Paramagnetic Breakdown of Superconductivity in Ultrasmall Metallic Grains

TL;DR

This paper investigates how superconductivity in ultrasmall metallic grains breaks down under magnetic fields, highlighting the dominance of paramagnetism over orbital effects and the impact of finite size on the transition nature.

Contribution

It introduces a generalized variational BCS approach to analyze magnetic breakdown of superconductivity in nanoscale grains, emphasizing the role of paramagnetism and finite size effects.

Findings

Paramagnetism dominates orbital diamagnetism in small grains.

The transition can shift from first-order to continuous due to finite size effects.

Mean-field approximation breaks down when level spacing approaches the bulk gap.

Abstract

We study the magnetic-field-induced breakdown of superconductivity in nm-scale metal grains having a mean electron level spacing $d \simeq \tilde\Delta$ (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 $\Delta$ breaks down for $d \simeq \tilde\Delta$.