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

TL;DR

This paper unifies different theoretical approaches to the anomalous Hall effect in Rashba systems, revealing a new hybrid skew scattering regime that dominates under certain conditions and can be experimentally observed.

Contribution

It provides an analytical framework unifying Keldysh, Boltzmann, and Kubo formalisms for AHE, identifying a novel hybrid skew scattering regime in Rashba systems.

Findings

Identifies a new hybrid skew scattering regime in AHE.

Unifies three linear response formalisms for AHE.

Predicts experimental detection via remote doping.

Abstract

We present the analytical description of the anomalous Hall effect (AHE) in a 2DEG ferromagnet within the Keldysh formalism. These results unify all three linear response approaches to anomalous Hall transport and close a long standing debate. 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, {\em 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, dominate when both subbands are occupied; this regime can be detected by variable remote doping experiments that we describe.