  The anomalous Hall effect (AHE) is highly sensitive to disorder in the
metallic phase. Here we show that statistical correlations between the charge
and spin disorder sectors strongly affect both the longitudinal conductivity
and the sign/magnitude of AHE. Correlations between mass and charge disorder
can be absorbed into an effective mass. In general, random gauge fields are
also present due to e.g. in-plane component of magnetization in topological
insulator, causing an anisotropy in conductivity. As the correlation between
the charge and gauge-mass components increases, so does the AHE, achieving its
universal value, and even exceed it, although the system is an impure metal.
The AHE can change sign when the anti-correlations reverse the effective mass,
a possible mechanism behind the sign change seen in recent experiments.

Disordered Systems and Neural Networks;Mesoscale and Nanoscale Physics