Real-space representation of the second Chern number

TL;DR

This paper extends real-space methods to compute the second Chern number, enabling analysis of higher-dimensional topological phases in disordered systems where momentum-space approaches are limited.

Contribution

It introduces a real-space formulation for the second Chern number and validates it using the disordered Wilson-Dirac model, advancing topological phase characterization.

Findings

Real-space approach successfully computes the second Chern number.

Method effectively captures topological properties in disordered systems.

Framework extends topological analysis beyond momentum-space limitations.

Abstract

We extend Kitaev's real-space formulation of the first Chern number to the second Chern number and establish a computational framework for its evaluation. To test its validity, we apply the derived formula to the disordered Wilson-Dirac model and analyze its ability to capture topological properties in the presence of disorder. Our results demonstrate that the real-space approach provides a viable method for characterizing higher-dimensional topological phases beyond momentum-space formulations.