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 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.
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 and has brought to light many 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 this 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 in this case hybridization enhances superconductivity and drives the crossover from weak to strong coupling which is analogous with the SOC in cold atoms. We obtain the quantum phase transitions between the normal and superfluid states, as the intensities 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.
Multi-band systems such as inter-metallic and heavy fermion compounds have quasi-particles arising from different orbitals at their Fermi surface. Since these quasi-particles have different masses or densities, there is a natural mismatch of the Fermi wavevectors associated with different orbitals. This makes these materials potential candidates to observe exotic superconducting phases as Sarma or FFLO phases, even in the absence of an external magnetic field. The distinct orbitals coexisting at the Fermi surface are generally hybridized and their degree of mixing can be controlled by external pressure. In this work we investigate the existence of an FFLO type of phase in a two-band BCS superconductor controlled by hybridization. At zero temperature, as hybridization (pressure) increases we find that the BCS state becomes unstable with respect to an inhomogeneous superconducting state characterized by a single wavevector q.
a b s t r a c tIn multi-band superconductors as inter-metallic systems and heavy fermions, external pressure can reduce the critical temperature and eventually destroy superconductivity driving these systems to the normal state. In many cases this transition is continuous and is associated with a superconducting quantum critical point (SQCP). In this work we study a two-band superconductor in the presence of hybridization V. This one-body mixing term is due to the overlap of the different wave-functions. It can be tuned by external pressure and turns out as an important control parameter to study the phase diagram and the nature of the phase transitions. We use a BCS approximation and include both interand intra-band attractive interactions. For negligible inter-band interactions, as hybridization (pressure) increases we find a SQCP separating a superconductor from a normal state at a critical value of the hybridization V c . We obtain the behavior of the electronic specific heat close to the SQCP and the shape of the critical line as V approaches V c .
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