Effect of inhomogeneous coupling on BCS superconductors

Abstract

We investigate the influence of inhomogeneity in the pairing coupling constant U͑r ជ͒ on dirty BCS superconductors, focusing on T c , the order parameter ⌬͑r ជ͒, and the energy gap E g ͑r ជ͒. 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 2E g / T c 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 KosterlitzThouless temperature T KT is also studied. We find that when the inhomogeneity length scale is much larger than the coherence length, 2E g / T KT can be larger than the usual BCS value. We use our results to qualitatively explain recent experimental observation of a surprisingly low value of 2E g / T c in thin films.

Pile on the metal

“…It is our hope that these results can provide guidance for a new generation of searches, of the sort pioneered by Yuli et al, 8 for higher-temperature superconductivity in engineered composite materials. More generally, this work extends previous work [10][11][12][13][14][15][16][17] on "optimal inhomogeneity for superconductivity" to situations more amenable to direct experimental manipulation.…”

Unified description of neutron superfluidity in the neutron-star crust with analogy to anisotropic multiband BCS superconductors

“…The conclusions of the present work may change in shallower regions of the crust where the matter is more inhomogeneous, as suggested by a recent study in dirty superconductors [48]. In addition we have neglected the change in composition with increasing temperature [34] which could affect the values of the pairing gaps (hence also the critical temperature) for T > ∼ 10 10 K. In particular we expect to find deviations of the ratio T c /∆ F from the BCS value≃ 0.58 when these thermal effects are taken into account.…”

Enhanced suppression of superconductivity in amorphous films with nano-scale patterning

“…The length scale of the inhomogeneity in coupling constant, L % 15 nm and n 0 % 10 nm are comparable to each other. This 'fast' modulation of the order parameter may account for some portion of the discrepancy between the calculation and the NHC data [29]. Additionally, the weak-coupling approximation employed here may underestimate the variation in k. The calculational discrepancy, like the robust T c ð d Bi Þ dependence, highlights the role of length scales much shorter than the interhole spacing $ 100 nm in determining the value of T c in NHC films.…”