  The gravitational dual of an insulator/superconductor transition driven by
increasing the chemical potential has recently been constructed. However, the
system was studied in a probe limit and only a part of the phase diagram was
obtained. We include the backreaction and construct the complete phase diagram
for this system. For fixed chemical potential there are typically two phase
transitions as the temperature is lowered. Surprisingly, for a certain range of
parameters, the system first becomes a superconductor and then becomes an
insulator as the temperature approaches zero. As a byproduct of our analysis,
we also construct the gravitational dual of a Bose-Einstein condensate of
glueballs in a confining gauge theory.
