Re-entrant spin susceptibility of a superconducting grain

TL;DR

This paper investigates how spin susceptibility in small superconducting grains varies with temperature, revealing re-entrant behavior for odd electron counts due to parity effects and pairing correlations, differing from bulk BCS predictions.

Contribution

It demonstrates the re-entrant spin susceptibility in small grains caused by parity effects, extending understanding beyond bulk superconductivity.

Findings

Odd electron grains show re-entrant susceptibility behavior.

Even electron grains have exponentially suppressed susceptibility at low T.

Re-entrant behavior persists even in ultrasmall grains with large level spacing.

Abstract

We study the spin susceptibility chi of a small, isolated superconducting grain. Due to the interplay between parity effects and pairing correlations, the dependence of chi on temperature T is qualitatively different from the standard BCS result valid in the bulk limit. If the number of electrons on the grain is odd, chi shows a re-entrant behavior as a function of temperature. This behavior persists even in the case of ultrasmall grains where the mean level spacing is much larger than the BCS gap. If the number of electrons is even, chi(T) is exponentially small at low temperatures.