Chern numbers as half-signature of the spectral localizer

Lozano Viesca E, Schober J, Schulz-Baldes H (2019)

Publication Type: Journal article

Publication year: 2019

Journal

Journal of Mathematical Physics American Institute of Physics (AIP)

Book Volume: 60

Article Number: 0721011

Journal Issue: 7

DOI: 10.1063/1.5094300

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.

Authors with CRIS profile

Jonas Schober
Hermann Schulz-Baldes Professur für Mathematik (Mathematische Physik)

Involved external institutions

National Autonomous University of Mexico / Universidad Nacional Autónoma de México (UNAM) MX Mexico (MX)

How to cite

APA:

Lozano Viesca, E., Schober, J., & Schulz-Baldes, H. (2019). Chern numbers as half-signature of the spectral localizer. Journal of Mathematical Physics, 60(7). https://dx.doi.org/10.1063/1.5094300

MLA:

Lozano Viesca, Edgar, Jonas Schober, and Hermann Schulz-Baldes. "Chern numbers as half-signature of the spectral localizer." Journal of Mathematical Physics 60.7 (2019).

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