Ultra-small metallic grains: Effect of statistical fluctuations of the chemical potential on superconducting correlations and vice versa

Abstract

Superconducting correlations in an isolated metallic grain are governed by the interplay between two energy scales: the mean level spacing δ and the bulk pairing gap Δ 0, which are strongly influenced by the position of the chemical potential with respect to the closest single-electron level. In turn superconducting correlations affect the position of the chemical potential. Within the parity projected BCS model we investigate the probability distribution of the chemical potential in a superconducting grain with randomly distributed single-electron levels. Taking into account statistical fluctuations of the chemical potential due to the pairing interaction, we find that such fluctuations have a significant impact on the critical level spacing δ c at which the superconducting correlations cease: the critical ratio δ c/Δ 0 at which superconductivity disappears is found to be increased. © 2012 IOP Publishing Ltd.