Anomalous Hall Effect in non-commutative mechanics

TL;DR

This paper explores how Berry curvature acts as a noncommutative parameter affecting electron trajectories, leading to a transverse shift in the anomalous Hall effect, akin to optical Hall phenomena.

Contribution

It introduces a non-commutative mechanics framework to explain the anomalous Hall effect with Berry curvature as a monopole in momentum space.

Findings

Berry curvature causes a transverse shift in electron trajectories.

The effect is analogous to optical Hall effects.

Monopole-like Berry curvature explains the anomalous Hall effect in ferromagnetic semiconductors.

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.