Engineering topology in graphene with chiral cavities

Strongly coupling materials to cavity fields can affect their electronic properties altering the phases of matter. We study monolayer graphene whose electrons are coupled to both left and right circularly polarized vacuum fluctuations, and time-reversal symmetry is broken due to a phase shift between the two polarizations. We develop a many-body perturbative theory, and derive cavity-mediated electronic interactions. This theory leads to a gap equation which predicts a topological band gap at Dirac nodes in vacuum and when the cavity is prepared in an excited Fock state. Remarkably, topological band gaps also open in light-matter hybridization points away from the Dirac nodes giving rise to photoelectron bands with high Chern numbers. We reveal that the physical mechanism behind this phenomenon is generic and due to the exchange of photons with electronic matter at the hybridization points. Specifically, the number and polarization of exchanged photons directly determine the band topology of graphene subject to enhanced chiral vacuum fluctuations. Hence, our theory shows that graphene-based materials could host Chern insulator phases in engineered electromagnetic environments, bridging cavity quantum electrodynamics to Floquet engineering of materials while protected from the ensuing heating effects.