Fermi-liquid corrections to the intrinsic anomalous Hall conductivity of topological metals

TL;DR

This paper demonstrates that Fermi-liquid interactions contribute to the intrinsic anomalous Hall conductivity in topological metals lacking time-reversal symmetry, extending the understanding of topological observables beyond Berry phase effects.

Contribution

It introduces the role of Fermi-liquid corrections in the intrinsic anomalous Hall conductivity, highlighting their importance alongside Berry phase contributions in topological metals.

Findings

Fermi-liquid corrections modify the anomalous Hall conductivity.

Vertex corrections are essential for accurate topological observable calculations.

Implications for metals near a doping-driven Mott transition.

Abstract

We show that topological metals lacking time-reversal symmetry have an intrinsic non-quantized component of the anomalous Hall conductivity which is contributed not only by the Berry phase of quasiparticles on the Fermi surface, but also by Fermi-liquid corrections due to the residual interactions among quasiparticles, the Landau f-parametes. These corrections pair up with those that modify the optical mass with respect to the quasiparticle effective one, or the charge compressibility with respect to the quasiparticle density of states. Our result supports recent claims that the correct expressions for topological observables include vertex corrections besides the topological invariants built just upon the Green's functions. Furthermore, it demonstrates that such corrections are naturally accounted for by Landau's Fermi liquid theory, here extended to the case in which coherence effects between bands crossing the chemical potential and those that are instead away from it play a crucial role, as in the anomalous Hall conductivity, and have important implications when those metals are on the verge of a doping-driven Mott transition, as we discuss.