Asymmetric superconductivity in metallic systems

Different types of superfluid ground states have been investigated in systems of two species of fermions with Fermi surfaces that do not match. This study is relevant for cold atomic systems, condensed matter physics, and quark matter. In this paper we consider this problem when the fermionic quasi-particles can transmute into one another and only their total number is conserved. We use a Bardeen-Cooper-Schrieffer (BCS) approximation to study superconductivity in two-band metallic systems with inter-and intra-band interactions. Tuning the hybridization between the bands varies the mismatch of the Fermi surfaces and produces different instabilities. For inter-band attractive interactions, we find a first-order normal-superconductor transition and a homogeneous metastable phase with gapless excitations. In the case of intra-band interactions, the transition from the superconductor to the normal state is continuous as hybridization increases and associated with a quantum critical point. The case when both interactions are present is also considered.