Cavity Induced Topology in Graphene

Strongly coupling materials to cavity fields can affect their electronic properties altering the phases of matter. We study the monolayer graphene whose electrons are coupled to both left and right circularly polarized photons, 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 sizable topological band gap at Dirac nodes in vacuum and when the cavity is prepared in an excited Fock state. Remarkably, band gaps also open in light-matter hybridization points away from the Dirac nodes giving rise to topological photo-electron bands with high Chern numbers. We reveal that the physical mechanism behind this phenomenon lies on the exchange of chiral photons with electronic matter at the hybridization points, and the number and polarization of exchanged photons determine the Chern number. This is a generic microscopic mechanism for the photo-electron band topology. Our theory shows that graphene-based materials, with no need of Floquet engineering and hence protected from the heating effects, host high Chern insulator phases when coupled to chiral cavity fields.