Charge and spin density response functions of the clean two-dimensional electron gas with Rashba spin-orbit coupling at finite momenta and frequencies

We analytically evaluate charge and spin density response functions of the clean two-dimensional electron gas with Rashba spin-orbit coupling at finite momenta and frequencies. On the basis of our exact expressions we discuss the accuracy of the long-wavelength and the quasiclassical approximations. We also derive the static limit of spin susceptibilities and demonstrate, in particular, how the Kohn-like anomalies in their derivatives are related to the spin-orbit modification of the Ruderman-Kittel-Kasuya-Yosida interaction. Taking into account screening and exchange effects of the Coulomb interaction, we describe the collective charge and spin density excitation modes which appear to be coupled due to nonvanishing spin-charge response function.