The non-commutative n-th Chern number

TL;DR

This paper develops a theory for higher Chern numbers in strongly disordered systems, establishing conditions for their quantization and invariance, with implications for topological insulators.

Contribution

It introduces a rigorous framework for non-commutative higher Chern numbers, addressing disorder effects in topological phases.

Findings

Proves sharp quantization of non-commutative Chern numbers.

Establishes homotopy invariance under disorder.

Connects mathematical theory to disordered topological insulators.

Abstract

The theory of the higher Chern numbers in the presence of strong disorder is developed. Sharp quantization and homotopy invariance conditions are provided. The relevance of the result to the field of strongly disordered topological insulators is discussed.