Floquet superconductor in holography

We study nonequilibrium steady states in a holographic superconductor under time periodic driving by an external rotating electric field. We obtain the dynamical phase diagram. Superconducting phase transition is of first or second order depending on the amplitude and frequency of the external source. The rotating electric field decreases the superconducting transition temperature. The system can also exhibit a first order transition inside the superconducting phase. It is suggested this transition exists all the way down to zero temperature. The existence of nonequilibrium thermodynamic potential for such steady solutions is also discussed from the holographic point of view. The current induced by the electric field is decomposed into normal and superconducting components, and this makes it clear that the superconducting one dominates in low temperatures.