  We show that a D3/D7 system (at zero quark mass limit) at finite isospin
chemical potential goes through a superconductor (superfluid) like phase
transition. This is similar to a flavored superfluid phase studied in QCD
literature, where mesonic operators condensate. We have studied the frequency
dependent conductivity of the condensate and found a delta function pole in the
zero frequency limit. This is an example of superconductivity in a string
theory context. Consequently we have found a superfluid/supercurrent type
solution and studied the associated phase diagram. The superconducting
transition changes from second order to first order at a critical superfluid
velocity. We have studied various properties of the superconducting system like
superfluid density, energy gap, second sound etc. We investigate the
possibility of the isospin chemical potential modifying the embedding of the
flavor branes by checking whether the transverse scalars also condense at low
temperature. This however does not seem to be the case.
