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HL: Fachverband Halbleiterphysik
HL 5: Topological insulators
HL 5.1: Vortrag
Montag, 1. April 2019, 09:30–09:45, H36
Mirror Chern number in the hybrid Wannier representation — •Tomáš Rauch1,2, Thomas Olsen3, David Vanderbilt4, and Ivo Souza2,5 — 1Friedrich-Schiller-University Jena, Germany — 2Centro de Física de Materiales, San Sebastián — 3Technical University of Denmark, Kongens Lyngby, Denmark — 4Rutgers University, Piscataway, New Jersey, USA — 5Ikerbasque Foundation, Bilbao, Spain
We formulate the mirror Chern number (MCN) of a two-dimensional insulator with reflection symmetry Mz in terms of hybrid Wannier functions (the eigenfunctions of PẑP, the position operator projected onto the valence bands) localized perpendicular to the mirror plane. Because PẑP and Mz anticommute, the spectrum of “Wannier bands” is symmetric about the mirror plane, and an excess of one mirror eigenvalue over the other in the occupied manifold leads to the appearance of flat bands on the mirror plane. In the absence of flat bands, pairs of dispersive bands may touch at isolated points on the mirror plane. These Dirac nodes are protected by reflection symmetry, and the MCN is given by the sum of their winding numbers. When flat bands are present the Dirac nodes are no longer protected, and the MCN is related instead to the Chern number of the flat bands. In some cases the magnitude of the MCN can be determined without constructing Mz explicitly. In three dimensions, the present formalism reveals a simple relation between the MCNs and the quantized axion angle θ, whose expression in the hybrid Wannier representation was previously obtained.