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, this 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.

• Received 17 April 2021
• Revised 8 July 2021
• Accepted 3 August 2021

DOI:https://doi.org/10.1103/PhysRevB.104.L081408