Mesoscopic superconductivity in ultrasmall metallic grains

TL;DR

This paper investigates mesoscopic superconductivity in ultrasmall metallic grains, focusing on the crossover from BCS to fluctuation-dominated regimes and how pairing correlations influence thermodynamic properties and magnetic responses.

Contribution

It provides a detailed analysis of the interplay between pairing and exchange interactions in chaotic metallic grains, especially under spin-orbit scattering, extending understanding beyond mean-field theory.

Findings

Signatures of pairing correlations in heat capacity and spin susceptibility.

Competition between pairing and exchange interactions in the absence of spin-orbit scattering.

Detectable effects of pairing in magnetic-field responses even in fluctuation-dominated regime.

Abstract

A nano-scale metallic grain (nanoparticle) with irregular boundaries in which the single-particle dynamics are chaotic is a zero-dimensional system described by the so-called universal Hamiltonian in the limit of a large number of electrons. The interaction part of this Hamiltonian includes a superconducting pairing term and a ferromagnetic exchange term. Spin-orbit scattering breaks spin symmetry and suppresses the exchange interaction term. Of particular interest is the fluctuation-dominated regime, typical of the smallest grains in the experiments, in which the bulk pairing gap is comparable to or smaller than the single-particle mean-level spacing, and the Bardeen-Cooper-Schrieffer (BCS) mean-field theory of superconductivity is no longer valid. Here we study the crossover between the BCS and fluctuation-dominated regimes in two limits. In the absence of spin-orbit scattering, the pairing and exchange interaction terms compete with each other. We describe the signatures of this competition in thermodynamic observables, the heat capacity and spin susceptibility. In the presence of strong spin-orbit scattering, the exchange interaction term can be ignored. We discuss how the magnetic-field response of discrete energy levels in such a nanoparticle is affected by pairing correlations. We identify signatures of pairing correlations in this response, which are detectable even in the fluctuation-dominated regime.