Chiral spin excitations in graphene with proximity-induced spin-orbit coupling

Interacting electron systems with spin-orbit coupling (SOC) support collective spin excitations (CSE) even in the absence of the magnetic field. Motivated by recent observations of CSE in the surface state of a 3D topological insulator, Bi2Se3, and in semiconductor heterostructures, we develop a theory of CSE in doped graphene with proximity-induced SOC both of Rashba or valley-Zeeman (VZ) types. We show that these two types of SOC lead to different spectra of CSE. For the case of Rashba SOC there exist, just like in a single-band 2D Fermi liquid (FL), three branches of CSE: a doubly degenerate branch (in-plane polarized), and a non-degenerate branch (out-of-plane polarized). However, there also exists another in-plane doubly-degenerate branch. Both branches show up as peaks in the spin susceptibility and optical conductivity. For graphene with VZ SOC, spin and pseudospin degrees of freedom are decoupled, and there exists only a single out-of-plane polarized branch of CSE. In contrast to the case of Rashba SOC, the VZ CSE shows up only the spin susceptibility but not in the optical conductivity. This difference in CSE spectra can be used to experimentally distinguish the two types of SOC in the experiment.