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

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.