Description
We study pairing induced superconductivity in large N
strongly coupled systems at finite density using holography.
In the weakly coupled dual gravitational theory the
mechanism is conventional BCS theory. An IR hard wall
cut-off is included to ensure that we can controllably
address the dynamics of a single confined Fermi surface. We
address in detail the interplay between the scalar order
parameter field and fermion pairing. Adding an explicitly
dynamical scalar operator with the same quantum numbers as
the fermion-pair, the theory experiences a BCS/BEC crossover
controlled by the relative scaling dimensions. We find the
novel result that this BCS/BEC crossover exposes resonances
in the canonical expectation value of the scalar operator.
This occurs not only when the scaling dimension is
degenerate with the Cooper pair, but also with that of
higher derivative paired operators. We speculate that a
proper definition of the order parameter which takes mixing
with these operators into account stays finite nevertheless.