Abstract
We present a kinetic equation approach to investigate the anomalous Hall effect in two-dimensional systems with magnetization considering both electron-impurity and electron-phonon scatterings. In our study, the spin-orbit interaction due to the external driving electric field as well as the extrinsic spin-orbit couplings induced by electron-impurity and electron-phonon scatterings are taken into account, while the intrinsic Rashba and Dresselhaus spin-orbit couplings are ignored. We derive the side-jump contributions to anomalous Hall current in terms of the distribution function and obtain the skew-scattering contribution by considering electron-impurity (and electron-phonon) scattering up to the second Born approximation. By performing a numerical calculation for InSb-based quantum wells, the temperature dependencies of the various components of anomalous Hall current are examined. We also discuss the roles of electron-impurity and electron-phonon scatterings in contributing to the total anomalous Hall current.
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