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Modulated phases of graphene quantum Hall polariton fluids

There is growing experimental interest in coupling cavity photons to the cyclotron resonance excitations of electron liquids in high-mobility semiconductor quantum wells or graphene sheets. These media offer unique platforms to carry out fundamental studies of exciton-polariton condensation and cavity quantum electrodynamics in a regime in which electron-electron interactions are expected to play a pivotal role. Focusing on graphene, we present a theoretical study of the impact of electron-electron interactions on a quantum Hall polariton fluid, that is a fluid of magneto-excitons resonantly coupled to cavity photons. We show that electron-electron interactions are responsible for an instability of graphene integer quantum Hall polariton fluids towards a modulated phase. We demonstrate that this phase can be detected by measuring the collective excitation spectra, which soften at a characteristic wave vector of the order of the inverse magnetic length.