Hybrid light-matter boundaries of graphene in a chiral cavity

Recent advances in chiral optical cavities coupled to two-dimensional materials have opened exciting opportunities to reshape electronic topology without external driving. In this talk, I will establish the bulk–boundary correspondence for graphene embedded in a circularly polarized cavity. By combining exact diagonalization of zigzag ribbons, a semi-analytic T-matrix for half-infinite lattices, and analytical insights from a Dirac–Jaynes–Cummings model, I will show that light–matter coupling induces topological gaps hosting pairs of unidirectional hybrid edge currents whose character depends on the Chern number, with some even optically bright. These chiral states persist across the entire photon ladder, exhibiting universal scaling of their dispersion, localization, and photon content controlled by the interaction strength. Finally, time-evolution simulations reveal how a dark edge excitation can be converted into a bright, long-lived, and unidirectional current. Together, these results provide clear experimental signatures of hybrid band topology and point toward reconfigurable chiral channels for next-generation quantum-optical devices.