Superconductivity in an almost localized Fermi liquid of quasiparticles with spin-dependent masses and effective-field induced by electron correlations

Paired state of nonstandard quasiparticles is analyzed in detail in two model situations. Namely, we consider the Cooper-pair bound state and the condensed phase of an almost localized Fermi liquid composed of quasiparticles in a narrow band with the spin-dependent masses and an effective field, both introduced earlier and induced by strong electronic correlations. Each of these novel characteristics is calculated in a self-consistent manner. We analyze the bound states as a function of Cooper-pair momentum $|\mathbf{Q}|$ in applied magnetic field in the strongly Pauli limiting case (i.e., when the orbital effects of applied magnetic field are disregarded). The spin-direction dependence of the effective mass makes the quasiparticles comprising Cooper-pair spin distinguishable in the quantum-mechanical sense, whereas the condensed gas of pairs may still be regarded as composed of identical entities. The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) condensed phase of moving pairs is by far more robust in the applied field for the case with spin-dependent masses than in the situation with equal masses of quasiparticles. Relative stability of the Bardeen-Cooper-Schrieffer vs FFLO phase is analyzed in detail on temperature-applied field plane. Although our calculations are carried out for a model situation, we can conclude that the spin-dependent masses should play an important role in stabilizing high-field low-temperature unconventional superconducting phases (FFLO, for instance) in systems such as ${\text{CeCoIn}}_{5}$, organic metals, and possibly others.