This work is placed in the context of solid-state systems in the regime of ultra-strong light-matter coupling. To date, the highest light-matter coupling strengths have been measured in experiments with polaritons in semiconductor systems under the conditions of the Integer Quantum Hall effect. Polaritons are excitations resulting from strong coupling of light with a dipole-carrying matter excitation. In Pellegrino et al. (2016), we studied the impact of electron-electron interaction on polaritons in cavities in the case of graphene under the conditions of the Integer Quantum Hall effect. By using a mean- field (Hartree-Fock) approach we have shown the possibility of formation of spatially modulated light-matter phases characterized by a wavelength that is dependent on the value of the applied static magnetic field and the concentration of carriers, which is tunable by varying the gate voltage.
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