On Holographic Superconductors with DC Current

We study direct currents in a simple holographic realization of a superconducting film. We investigate how the presence of a DC current affects the superconducting phase transition, which becomes first order for any non-vanishing value of the current, as well as several other properties of the superconductor such as the AC conductivity. Near the critical temperature we find a quantitative agreement with several properties of Ginzburg-Landau superconducting films, for example the squared ratio of the maximal and minimal condensate is equal to two thirds. We also comment on the extension of our construction to holographic Josephson junctions.