Topological quantum criticality of the disordered Chern insulator

TL;DR

This paper investigates the critical states in disordered Chern insulators, identifying conditions for their existence and properties, and mapping a critical surface in the phase space through analytical and numerical methods.

Contribution

It introduces geometric criteria for identifying critical states in disordered Chern insulators and extends their analysis into strong disorder regimes.

Findings

Critical states exist with diverging localization length.

A critical surface is mapped in energy, disorder, and topological parameters.

Numerical analysis confirms the multifractal nature of critical states.

Abstract

We consider the two-dimensional topological Chern insulator in the presence of static disorder. Generic quantum states in this system are Anderson localized. However, topology requires the presence of a subset of critical states, with diverging localization length (the Chern insulator analog of the `center of the Landau band states' of the quantum Hall insulator.) We discuss geometric criteria for the identification of these states at weak disorder, and their extension into the regime of strong disorder by analytical methods. In this way, we chart a critical surface embedded in a phase space spanned by energy, topological control parameter, and disorder strength. Our analytical predictions are supplemented by a numerical analysis of the position of the critical states, and their multifractal properties.