Theory of dc and dynamical conductivity in graphene-based chiral superconductors

Motivated by the recent evidence for chiral superconductivity in multilayer graphene, we theoretically study the response function of superconductors in single band systems with Berry curvature. We calculate, in the weak coupling limit, the dc and ac (transverse and longitudinal) response functions of the superconductor and argue based on these calculations that the vortices must carry charge, similar to previous predictions of p+ip superconductors, that are related to the normal state Hall conductivity. We confirm this prediction by numerical calculations of the charge of vortices. We then discuss the effect of screening and consequences for transport in the vortex deconfined phase.