Hybrid skew scattering regime of the anomalous Hall effect in Rashba systems: Unifying Keldysh, Boltzmann, and Kubo formalisms

We present the analytical description of the anomalous Hall effect (AHE) in a two-dimensional electron gas (2DEG) ferromagnet within the Keldysh formalism. These results unify the three linear-response approaches to AHE and close the debate on previous discrepancies. We are able to identify a new extrinsic AHE regime dominated by a hybrid skew scattering mechanism. This new contribution is inversely proportional to the impurity concentration, resembling the normal skew scattering, but independent of the impurity strength, resembling the side-jump mechanism. Within the Kubo formalism this regime is captured by higher order diagrams which, although weak, can dominate when both subbands are occupied; this regime can be detected by variable remote doping experiments.