Quantum criticality at the Chern-to-normal insulator transition

Abstract

Using the noncommutative Kubo formula for aperiodic solids and a recently developed numerical implementation, we study the conductivity $\ensuremath{\sigma}$ and resistivity $\ensuremath{\rho}$ tensors as functions of Fermi level ${E}_{F}$ and temperature $T$ 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 ${\ensuremath{\rho}}_{xx}$ 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 ${\ensuremath{\sigma}}_{xx}^{c}$ twice as large, an ellipse rather than a semicircle law, and absence of the quantized Hall insulator phase.