Combined effect of electron-electron interactions and spin-orbit scattering in metal nanoparticles

Gorokhov, D. A.; Brouwer, Piet W.

doi:10.1103/physrevb.69.155417

Cited by 22 publications

(32 citation statements)

References 37 publications

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“…The parameter J s is the exchange coupling constant (estimated values of J s for a variety of materials were tabulated in Ref. [15]). …”

mentioning

confidence: 99%

“…2a. The exchange interaction strength J s /δ is a material constant and for most metals is smaller or comparable to J s /δ ∼ 0.6 [15]. In contrast, the pairing ratio ∆/δ can be made larger by using a smaller grain.…”

mentioning

confidence: 99%

“…Thus, we find that mesoscopic fluctuations increase the parameter regime for which coexistence of pairing and exchange correlations can be measured. The coexistence regime should be directly observable in Platinum, which has recently been shown to be superconducting in granular form [22] and also has a relatively large exchange interaction strength of J s /δ ∼ 0.59 − 0.72 [15]. In experiments it might be difficult to vary the exchange interaction strength (a material constant).…”

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confidence: 99%

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

Schmidt

Alhassid

2008

Phys. Rev. Lett.

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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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“…The parameter J s is the exchange coupling constant (estimated values of J s for a variety of materials were tabulated in Ref. [15]). …”

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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

Schmidt

Alhassid

2008

Phys. Rev. Lett.

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“…It is independent of the particular statistics of the single-electron energies or of the relative contributions of orbital and spin magnetism to the splitting of energy levels. Since the exchange interaction (which is not fully suppressed when spin-orbit is not strong) affects g-factors statistics [51,52], we conclude that the robustness of the g-factor statistic can be a good test to determine the importance of exchange correlations in the grain.…”

Section: Superconducting Nanoparticles With Spin-orbit Scattering: Mamentioning

confidence: 99%

Mesoscopic superconductivity in ultrasmall metallic grains

Alhassid¹,

Nesterov²

2014

AIP Conference Proceedings

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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.

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“…A different mechanism leading to very large spin g-factors has been proposed for normal metal particles, but large g-factors have not been confirmed until now, probably because of the weak electron-electron interactions in normal metals. [12,13] By switching the material from normal metal to a ferromagnet, the electron-electron interactions strengthen, making it more probable to observe large gfactors. Very large g-factors have been observed recently in semiconducting quantum wires and dots, where they represent the orbital contribution.…”

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Giant electron-spingfactors in a ferromagnetic nanoparticle

Gartland¹,

Birk²,

Jiang³

et al. 2013

Phys. Rev. B

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We utilize single-electron tunneling spectroscopy to measure the discrete energy levels in a nanometer-scale cobalt particle at T=60mK, and find effective single-electron spin g-factors ≈ 7.3. These large g-factors do not result from the typical orbital contribution to g-factors, since the orbital angular momentum is quenched. Instead, they are due to non-trivial many-body excitations. A kink in the plot of conductance vs. voltage and magnetic field is a signature of degenerate total spin on the particle. Spin-Orbit interactions cause the new particle eigenstates to have 'spin' that is an admixture of pure spin states. Fluctuations in the discrete energy level spacing allow for the total change in 'spin' on the particle during a single-electron tunneling event to be ∆S ′ = 3/2, leading to a g-factor around 6.

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Combined effect of electron-electron interactions and spin-orbit scattering in metal nanoparticles

Cited by 22 publications

References 37 publications

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

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

Mesoscopic superconductivity in ultrasmall metallic grains

Giant electron-spingfactors in a ferromagnetic nanoparticle

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