A New Numerical Method for $\mathbb{Z}_2$ Topological Insulators with Strong Disorder
| Autor: | Hosho Katsura, Tohru Koma, Yutaka Akagi |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Physics
Condensed Matter - Mesoscale and Nanoscale Physics Periodic table (large cells) Numerical analysis Structure (category theory) FOS: Physical sciences General Physics and Astronomy Disordered Systems and Neural Networks (cond-mat.dis-nn) Condensed Matter - Disordered Systems and Neural Networks 01 natural sciences Spectrum (topology) 010305 fluids & plasmas Topological insulator Mesoscale and Nanoscale Physics (cond-mat.mes-hall) 0103 physical sciences 010306 general physics Mathematical physics |
| Popis: | We propose a new method to numerically compute the $\mathbb{Z}_2$ indices for disordered topological insulators in Kitaev's periodic table. All of the $\mathbb{Z}_2$ indices are known to be derived from the index formulae which are expressed in terms of a pair of projections introduced by Avron, Seiler, and Simon. For a given pair of projections, the corresponding index is determined by the spectrum of the difference between the two projections. This difference exhibits remarkable and useful properties, as it is compact and has a supersymmetric structure in the spectrum. These properties make it possible to numerically determine the indices of disordered topological insulators highly efficiently. The method is demonstrated for the Bernevig-Hughes-Zhang and Wilson-Dirac models whose topological phases are characterized by a $\mathbb{Z}_2$ index in two and three dimensions, respectively. 5 pages, 3 figures |
| Databáze: | OpenAIRE |
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