Anomalous Hall Effect in non-commutative mechanics

Abstract

The anomalous velocity term in the semiclassical model of a Bloch electron deviates the trajectory from the conventional one. When the Berry curvature (alias noncommutative parameter) is a monopole in momentum space as found recently in some ferromagnetic semiconductors while observing the anomalous Hall effect, we get a transverse shift, similar to that in the optical Hall effect.Comment: 4 pages. A figure added. To be published in Phys. Lett.