Parity-Affected Superconductivity in Ultrasmall Metallic Grains

TL;DR

This paper studies how superconductivity in ultra-small metallic grains depends on particle size and electron parity, revealing measurable differences between even and odd electron counts.

Contribution

It provides a parity-dependent analysis of superconductivity breakdown in ultrasmall grains using a modified BCS model, highlighting measurable effects.

Findings

Critical level spacing and temperature are parity dependent.

Odd electron grains have smaller critical parameters than even ones.

Differences are experimentally measurable.

Abstract

We investigate the breakdown of BCS superconductivity in {\em ultra}\/small metallic grains as a function of particle size (characterized by the mean spacing $d$ between discrete electronic eigenstates), and the parity ($P$ = even/odd) of the number of electrons on the island. Assuming equally spaced levels, we solve the parity-dependent BCS gap equation for the order parameter $\Delta_P (d,T)$. Both the $T=0$ critical level spacing $d_{c,P} $ and the critical temperature $T_{c,P} (d)$ at which $\Delta_P = 0$ are parity dependent, and both are so much smaller in the odd than the even case that these differences should be measurable in current experiments.