  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.
