Strongly coupling materials to cavity fields can affect the material’s electronic properties altering the phases of matter. In this talk, I will first discuss the hybrid light-matter band topology of the monolayer graphene whose electrons can be coupled to both left and right circularly polarized vacuum fluctuations, and time-reversal symmetry is broken due to an asymmetry between the two polarizations. This discussion will show how the quantum nature of photons affects the topology of the correlated light-matter hybrid wave function. A central finding of Ref. [1] is a relation between the Berry phase and the properties of exchanged photons with matter at light-matter hybridization points in the Brillouin zone. This physics turns out to be generic, as it also emerges in stacked graphene layers [2]. I will then introduce a quantum optics model to capture the properties of the topological light-matter hybridization gaps and show the presence of chiral edge modes in these gaps [3]. For the rest of the talk, I will describe a newly proposed photonic crystal chiral cavity [4], and its recent realization [5].

[1] Physical Review B 110 (12), L121101 (2024)
[2] arXiv: 2504.03842
[3] arXiv: 2510.13373
[4] Nature Communications 16 (1), 5270 (2025)
[5] arXiv: 2509.14366