Magnetic susceptibility of ultra-small superconductor grains

TL;DR

This paper develops a simplified model to analyze the magnetic susceptibility of ultra-small superconductor grains, revealing stable signatures of pairing correlations that differ from normal grains across various sizes and energy level distributions.

Contribution

A new approximation based on the Richardson solution for the reduced BCS Hamiltonian is introduced to study magnetic responses in ultra-small superconducting grains.

Findings

Magnetic susceptibility profiles differ qualitatively from normal grains.

Signatures of pairing correlations are stable across grain size variations.

These signatures are independent of the statistical distribution of energy levels.

Abstract

For assemblies of superconductor nanograins, the magnetic response is analyzed as a function of both temperature and magnetic field. In order to describe the interaction energy of electron pairs for a huge number of many-particle states, involved in calculations, we develop a simple approximation, based on the Richardson solution for the reduced BCS Hamiltonian and applicable over a wide range of the grain sizes and interaction strengths at arbitrary distributions of single-electron energy levels in a grain. Our study is focused upon ultra-small grains, where both the mean value of the nearest-neighbor spacing of single-electron energy levels in a grain and variations of this spacing from grain to grain significantly exceed the superconducting gap in bulk samples of the same material. For these ultra-small superconductor grains, the overall profiles of the magnetic susceptibility as a function of magnetic field and temperature are demonstrated to be qualitatively different from those for normal grains. We show that the analyzed signatures of pairing correlations are sufficiently stable with respect to variations of the average value of the grain size and its dispersion over an assembly of nanograins. The presence of these signatures does not depend on a particular choice of statistics, obeyed by single-electron energy levels in grains.