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.

arXiv commentto appear in JMP

References in corpus (6)

• The Non-Commutative Geometry of the Quantum Hall Effect
• K-Theory and Pseudospectra for Topological Insulators
• Index pairings in presence of symmetries with applications to topological insulators
• Z_2 indices and factorization properties of odd symmetric Fredholm operators
• Spectral flows of dilations of Fredholm operators
• Localization and Chern numbers for weakly disordered BdG operators

Cited by in corpus (8)

• On the Bott index of unitary matrices on a finite torus
• Real-space topological localizer index to fully characterize the dislocation skin effect
• Two-Dimensional Time-Reversal-Invariant Topological Insulators via Fredholm Theory
• Even spheres as joint spectra of matrix models
• Topological zero-modes of the spectral localizer of trivial metals
• Global and Local Topological Crystalline Markers for Rotation-Symmetric Insulators
• Majorana-metal transition in a disordered superconductor: percolation in a landscape of topological domain walls
• Gapless superconductivity and its real-space topology in quasicrystals