Anisotropic superconductivity in the two-dimensional electron-phonon system

The properties of the d-wave superconducting state in the two-dimensional system have been studied. It has been assumed, that the pairing mechanism is based on the electron-phonon and the electron-electron-phonon interactions. The obtained results have shown the energy gap amplitude ($\Delta_{tot}$) crossover, from the BCS to non-BCS behavior, as the value of the electron-electron-phonon potential increases. The model has been tested for the ${\rm La_{2-x}Sr_{x}CuO_{4}}$ and ${\rm Bi_{2}Sr_{2}CaCu_{2}O_{8+\delta}}$ high-$T_{C}$ superconductors. It has been shown, that the dependence of the $2\Delta^{(0)}_{tot}/k_{B}T_{C}$ ratio on the hole density is in agreement with the experimental data.