Time reversal symmetry breaking holographic superconductor in constant external magnetic field

It is known that a classical SU(2) Einstein-Yang-Mills theory in 3 + 1 dimensional anti-de Sitter spacetime can provide a holographic dual to a 2 + 1 dimensional time reversal symmetry breaking superconductor with a pseudogap. We study the properties of this holographic superconductor in the presence of an applied constant external magnetic field, neglecting backreaction on the geometry. The superconductor is immersed into a constant external magnetic field by adding a radially (the extra dimension) dependent magnetic field to the black hole. As for real superconductors, there is a critical magnetic field above which no superconductivity can appear. The continuity of the first derivative of the free energy difference between the superconducting phase and the normal phase at the critical temperature suggests that the superconducting phase transition with applied magnetic field is of second order.