Supercurrent in p-wave Holographic Superconductor

The p-wave and $p+ip$-wave holographic superconductors with fixed DC supercurrent are studied by introducing a non-vanishing vector potential. We find that close to the critical temperature $T_c$ of zero current, the numerical results of both the p wave model and the $p+ip$ model are the same as those of Ginzburg-Landau (G-L) theory, for example, the critical current $j_c \sim (T_c-T)^{3/2}$ and the phase transition in the presence of a DC current is a first order transition. Besides the similar results between both models, the $p+ip$ superconductor shows isotropic behavior for the supercurrent, while the p-wave superconductor shows anisotropic behavior for the supercurrent.