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Paired state of nonstandard quasiparticles is analyzed in detail in two modelsituations. Namely, we consider the Cooper-pair bound state and the condensedphase of an almost localized Fermi liquid (ALFL) composed of quasiparticles ina narrow-band with the spin-dependent masses (SDM) and an effective field, bothintroduced earlier and induced by strong electronic correlations. Each of thesenovel characteristics are calculated in a self-consistent manner. We analyzethe bound states as a function of Cooper-pair momentum q in applied magneticfield in the strongly Pauli limiting case (i.e. when the orbital effects ofapplied magnetic field are disregarded). The spin-direction dependence of theeffective mass makes the quasiparticles comprising Cooper pair spindistinguishable in the quantum mechanical sense, whereas the condensed gas ofpairs may still be regarded as composed of identical entities. TheFulde-Ferrell-Larkin-Ovchinnikov (FFLO) condensed phase of moving pairs is byfar more robust in the applied field for the case with spin-dependent massesthan in the situation with equal masses of quasiparticles. Relative stabilityof the Bardeen-Cooper-Schrieffer (BCS) vs. FFLO phase is analyzed in detail ontemperature - applied field plane. Although our calculations are carried outfor a model situation, we can conclude that the spin-dependent masses shouldplay an important role in stabilizing high-field low-temperature (HFLT)unconventional superconducting phases (FFLO being an instance) in systems suchas CeCoIn_5, organic metals, and possibly others.

physical review. b, condensed matter and materials physics

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