Quantum Kinetic Theory of the Spin Hall Effect for Disordered Graphene with Rashba Spin-Orbit Coupling

The spin Hall effect for the model Hamiltonian of graphene with Rashba spin-orbit coupling is analyzed by means of a recently derived quantum kinetic theory of the linear response for multi-band electron systems. The latter expresses the interband part of the density matrix in terms of the intraband occupation numbers, which can be obtained as solutions of a Boltzmann transport equation. The analysis, which, in the case of the model here considered, can be carried out in a completely analytical way, thus provides an effective pedagogical illustration of the general theory. While our results agree with those previously obtained with alternative approaches for the same model, our comparatively simpler and more physically transparent derivation illustrates the advantages of our formalism when dealing with non trivial multi-band Hamiltonians.