A $d$-wave holographic superconductor in the presence of a constant magnetic field is studied by the perturbation method. We obtain both droplet and triangular vortex lattice solutions. The results are the same as that of an $s$-wave holographic superconductor. The non-Abelian holographic superconductor with $p+ip$-wave background in the presence of a magnetic field is also studied. Unlike the $d$-wave and $s$-wave models, it is found that the non-Abelian model has only a droplet solution.

• Received 14 August 2010

DOI:https://doi.org/10.1103/PhysRevD.82.126008