Anomalous Hall effect in Rashba two-dimensional electron systems based on narrow-band semiconductors: side-jump and skew scattering mechanisms

TL;DR

This paper investigates the anomalous Hall effect in two-dimensional narrow-band semiconductors with Rashba and extrinsic spin-orbit couplings, identifying contributions from side-jump and skew scattering mechanisms through a kinetic equation approach.

Contribution

It introduces a comprehensive kinetic equation framework to analyze both side-jump and skew scattering contributions to the anomalous Hall effect in Rashba systems, including effects of external electric fields.

Findings

Side-jump current includes contributions from extrinsic and Rashba SO couplings.

Skew scattering arises from anisotropic distribution functions influenced by Rashba and extrinsic SO.

Numerical results show dependencies of Hall conductivities on magnetization and Rashba coupling.

Abstract

We employ a helicity-basis kinetic equation approach to investigate the anomalous Hall effect in two-dimensional narrow-band semiconductors considering both Rashba and extrinsic spin-orbit (SO) couplings, as well as a SO coupling directly induced by an external driving electric field. Taking account of long-range electron-impurity scattering up to the second Born approximation, we find that the various components of the anomalous Hall current fit into two classes: (a) side-jump and (b) skew scattering anomalous Hall currents. The side-jump anomalous Hall current involves contributions not only from the extrinsic SO coupling but also from the SO coupling due to the driving electric field. It also contains a component which arises from the Rashba SO coupling and relates to the off-diagonal elements of the helicity-basis distribution function. The skew scattering anomalous Hall effect arises from the anisotropy of the diagonal elements of the distribution function and it is a result of both the Rashba and extrinsic SO interactions. Further, we perform a numerical calculation to study the anomalous Hall effect in a typical InSb/AlInSb quantum well. The dependencies of the side-jump and skew scattering anomalous Hall conductivities on magnetization and on the Rashba SO coupling constant are examined.