  We consider the d=3 N=8 SCFT dual to AdS_4\times S^7 when held at finite
temperature and chemical potential with respect to a diagonal U(1)_R\subset
SO(8) global symmetry and construct black brane solutions of D=11 supergravity
that are associated with the superfluid instability with the highest known
critical temperature. We construct a rich array of solutions using different
sub-truncations of SO(8) gauged supergravity finding results that strongly
depend on the truncation used. Our constructions include black brane solutions
associated with the Gubser-Mitra instability which preserve the U(1)_R
symmetry, and these, in turn, can have further superfluid instabilities. In
addition, we also construct superfluid black branes that at zero temperature
are domain walls that interpolate between the SO(8) AdS_4 vacuum in the UV, in
an alternative quantisation, and the supersymmetric SU(3)\times U(1) AdS_4
vacuum in the IR.
