Absence of Skew Scattering in Two-Dimensional Systems: Testing the Origins of the Anomalous Hall Effect

We study the anomalous Hall conductivity in spin-polarized, asymmetrically confined two-dimensional electron and hole systems, taking into account the intrinsic, side-jump, and skew-scattering contributions to the transport. We find that the skew scattering, principally responsible for the extrinsic contribution to the anomalous Hall effect, vanishes for the two-dimensional electron system if both chiral Rashba subbands are partially occupied, and vanishes always for the two-dimensional hole gas studied here, regardless of the band filling. Our prediction can be tested with the proposed coplanar two-dimensional electron-hole gas device and can be used as a benchmark to understand the crossover from the intrinsic to the extrinsic anomalous Hall effect.

Figure 1

Diagramatic representatation of the skew-scattering contribution to ${\sigma }_{yx}$. Both current vertices, denoted by squares, are renormalized by ladder vertex corrections.

Figure 2

Top panel: Top-view schematics of the Hall bar with coplanar 2D hole and electron gases. Spin-polarized carriers are generated by shining circularly polarized light on the $p\mathrm{\text{−}}n$ junction. Center bottom panel: Cross section of the heterostructure containing $p$-type and $n$-type $\mathrm{AlGaAs}/\mathrm{GaAs}$ single junctions. The left band diagram shows the unetched part of the wafer with the 2D hole gas, the right band diagram shows the 2D electron gas in the etched section of the wafer.