Mesoscopic interplay of superconductivity and ferromagnetism in ultra-small metallic grains

TL;DR

This paper reviews how electron-electron interactions influence the ground-state spin and transport in ultra-small metallic grains, highlighting the coexistence of superconductivity and ferromagnetism and their signatures in conductance measurements.

Contribution

It introduces a combined Hamiltonian model for superconducting and ferromagnetic correlations in mesoscopic grains and maps the phase diagram in the fluctuation-dominated regime.

Findings

Coexistence regime of pairing and spin exchange correlations identified.

Measurable conductance signatures of superconductivity and ferromagnetism competition.

Ground-state phase diagram mapped in the regime where level spacing is comparable to pairing gap.

Abstract

We review the effects of electron-electron interactions on the ground-state spin and the transport properties of ultra-small chaotic metallic grains. Our studies are based on an effective Hamiltonian that combines a superconducting BCS-like term and a ferromagnetic Stoner-like term. Such terms originate in pairing and spin exchange correlations, respectively. This description is valid in the limit of a large dimensionless Thouless conductance. We present the ground-state phase diagram in the fluctuation-dominated regime where the single-particle mean level spacing is comparable to the bulk BCS pairing gap. This phase diagram contains a regime in which pairing and spin exchange correlations coexist in the ground-state wave function. We discuss the calculation of the tunneling conductance for an almost-isolated grain in the Coulomb-blockade regime, and present measurable signatures of the competition between superconductivity and ferromagnetism in the mesoscopic fluctuations of the conductance.