Critical behavior of the transport coefficients at the Chern-to-normal insulator transition

Using the non-commutative Kubo formula for disordered lattice systems, we mapped the conductivity tensor $\sigma_{xx}$($E_F$,$T$) and $\sigma_{xy}$($E_F$,$T$) as function of Fermi level $E_F$ and temperature $T$, for a model of a Chern insulator in the presence of strong disorder. In line with previous studies, $\sigma_{xy}$ displays a quantized non-trivial value near the half-filling, value that changes rapidly to a trivial value as $E_F$ crosses a critical value $E^c_F$. As expected, the $T$-dependence of $\sigma_{xx}$ display the typical signature of the insulating behavior, except at $E^c_F$. Examining the resistivity tensor $\hat\rho=\hat\sigma^{-1}$, we found that the data looks extremely similar to the experimental data for the plateau-insulator transition in the Integer Quantum Hall Effect: 1)$\rho_{xx}$($E_F$,$T$) vs $E_F$ plots for various temperatures intersect each other at precisely one point; 2) At this $E^c_F$, $\rho_{xx} \approx 1$ and $\sigma_{xy} \approx 0.5$; 3) The plots near $E^c_F$ for different temperatures collapse into one curve when rescaled with an exponent that is consistent with the universally accepted value.