  We explore the low-temperature behavior of the Abelian Higgs model in AdS_4,
away from the probe limit in which back-reaction of matter fields on the metric
can be neglected. Over a significant range of charges for the complex scalar,
we observe a second order phase transition at finite temperature. The
symmetry-breaking states are superconducting black holes. At least when the
charge of the scalar is not too small, we observe at low temperatures the
emergence of a domain wall structure characterized by a definite index of
refraction. We also compute the conductivity as a function of frequency.
