Chern numbers as half-signature of the spectral localizer
Abstract
Two recent papers proved that complex index pairings can be calculated as the half-signature of a finite dimensional matrix, called the spectral localizer. This paper contains a new proof of this connection for even index pairings based on a spectral flow argument. It also provides a numerical study of the spectral gap and the half-signature of the spectral localizer for a typical two-dimensional disordered topological insulator in the regime of a mobility gap at the Fermi energy. This regime is not covered by the above mathematical results (which suppose a bulk gap), but nevertheless the half-signature of the spectral localizer is a clear indicator of a topological phase.
- Publication:
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Journal of Mathematical Physics
- Pub Date:
- July 2019
- DOI:
- 10.1063/1.5094300
- arXiv:
- arXiv:1907.11382
- Bibcode:
- 2019JMP....60g2101L
- Keywords:
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- Mathematical Physics
- E-Print:
- to appear in JMP