Tunable Topological Phases in Multilayer Graphene Coupled to a Chiral Cavity

Coupling photonic cavity fields to electronic degrees of freedom in 2D materials introduces an additional control knob to the toolbox of solid-state engineering. Here we demonstrate a subtle competition between cavity frequency and interlayer tunneling in graphene stacks that is responsible for topological phase transitions in light-matter Hilbert space and that cannot be captured by mean-field theory in vacuum. A systematic exploration of multilayer graphene heterostructures and stacking configurations in a chiral tHz cavity reveals that linear dispersion enhances the low-energy cavity-induced topological gap. Furthermore, in bilayer graphene, a displacement field drives the low-energy vacuum band from valley-Chern to Chern insulator, comprising a gate-tunable topological phase transition. Our findings pave the way for future control and engineering of graphene heterostructures with chiral cavity fields.