We study the one dimensional s-wave holographic superconductor by turning on the vector potential $A_x$ in the bulk, which behaves as $A_x=A_x^{ (0)} \ln z+ A_x^{ (1)}$ on the boundary. By solving the model with fixed $A_x^{ (0)}$, we find that if we identify the $A_x^{ (0)}$ with the supercurrent $j_x$ of the holographic superconductor, the results agree with the Gindzburg- Landau theory. For example, $A_x^{ (0)}$ will break the superconductivity, and the critical value of $A_x^{ (0)}$ is proportional to $(T_c-T)^{ 3/2}$.
Categories: hep-th