Superradiant quantum phase transition for Landau polaritons with Rashba and Zeeman couplings

We develop a theory of cavity quantum electrodynamics for a two-dimensional electron gas in the presence of Rashba spin-orbit and Zeeman couplings and perpendicular magnetic field, coupled to a spatially nonuniform quantum photon field. We show that the superradiant quantum phase transition (SQPT), also known as photon condensation, can, in principle, occur through a pure in-plane Zeeman coupling, but it requires extremely small (unrealistic) quantum well widths or extremely fine tuning of the effective Land?? factor which makes two Landau levels coincide. Landau-level crossings can also be induced by the Rashba spin-orbit coupling and they promote the SQPT, which can be obtained for certain values of the effective Land?? factor and filling factors.