Paramagnetic Breakdown of Superconductivity in Ultrasmall Metallic Grains

Abstract

We study the magnetic-field-induced breakdown of superconductivity in nm-scale metal grains having a mean electron level spacing $d\ensuremath{\simeq}\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\Delta}}$ (bulk gap). Using a generalized variational BCS approach that yields good qualitative agreement with measured spectra, we argue that Pauli paramagnetism dominates orbital diamagnetism, as in the case of thin films in a parallel magnetic field. However, the first-order transition observed for the latter can be made continuous by finite size effects. The mean-field procedure of describing the system by a single pairing parameter \ensuremath{\Delta} breaks down for $d\ensuremath{\simeq}\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\Delta}}$.