Anisotropic Electron Coupling as a Phenomenological Model for High-Temperature Superconductors

Abstract

A three-dimensional weak coupling BCS model with an {\it anisotropic} pairing interaction in momentum space is reported. It exhibits an anisotropic gap in accord with recent experimental observations for high-$T_c$ oxides. The gap ratio ${2 \Delta / k_B T_c }$ is calculated as function of the anisotropy ratio of the electron pairing. It is found that the mean gap ratio decreases with increasing anisotropy of the electron pairing, whereas the maximum gap ratio increases. Assuming a unique strength of the effective electron interaction the transition temperature turns out to be always larger than in the isotropic case. The temperature dependence of the gap in the Cu-O plane and along the c-axis of YBaCuO is presented.