nLab anomalous velocity

Contents

Idea

In crystalline materials whose Berry curvature Ω\Omega of the valence band is non-vanishing over the Brillouin torus of crystal momenta, the semiclassical equation of motion for movement of electron states in momentum space contains an extra “anomalous” term proportional to Ω\Omega. This is a momentum-space analogue of what for electrons moving through position space in the presence of magnetic field flux density FF is the Lorentz force.

Accordingly, like the Lorentz force in the presence of an ambient magnetic field (the latter being the curvature of the electromagnetic gauge potential) is the cause of the Hall effect, so this anomalous velocity, induced instead by Berry curvature in momentum space, is the cause of the anomalous Hall effect.

References

The original articles:

From the point of view of relativistic field theory:

Review:

Last revised on June 3, 2025 at 18:50:59. See the history of this page for a list of all contributions to it.