The plasma oscillations in a two-dimensional electron-hole liquid under influence Rashba spin-orbit coupling

The plasma oscillations of the two-dimensional electron-hole system in the presence of a Rashba spin-orbit coupling are studied. Only the intra-Landau level excitations are taken into account when the electrons and holes are situated on their lowest Landau levels, the filling factor $v^{2}$ being less than 1. The ground state of the two-dimensional electron-hole system is supposed to be the electron-hole liquid. The dispersion relations for the optical and acoustical plasmon modes were obtained. The acoustical plasmon branch has a linear dispersion law in the range of small wave vectors and monotonically increases with saturation at higher values of wave vectors. The optical plasmon branch has a quadratic dependence in the range of long wavelength and a monotonic increasing with saturation as in the case of acoustical branch.