Paramagnetic breakdown of superconductivity in ultrasmall metallic grains

We study the magnetic-field-induced breakdown of superconductivity in nm-scale metal grains having a mean electron level spacing d similar or equal to <(Delta)over tilde> (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 Delta breaks down for d similar or equal to <(Delta)over tilde>.