Equilibrium spin current in graphene with Rashba spin-orbit coupling

The existence of a background spin current under thermodynamic equilibrium is an interesting phenomenon in the two-dimensional electron gas with Rashba spin-orbit coupling (RSOC). Here we study the equilibrium spin current (ESC) in graphene with RSOC. For an infinite graphene with uniform RSOC, we found that the ESC is proportional to λ(2) with λ the Rashba strength and mainly comes from the energy window [-λ, λ] near Dirac points. In the regime of energy far away from Dirac points, the λ(3) dependence as that in a normal two-dimensional electron gas is recovered. In a system with a normal graphene strip inserted between two Rashba graphene sheets, we found that the ESC can penetrate through the normal graphene layer (perpendicular to the interface). This unique effect can be understood by considering the spin-filtered scattering from the normal region to the RSOC region. The finding of the ESC through the normal region without RSOC advances the understanding of ESC and provides a new way to generate a pure spin current in graphene. For an experimentally accessible strength of Rashba spin-orbit coupling, the ESC remains over room temperature.