Pair-correlations and magnetic susceptibility of small Al-grains

TL;DR

This paper investigates how pairing correlations and magnetic susceptibility behave in small spherical aluminum grains, revealing size-dependent effects and differences between statistical ensembles.

Contribution

It provides a detailed analysis of pair correlations and susceptibility in small grains, adjusting the BCS Hamiltonian to experimental data and comparing ensemble effects.

Findings

Gap parameter increases in small grains due to shell effects.

Sharp phase transition at T_c is smoothed out in the canonical ensemble.

Superconductivity reduces but does not eliminate paramagnetic susceptibility.

Abstract

Paircorrelations and the magnetic susceptibility of electrons in a spherical cavity are studied both for grand canonical and the canonical ensemble. The coupling constant of the $BCS$ Hamiltonian is adjusted to experimental values of the gap parameter. The gap parameter is found to increase for small grains as a consequence of the pronounced shell structure in the spectrum of the spherical cavity. The sharp phase transition at $T_c$ is smeared out for the canonical ensemble. The strong paramagnetic susceptibility of the normal electrons in the cavity is reduced by the superconductivity, but it remains positive.