TY - JOUR

T1 - Topology invisible to eigenvalues in obstructed atomic insulators

AU - Cano, Jennifer

AU - Elcoro, L.

AU - Aroyo, M. I.

AU - Bernevig, B. Andrei

AU - Bradlyn, Barry

N1 - Funding Information:
The authors acknowledge M. Garcia Vergniory, Z. Wang, and B. Wieder for helpful conversations while working on earlier publications. J.C. acknowledges support from the Flatiron Institute, a division of the Simons Foundation, and the National Science Foundation under Grant No. DMR-1942447. B.B. acknowledges support from the Alfred P. Sloan Foundation, and the National Science Foundation under Grant No. DMR-1945058. B.A.B.'s work was primarily supported by the DOE Grant No. DE-SC0016239, the Schmidt Fund for Innovative Research, Simons Investigator Grant No. 404513, and the Packard Foundation. B.A.B. also acknowledges support from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (Grant Agreement No. 101020833). M.I.A. and L.E. are supported by the Government of the Basque Country (Project No. IT1301-19) and the Spanish Ministry of Science and Innovation (PID2019-106644GB-I00).
Publisher Copyright:
© 2022 American Physical Society.

PY - 2022/3/15

Y1 - 2022/3/15

N2 - We consider the extent to which symmetry eigenvalues reveal the topological character of bands. Specifically, we compare distinct atomic limit phases (band representations) that share the same irreducible representations (irreps) at all points in the Brillouin zone and, therefore, appear equivalent in a classification based on eigenvalues. We derive examples where such "irrep-equivalent"phases can be distinguished by a quantized Berry phase or generalization thereof. These examples constitute a generalization of the Su-Schrieffer-Heeger chain: neither phase is topological, in the sense that localized Wannier functions exist, yet there is a topological obstruction between them. We refer to two phases as "Berry obstructed atomic limits"if they have the same irreps, but differ by Berry phases. This is a distinct notion from eigenvalue obstructed atomic limits, which differ in their symmetry irreps at some point in the Brillouin zone. We compute exhaustive lists of elementary band representations that are irrep equivalent, in all space groups, with and without time-reversal symmetry and spin-orbit coupling, and use group theory to derive a set of necessary conditions for irrep equivalence. Finally, we conjecture, and in some cases prove, that irrep-equivalent elementary band representations that are not equivalent can be distinguished by a topological invariant.

AB - We consider the extent to which symmetry eigenvalues reveal the topological character of bands. Specifically, we compare distinct atomic limit phases (band representations) that share the same irreducible representations (irreps) at all points in the Brillouin zone and, therefore, appear equivalent in a classification based on eigenvalues. We derive examples where such "irrep-equivalent"phases can be distinguished by a quantized Berry phase or generalization thereof. These examples constitute a generalization of the Su-Schrieffer-Heeger chain: neither phase is topological, in the sense that localized Wannier functions exist, yet there is a topological obstruction between them. We refer to two phases as "Berry obstructed atomic limits"if they have the same irreps, but differ by Berry phases. This is a distinct notion from eigenvalue obstructed atomic limits, which differ in their symmetry irreps at some point in the Brillouin zone. We compute exhaustive lists of elementary band representations that are irrep equivalent, in all space groups, with and without time-reversal symmetry and spin-orbit coupling, and use group theory to derive a set of necessary conditions for irrep equivalence. Finally, we conjecture, and in some cases prove, that irrep-equivalent elementary band representations that are not equivalent can be distinguished by a topological invariant.

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U2 - 10.1103/PhysRevB.105.125115

DO - 10.1103/PhysRevB.105.125115

M3 - Article

AN - SCOPUS:85126911955

VL - 105

JO - Physical Review B

JF - Physical Review B

SN - 2469-9950

IS - 12

M1 - 125115

ER -