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We study the anomalous Hall conductivity in spin-polarized, asymmetricallyconfined two-dimensional electron and hole systems, focusing on skew-scatteringcontributions to the transport. We find that the skew scattering, principallyresponsible for the extrinsic contribution to the anomalous Hall effect,vanishes for the two-dimensional electron system if both chiral Rashba subbandsare partially occupied, and vanishes always for the two-dimensional hole gasstudied here, regardless of the band filling. Our prediction can be tested withthe proposed coplanar two-dimensional electron/hole gas device and can be usedas a benchmark to understand the crossover from the intrisic to the extrinsicanomalous Hall effect.Comment: 4 pages, 2 figures include

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