  It has been shown that a gravitational dual to a superconductor can be
obtained by coupling anti-de Sitter gravity to a Maxwell field and charged
scalar. We review our earlier analysis of this theory and extend it in two
directions. First, we consider all values for the charge of the scalar field.
Away from the large charge limit, backreaction on the spacetime metric is
important. While the qualitative behaviour of the dual superconductor is found
to be similar for all charges, in the limit of arbitrarily small charge a new
type of black hole instability is found. We go on to add a perpendicular
magnetic field B and obtain the London equation and magnetic penetration depth.
We show that these holographic superconductors are Type II, i.e., starting in a
normal phase at large B and low temperatures, they develop superconducting
droplets as B is reduced.
