2021-05-09T18:41:34Z
https://digital.csic.es/dspace-oai/request
oai:digital.csic.es:10261/218329
2020-09-04T11:56:23Z
com_10261_115
com_10261_3
col_10261_368
http://hdl.handle.net/10261/218329
http://dx.doi.org/10.1103/PhysRevB.101.155130
399102
Axion coupling in the hybrid Wannier representation
American Physical Society
2020
Varnava, Nicodemos
Souza, Ivo
Vanderbilt, David
2020
Many magnetic point-group symmetries induce a topological classification on crystalline insulators, dividing them into those that have a nonzero quantized Chern-Simons magnetoelectric coupling (“axion-odd” or “topological”) and those that do not (“axion-even” or “trivial”). For time-reversal or inversion symmetries, the resulting topological state is usually denoted as a “strong topological insulator” or an “axion insulator,” respectively, but many other symmetries can also protect this “axion Z2” index. Topological states are often insightfully characterized by choosing one crystallographic direction of interest and inspecting the hybrid Wannier (or equivalently, the non-Abelian Wilson-loop) band structure, considered as a function of the two-dimensional Brillouin zone in the orthogonal directions. Here, we systematically classify the axion-quantizing symmetries and explore the implications of such symmetries on the Wannier band structure. Conversely, we clarify the conditions under which the axion Z2 index can be deduced from the Wannier band structure. In particular, we identify cases in which a counting of Dirac touchings between Wannier bands, or a calculation of the Chern number of certain Wannier bands, or both, allows for a direct determination of the axion Z2 index. We also discuss when such symmetries impose a “flow” on the Wannier bands, such that they are always glued to higher and lower bands by degeneracies somewhere in the projected Brillouin zone, and the related question of when the corresponding surfaces can remain gapped, thus exhibiting a half-quantized surface anomalous Hall conductivity. Our formal arguments are confirmed and illustrated in the context of tight-binding models for several paradigmatic axion-odd symmetries, including time reversal, inversion, simple mirror, and glide mirror symmetries.
Ministerio de Economía y Competitividad (España)
Ministerio de Ciencia e Innovación (España)
Institute for Quantum Information and Matter (US)
Department of Energy (US)
Physical Review B
2020
101
155130