Topological Insulators,Weyl Semimetals and Topological Superconductors A Transport View

TL;DR

This paper explores the topological classification of electronic bands, emphasizing how topological invariants relate to physical properties like zero modes, with applications to topological insulators and superconductors.

Contribution

It introduces a method to compute connection and curvature for electronic bands, linking topological invariants to physical phenomena in topological materials.

Findings

Topological invariants determine the existence of zero modes.

The method applies to topological insulators and superconductors.

Physical properties are governed by band topology.

Abstract

The electronic bands are classified according to their topology. We compute the connection and curvature for the electronic bands and show that the physical properties are determined by topological invariants which are equivalent to the existence of the zero modes. We apply this method to the Topological Insulators and Topogical Superconductors.