2:54PM 
U54.00002: Real Space Invariants: Spectral Flow of Fragile Topological State under Twisted Boundary Conditions Zhida Song, Luis Elcoro, Nicolas Regnault, Andrei Bernevig In this paper, we propose the twisted boundary condition as a generic approach to theoretically and experimentally detect the fragile topological state. We prove that, when the fragile phase can be written as a difference of a trivial atomic insulator and the socalled obstructed atomic insulator, the gap between the fragile phase and other bands must close under a specific twist of 
Thursday, March 5, 2020 2:54PM  3:06PM 
U54.00003: Abstract Withdrawn

Thursday, March 5, 2020 3:06PM  3:18PM 
U54.00004: Fragile Topology Protected by Inversion Symmetry: Diagnosis, BulkBoundary Correspondence, and Wilson Loop Yoonseok Hwang, Junyeong Ahn, BohmJung Yang We study the bulk and boundary properties of fragile topological insulators (TIs) protected by inversion symmetry, mostly focusing on the class A insulator. First, we propose an efficient method for diagnosing fragile band topology by using the symmetry data in momentum space. Second, we study the bulkboundary correspondence of fragile TIs protected by inversion symmetry. In particular, we show that a minimal fragile TI with the filling anomaly corresponds to the dD (d+1)thorder TI. Although dD (d+1)thorder TIs have no ingap states, the boundary mass terms carry an odd winding number along the boundary, which induces localized charges on the boundary at the positions where the boundary mass terms change abruptly. Also by studying the (nested) Wilson loop spectra, we show that all the spectral windings of the (nested) Wilson loop should be unwound to resolve the Wannier obstruction of fragile TIs. By counting the minimal number of bands required to unwind the spectral winding of the Wilson loop and nested Wilson loop, we determine the minimal number of bands to resolve the Wannier obstruction, which is consistent with our diagnosis method of fragile topology. 
Thursday, March 5, 2020 3:18PM  3:30PM 
U54.00005: Crystalline topological phases without symmetry indicators Sander Kooi, Guido van Miert, Carmine Ortix Topological insulating phases of matter are quantum phases that cannot be deformed to atomic insulators. They generically feature protected anomalous surface states, which can be used for applications in spintronics and quantum computation. 
Thursday, March 5, 2020 3:30PM  3:42PM 
U54.00006: Topology of chiral insulators Marcelo Guzmán, Denis Bartolo, David Carpentier Building on direct analogies with electronic matter, the concepts of topological insulator and topological protection have been successfully applied to a host of different physical systems as diverse as photonic metamaterials, geophysical fluids and mechanical structures. In this work, we focus on materials, or metamaterials, having a chiral symmetry, such as crystals with a sublattice symmetry and all mechanical systems assembled from beads and springs. 
Thursday, March 5, 2020 3:42PM  3:54PM 
U54.00007: Boundary obstructed topological phases Eslam Khalaf, Wladimir A Benalcazar, Taylor L Hughes, Raquel Queiroz Symmetry protected topological (SPT) phases are gapped phases of matter that cannot be deformed to a trivial phase without breaking the symmetry or closing the bulk gap. Here, we introduce a new notion of a topological obstruction that is not captured by bulk energy gap closings in periodic boundary conditions. More specifically, we say two bulk Hamiltonians belong to distinct boundary obstructed topological ‘phases’ (BOTPs) if they can be deformed to each other on a system with periodic boundaries, but not for symmetric open boundaries without closing the gap at a high symmetry region on the surface. BOTPs are not topological phases of matter in the standard sense since they are adiabatically deformable to each other on a torus but, similar to SPTs, they are associated with surface states or fractional corner charges in the open system. We show that the doublemirror quadrupole model of [Science, 357(6346), 2018] is a prototypical example of such phases, and present a detailed analysis of boundary obstructions in this model. In addition, we introduce several threedimensional models having boundary obstructions, which are characterized either by surface states or fractional corner charges and discuss their general formulation in terms of Wannier band representations. 
Thursday, March 5, 2020 3:54PM  4:06PM 
U54.00008: Topological Crystalline States with Nontrivial Relative Group Cohomology Sydney R Timmerman, Yi Li The method of relative homotopy group has been know useful to characterize the surface defects that are not trivial extensions of bulk defects. We develop the method of relative group cohomology to study novel topological crystalline states characterized by nontrivial relative group cohomology and their relation to fragile topological crystalline states. 
Thursday, March 5, 2020 4:06PM  4:18PM 
U54.00009: Topological Invariants of a FillingEnforced Quantum Band Insulator Abijith Krishnan, Hoi Chun Po, Ashvin Vishwanath

Thursday, March 5, 2020 4:18PM  4:30PM 
U54.00010: Fermions in Z_{N} Gauge Fields: From Chern Insulators to HigherOrder Topological Insulators Vijay Shenoy, Shubham Rana Fermions coupled to gauge fields defined on the links of 
Thursday, March 5, 2020 4:30PM  4:42PM 
U54.00011: TypeII quadrupole topological insulators Yanbin Yang, Kai Li, Luming Duan, Yong Xu Recently, the formulation of polarization based on the Berry phase has been extended to 
Thursday, March 5, 2020 4:42PM  4:54PM 
U54.00012: Layer Construction of Topological Crystalline Insulator LaSbTe Yuting Qian, Zhiyun Tan, Tan Zhang, Jiacheng Gao, Zhijun Wang, Zhong Fang, Chen Fang, Hongming Weng Topological crystalline insulator (TCI) is one of the symmetryprotected topological states. Any TCI can be looked as a simple product state of several decoupled twodimensional (2D) topologically nontrivial layers in its lattice respecting its crystalline symmetries, so called layer construction (LC) scheme. In this work, based on firstprinciples calculations we have revealed that both the tetragonal LaSbTe (tLaSbTe) and the orthorhombic LaSbTe (oLaSbTe) can be looked as a stacking of 2D topological insulators in each lattice space. The structural phase transition from tLaSbTe to oLaSbTe due to soft phonon modes demonstrates how the real space change can lead to the modification of topological states. Their symmetrybased indicators and topological invariants have been analyzed based on LC. We propose that LaSbTe is an ideal paradigm perfectly demonstrating the LC scheme, which bridges the crystal structures in real space to the band topology in momentum space. 

U54.00013: Fillingenforced Dirac loops and their evolutions under various perturbations Dexi Shao Based on symmetry analysis, we find that fillingenforced Dirac loops (FEDLs) in nonmagnetic systems exist in only five space groups. We further explore all possible configurations of these FEDLs in these space groups, and classify them accordingly. We study the evolutions of the FEDLs under various types of perturbations such as applied strain or field. It is interesting that the FEDLmaterials can serve as both parent materials of nodal semimetals having Dirac points or nodalloops, and topological insulators/topological crystalline insulators. Many the FEDLmaterials are predicted in DFT calculations. 
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