ON POSSIBLE FORMALISM OF ANISOTROPIC FERMI LIQUID AND BCS–TYPE SUPERCONDUCTIVITY

Abstract

We prove that an arbitrary crystal with anisotropic lattice and partially filled conduction band, for which one-electron energy spectrum is known, can be considered, after some curvilinear transformation of the reciprocal lattice as the Fermi liquid of the Landau–type quasiparticles in the isotropic system. However, the additional scalar field modifying the size of quantum-mechanical states in the reciprocal space has to be included. It is shown that the established formalism can be employed for two- and three-dimensional systems. As an example one-band Hubbard model has been investigated in details. The new precise formulas for the postulated scalar field and the density of states are derived. Additionally, assuming the microscopic mechanism which leads to the pairing interaction in a crystal, the anisotropic Fermi liquid formalism is extended to superconducting system according to the BCS theory principles. The obtained results enable us to explain and understand the great success of the BCS theory.