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We apply the concept of generalized (almost localized) Fermi liquid and associated with it unconventional superconductivity with Cooper pairs composed of quasiparticles with the spin dependent masses (in an applied field) and with the effective field, both induced by electron correlations. The pairing among quasiparticles takes place either in reciprocal space (Sect. 2) or in real space (Sect. 3) and is induced by the kinetic exchange of either superexchange (in the generic narrow-band situation) or Kondo-type interaction (in the Kondo-lattice limit of the periodic Anderson model). While the main features of this type of Fermi liquid have been introduced earlier, we present here a picture which is applicable to both heavy-fermion and high-T-c superconductivity within a single narrow-band representation of correlated states. Our approach introduces a set of additional concepts (spin-dependent masses, effective fields induced by electron correlations), for which the Landau concept of the Fermi liquid represents still a workable scheme. In the limit of the Kondo lattice, we present the phase diagram incorporating the Fulde-Ferrell-Larkin-Ovchinnikov phase within the BCS-type of pairing, whereas in that of the t-J model we show that the proper choice of renormalization factors and constraints is crucial for the mean-field description of the superconducting state.

Unconventional Superconducting States of an Almost Localized Fermionic Liquid with Nonstandard Quasiparticles: Generalized Gutzwiller Approach