The simple generalized BCS-type model for the acoustic plasmon induced d-wave superconductivity in high-T-c layered cuprate compounds

A simple analytically treated model is presented for high-T-c superconducti vity in layered cuprate compounds. This model assumes a cylindrical Fermi-s urface with circular cross-section, but anisotropic Fermi-velocity (density of states), which is approximated by a steplike function on azimuth angle. The system under these assumptions is shown to support in the long wavelen gth limit collective charge-density excitations with acoustic spectrum (aco ustic plasmons), which suppress the Coulomb interelectron repulsion for sma ll transferred momenta. This result leads to the second essential feature o f the proposed model: besides the standard assumptions of the BCS scheme th e effective potential of interelectron interaction is characterized by addi tional step-like dependence on the absolute value of two-dimensional transf erred quasimomenta, The effective constants of the Cooper pairing in anisot ropic s- and d-wave channels are evaluated. It is shown, that the plasmon m echanism gives rise to the pairing in the d-wave channel, despite the fully isotropic (in two dimensions) model potential. The Umklapp processes are t aken into account and are shown to increase the pairing constants.