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Topological indices in condensed matter

Hermann Schulz-Baldes

Abstract

This contribution describes the mathematical theory of topological indices in solid state systems composed of non-interacting Fermions. In particular, this covers the spectral localizer and the bulk-boundary correspondence.

Topological indices in condensed matter

Abstract

This contribution describes the mathematical theory of topological indices in solid state systems composed of non-interacting Fermions. In particular, this covers the spectral localizer and the bulk-boundary correspondence.
Paper Structure (7 sections, 29 equations, 1 table)

This paper contains 7 sections, 29 equations, 1 table.

Table of Contents

  1. Short history
  2. Topological indices of covariant systems
  3. Index theorems
  4. ${\mathbb Z}_2$-invariants
  5. Spectral localizer
  6. Connecting indices via exact sequences
  7. Delocalization of boundary states