Invariants of disordered semimetals via the spectral localizer

TL;DR

This paper extends the spectral localizer method to disordered semimetals, enabling efficient numerical detection of topological invariants, Dirac/Weyl points, and surface states in complex materials.

Contribution

The authors adapt the spectral localizer technique to disordered semimetals, providing a new computational tool for topological analysis.

Findings

Successfully detects Dirac and Weyl points in disordered systems.

Accesses weak topological invariants indicating surface states.

Extends spectral localizer applicability beyond topological insulators.

Abstract

The spectral localizer consists of placing the Hamiltonian in a Dirac trap. For topological insulators its spectral asymmetry is equal to the topological invariants, providing a highly efficient tool for numerical computation. Here this technique is extended to disordered semimetals and allows to access the number of Dirac or Weyl points as well as weak invariants. These latter invariants imply the existence of surface states.