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

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

2006-09-18

arxiv.org/abs/cond-mat/0609412v1

Physics

Condensed Matter

Materials Science

16 pages, 4 figures, accepted for publication in PRB

Scientific paper

10.1103/PhysRevB.74.165316

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.

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