Cavity magnetotransport of a two-dimensional electron gas in the ultrastrong coupling regime

We present a theory predicting how the linear magneto-conductivity tensor of a two-dimensional electron gas is changed by the ultrastrong coupling to a fully confined photon mode, proving how a passive cavity resonator can profoundly modify the dc electronic transport even when no real photon is injected. We show that the modification of the transport is due to: (i) dressing of both ground and excited states by the ultrastrong light-matter coupling; (ii) the diamagnetic current contribution due to the cavity mode. We demonstrate that in the regime of Shubnikov-de Haas oscillations the envelope of the longitudinal magnetoresistance as a function of the magnetic field can be significantly modified and becomes anisotropic, depending on the direction with respect to the cavity mode polarization vector.