We use holography to study the ground state of a system with interacting
bosonic and fermionic degrees of freedom at finite density. The gravitational
model consists of Einstein-Maxwell gravity coupled to a perfect fluid of
charged fermions and to a charged scalar field which interact through a
current-current interaction. When the scalar field is non-trivial, in addition
to compact electron stars, the screening of the fermion electric charge by the
scalar condensate allows the formation of solutions where the fermion fluid is
made of antiparticles, as well as solutions with coexisting, separated regions
of particle-like and antiparticle-like fermion fluids. We show that, when the
latter solutions exist, they are thermodynamically favored. By computing the
two-point Green function of the boundary fermionic operator we show that, in
addition to the charged scalar condensate, the dual field theory state exhibits
electron-like and/or hole-like Fermi surfaces. Compared to fluid-only
solutions, the presence of the scalar condensate destroys the Fermi surfaces
with lowest Fermi momenta. We interpret this as a signal of the onset of
superconductivity.Comment: 46 pages, 17 figure
