Vacuum anomalous Hall effect in gyrotropic cavity

TL;DR

This paper demonstrates that vacuum fluctuations in a gyrotropic cavity induce a topologically nontrivial state in an electron gas, resulting in an anomalous Hall effect, edge currents, and magnetization, with analytical expressions derived.

Contribution

It reveals how light-matter interactions in a gyrotropic cavity induce a topological electron state with measurable Hall effects, providing analytical formulas for these phenomena.

Findings

Vacuum fluctuations induce a nonzero Berry curvature.

The system exhibits an anomalous Hall effect and edge currents.

Analytical expressions for Hall conductivity and magnetization are derived.

Abstract

We consider the ground state of an electron gas embedded in a quantum gyrotropic cavity. We show that the light-matter interaction leads to a nontrivial topology of the many-body electron-photon wave function characterized by a nonzero Berry curvature. Physically, the latter manifests as the anomalous Hall effect, appearance of equilibrium edge/surface currents and orbital magnetization induced by vacuum fluctuations. Remarkably, closed analytical expressions for the anomalous Hall conductivity and macroscopic magnetization are obtained for the interacting many-body case.