Holographic Abrikosov Lattices

We study black hole solutions of $D=4$ Einstein-Maxwell theory coupled to a charged scalar field that are holographically dual to a $d=3$ conformal field theory with a non-vanishing chemical potential and constant magnetic field. We numerically construct black hole solutions that are dual to a superfluid phase with a periodic lattice of vortices. For the specific model we investigate, we find that the thermodynamically preferred configuration is given by a triangular lattice and moreover the vortices are associated with the lowest Landau level. We also construct black holes describing a lattice of vortices associated with the next to lowest Landau level and while theses are not thermodynamically preferred they exhibit some interesting features that could be realised for other holographic models.