The Simple Generalized BCS-Type Model for the Acoustic Plasmon Induced d-Wave Superconductivity in High-Tc Layered Cuprate Compounds

Abstract

A simple analytically treated model is presented for high-T c superconductivity in layered cuprate compounds. This model assumes a cylindrical Fermi-surface with circular cross-section, but anisotropic Fermi-velocity (density of states), which is approximated by a step-like function on azimuth angle. The system under these assumptions is shown to support in the long wavelength limit collective charge-density excitations with acoustic spectrum (acoustic plasmons), which suppress the Coulomb interelectron repulsion for small transferred momenta. This result leads to the second essential feature of the proposed model: besides the standard assumptions of the BCS scheme the effective potential of interelectron interaction is characterized by additional step-like dependence on the absolute value of two-dimensional transferred quasimomenta. The effective constants of the Cooper pairing in anisotropic s- and d-wave channels are evaluated. It is shown, that the plasmon mechanism gives rise to the pairing in the d-wave channel despite the fully isotropic (in two dimensions) model potential. The Umklapp processes are taken into account and are shown to increase the pairing constants.