Anisotropy in μ* for superconducting aluminum

Abstract

Using two models for an anisotropic Coulomb pseudopotential parameter μ*(k), we have calculated approximate upper and lower limits for the anisotropic gap edge of superconducting aluminum as a function of wavevector direction over the Fermi surface. We consider all sources of anisotropy, i.e., anisotropic phonon dispersion curves and anisotropic Fermi surface, to determine the electron-phonon spectral functions α ²_k (ω)F _k(ω) and the matrix elements of the screened Coulomb repulsion. We find values of the gap anisotropy parameter 〈a²〉 and of the ratio between the pure single-crystal and isotropic dirty limit critical temperatures that agree better with experimental results than the values found using a constant μ*. Disagreement between theory and experiment remains for the variation of Δ_o(k) itself over the Fermi surface.