Anomalous Hall effect with massive Dirac fermions
The anomalous Hall effect arises in systems with both spin-orbit coupling and magnetization.
We study the minimal model of the anomalous Hall effect based on the massive Dirac Hamiltonian and consider two
limiting cases of weak (Gaussian) and strong (Poisson) impurities.
The standard diagrammatic approach to the problem is limited to computation of ladder diagrams.
We demonstrate that this is insufficient in the case of Gaussian disorder. An important additional contribution comes from
scattering on pairs of closely located defects and essentially modifies previously obtained results for anomalous Hall conductivity.
n the case of Poisson disorder, we go beyond semiclassical limit and calculate weak
localization corrections. Unlike the case of ordinary Hall effect, we identify a finite quantum correction to anomalous Hall resistivity.
Depending on the structure of impurities, this correction can have any sign and interpolates smoothly between universal orthogonal
(localization) and symplectic (antilocalization) limits.