Chern numbers as halfsignature of the spectral localizer
Abstract
Two recent papers proved that complex index pairings can be calculated as the halfsignature 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 halfsignature of the spectral localizer for a typical twodimensional 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 halfsignature of the spectral localizer is a clear indicator of a topological phase.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 July 2019
 DOI:
 10.1063/1.5094300
 arXiv:
 arXiv:1907.11382
 Bibcode:
 2019JMP....60g2101L
 Keywords:

 Mathematical Physics
 EPrint:
 to appear in JMP