Mirror Chern numbers in the hybrid Wannier representation
| Autor: | Ivo Souza, David Vanderbilt, Thomas Olsen, Tomáš Rauch |
|---|---|
| Přispěvatelé: | National Science Foundation (US), German Research Foundation, Ministerio de Economía y Competitividad (España) |
| Rok vydání: | 2021 |
| Předmět: |
Physics
Wannier function Toy model Chern class Condensed Matter - Mesoscale and Nanoscale Physics FOS: Physical sciences 02 engineering and technology 021001 nanoscience & nanotechnology Coupling (probability) 01 natural sciences Brillouin zone Quantum mechanics Mesoscale and Nanoscale Physics (cond-mat.mes-hall) 0103 physical sciences Homogeneous space 010306 general physics 0210 nano-technology Electronic band structure Mirror symmetry |
| Zdroj: | Rauch, T, Olsen, T, Vanderbilt, D & Souza, I 2021, ' Mirror Chern numbers in the hybrid Wannier representation ', Physical Review B, vol. 103, no. 19, 195103 . https://doi.org/10.1103/PhysRevB.103.195103 Digital.CSIC. Repositorio Institucional del CSIC instname |
| ISSN: | 2469-9969 2469-9950 |
| Popis: | The topology of electronic states in band insulators with mirror symmetry can be classified in two different ways. One is in terms of the mirror Chern number, an integer that counts the number of protected Dirac cones in the Brillouin zone of high-symmetry surfaces. The other is via a Z2 index that distinguishes between systems that have a nonzero quantized orbital magnetoelectric coupling (“axion-odd”), and those that do not (“axion-even”); this classification can also be induced by other symmetries in the magnetic point group, including time reversal and inversion. A systematic characterization of the axion Z2 topology has previously been obtained by representing the valence states in terms of hybrid Wannier functions localized along one chosen crystallographic direction, and inspecting the associated Wannier band structure. Here we focus on mirror symmetry, and extend that characterization to the mirror Chern number. We choose the direction orthogonal to the mirror plane as the Wannierization direction and show that the mirror Chern number can be determined from the winding numbers of the touching points between Wannier bands on mirror-invariant planes and from the Chern numbers of flat bands pinned to those planes. In this representation, the relation between the mirror Chern number and the axion Z2 index is readily established. The formalism is illustrated by means of ab initio calculations for SnTe in the monolayer and bulk forms, complemented by tight-binding calculations for a toy model. Work by T.R. was supported by the Deutsche Forschungsgemeinschaft Grant No. Ra 3025/1-1 from the Deutsche Forschungsgemeinschaft. Work by D.V. was supported by National Science Foundation Grant DMR-1954856. Work by I.S. was supported by Grant No. FIS2016-77188-P from the Spanish Ministerio de Economía y Competitividad. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|