Effect of inhomogeneous coupling on BCS superconductors

Abstract

We investigate the influence of inhomogeneity in the pairing coupling constant U(r-vector) on dirty BCS superconductors, focusing on Tc, the order parameter Delta(r-vector), and the energy gap Eg(r-vector). Within mean-field theory, we find that when the length scale of the inhomogeneity is comparable to or larger than the coherence length, the ratio 2Eg/Tc is significantly reduced from that of a homogeneous superconductor, while in the opposite limit, this ratio stays unmodified. In two dimensions, when strong phase fluctuations are included, the Kosterlitz-Thouless temperature TKT is also studied. We find that when the inhomogeneity length scale is much larger than the coherence length, 2Eg/TKT can be larger than the usual BCS value. We use our results to qualitatively explain recent experimental observation of a surprisingly low value of 2Eg/Tc in thin films.