Quantum criticality at the Chern-to-normal insulator transition

TL;DR

This paper investigates the quantum critical behavior at the transition from Chern insulators to normal insulators using advanced numerical methods, revealing universal scaling laws and notable differences from quantum Hall effect experiments.

Contribution

It applies a non-commutative Kubo formula and numerical techniques to analyze transport at the Chern-to-trivial insulator transition, uncovering universal scaling and key differences from experimental observations.

Findings

Resistivity curves intersect at a single critical point.

Scaling law with an exponent close to the universal value for the unitary class.

Critical conductance is twice as large as in experiments.

Abstract

Using the non-commutative Kubo formula for aperiodic solids [1-3] and a recently developed numerical implementation [4], we study the conductivity $\sigma$ and resistivity $\rho$ tensors as functions of Fermi level and temperature, for models of strongly disordered Chern insulators. The formalism enabled us to converge the transport coefficients at temperatures low enough to enter the quantum critical regime at the Chern-to-trivial insulator transition. We find that the $\rho_{xx}$-curves at different temperatures intersect each other at one single critical point, and that they obey a single-parameter scaling law with an exponent close to the universally accepted value for the unitary symmetry class. However, when compared with the established experimental facts on the plateau-insulator transition in the Integer Quantum Hall Effect, we find a universal critical conductance $\sigma_{xx}^c$ twice as large, an ellipse rather than a semi-circle law, and absence of the quantized Hall insulator phase.