Vortex lattice for a holographic superconductor

We investigate the vortex lattice solution in a (2+1)-dimensional holographic model of superconductors constructed from a charged scalar condensate. The solution is obtained perturbatively near the second-order phase transition and is a holographic realization of the Abrikosov lattice. Below a critical value of the magnetic field, the solution has a lower free energy than the normal state. Both the free-energy density and the superconducting current are expressed by nonlocal functions, but they reduce to the expressions in the Ginzburg-Landau theory at long wavelengths. As a result, a triangular lattice becomes the most favorable solution thermodynamically, as in the Ginzburg-Landau theory of type II superconductors.