Chiral spin modes in doped graphene with Rashba spin-orbit coupling

Recently chiral spin modes have been observed on the surface states of 3D topological insulator, Bi₂Se₃. These modes have also been claimed to exist in the spin-orbit coupled two-dimensional Fermi liquid. Motivated by these observations, we investigate collective spin-excitations in doped graphene grown on transition metal dichalcogenide, e.g., WS₂ , where the dominant spin-orbit coupling is of the Rashba type. We consider optical conductivity and spin-susceptibility of such a system and identify specific resonances. We study the effect of electron-electron interactions on these observables and find that it couples spin and pseudo spin degrees of freedom, which were otherwise decoupled. This leads to interesting features like the modification of Rashba continuum as well as the breaking of degeneracy of the collective mode outside the continuum.