Berry Curvature on the Fermi Surface: Anomalous Hall Effect as a Topological Fermi-Liquid Property

TL;DR

This paper demonstrates that the intrinsic anomalous Hall effect in metallic ferromagnets is governed by Berry phases on the Fermi surface, establishing it as a topological Fermi-liquid property rather than a bulk property.

Contribution

It introduces Berry phases as a topological factor in Fermi-liquid theory, linking the anomalous Hall effect to Fermi surface properties in ferromagnets.

Findings

The anomalous Hall effect is controlled by Berry phases on the Fermi surface.

Berry phases are essential topological ingredients in Fermi-liquid theory with broken symmetries.

The effect is a Fermi-liquid property, not a bulk Fermi sea property.

Abstract

The intrinsic anomalous Hall effect in metallic ferromagnets is shown to be controlled by Berry phases accumulated by adiabatic motion of quasiparticles on the Fermi surface, and is purely a Fermi-liquid property, not a ``bulk'' Fermi sea property like Landau diamagnetism, as has been previously supposed. Berry phases are a new topological ingredient that must be added to Landau Fermi-liquid theory in the presence of broken inversion or time-reversal symmetry.