  We describe the simplest holographic model for an s-wave unbalanced
superconductor in 2+1 dimensions. We study its phase diagram and linear
response features with particular attention to the possibility of spatially
modulated phases (LOFF) and mixed spin-electric properties. The normal phase of
the model at hand allows us to analyze a strong-coupling generalization of Mott
two-current model for spintronic systems; the superconducting phase features an
interesting DC spin-superconductivity without spin-symmetry breaking .
