The study of multi-band superconductivity is relevant for a variety of systems, from ultra cold atoms with population imbalance to particle physics, and condensed matter. As a consequence, this problem has been widely investigated bringing to light m
any new and interesting phenomena. In this work we point out and explore a correspondence between a two-band metal with a $k$-dependent hybridization and a uniformly polarized fermionic system in the presence of spin-orbit coupling (SOC). We study the ground state phase diagram of the metal in the presence of an attractive interaction. We find remarkable superconducting properties whenever hybridization mixes orbitals of different parities in neighboring sites. We show that this mechanism enhances superconductivity and drives the crossover from weak to strong coupling in analogy with SOC in cold atoms. We obtain the quantum phase transitions between the normal and superfluid states, as the intensity of different parameters characterizing the metal are varied, including Lifshitz transitions, with no symmetry breaking, associated with the appearance of soft modes in the Fermi surface.
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 w
e consider this problem in the case the fermionic quasi-particles can transmute into one another and only their total number is conserved. We use a 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 and a homogeneous metastable phase with gapless excitations. In the case of intra-band interactions, the transition from the superconductor to the normal state as hybridization increases is continuous and associated with a quantum critical point. The case when both interactions are present is also considered.
