Mesoscopic Competition of Superconductivity and Ferromagnetism: Conductance Peak Statistics for Metallic Grains

Abstract

We investigate the competition between superconductivity and ferromagnetism in chaotic ultrasmall metallic grains in a regime where both phases can coexist. We use an effective Hamiltonian that combines a BCS-like pairing term and a ferromagnetic Stoner-like spin exchange term. We study the transport properties of the grain in the Coulomb blockade regime and identify signatures of the coexistence between pairing and exchange correlations in the mesoscopic fluctuations of the conductance peak spacings and peak heights.Although superconductivity and ferromagnetism compete with each other, the coexistence of both states has recently been reported in heavy-fermion systems [1] and high-T c superconductors [2]. This observed coexistence has led to enormous renewed interest in those materials. A main objective is to find systems in which ferromagnetism and superconductivity can be easily transformed into each other by changing an experimentally controllable parameter.In nano-sized metallic grains a coexistence regime has been predicted theoretically [3,4,5]. It was shown that the presence of spin jumps in the ground-state phase diagram of a single grain is a unique signature of this coexistence and that an external Zeeman field can be used to control and tune the size of this regime [5].Experimentally, the competition between superconductivity and ferromagnetism in metallic grains has not yet been investigated, in part, because fabrication and control of nanoscopic metallic devices is very challenging. The first nanoscopic single-electron transistors (SETs) with superconducting islands were produced by breaking nanowires into small pieces [6]. Discrete energy levels and pairing effects were observed in a single grain by measuring the tunneling conductance (for a review see [7]). Itinerant ferromagnetism has been studied as well in normal metallic grains such as Cobalt [8]. During the last decade, production and gating of metallic grains has been considerably improved, e.g., using chemically synthesized grains and electromigration [9,10]. A very recent development is the observation of superconductivity in doped silicon, which might further simplify the production and control of mesoscopic superconducting devices [11].Here we calculate the tunneling conductance in the Coulomb blockade regime for an ensemble of almostisolated metallic grains using a rate equation approach [12]. Our analysis is based on an effective Hamiltonian for chaotic or disordered systems, which combines a superconducting BCS-like term and a ferromagnetic Stoner-like term originating in pairing and spin exchange correlations, respectively [13,14]. By renormalizing the pairing coupling constant, we can derive accurate results using exact diagonalization of the many-body Hamiltonian within a truncated band.We propose that signatures of the coexistence of pairing and ferromagnetic correlations can be observed in the mesoscopic fluctuations of the conductance peaks in superconducting grains with a sufficiently strong exchange interaction. We find a regi...

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