Spin-orbit scattering in superconducting nanoparticles
Y. Alhassid, K. N. Nesterov
备注：
10 pages, 6 figures, submitted for a special volume of Fortschritte der Physik (Progress of Physics), dedicated to the conference on Frontiers of Quantum and Mesoscopic Thermodynamics (FQMT15)
We review interaction effects in chaotic metallic nanoparticles. Their single-particle Hamiltonian is described by the proper random-matrix ensemble while the dominant interaction terms are invariants under a change of the single-particle basis. In the absence of spin-orbit scattering, the non-trivial invariants consist of a pairing interaction, which leads to superconductivity in the bulk, and a ferromagnetic exchange interaction. Spin-orbit scattering breaks spin-rotation invariance and when it is sufficiently strong, the only dominant nontrivial interaction is the pairing interaction. We discuss how the magnetic response of discrete energy levels of the nanoparticle (which can be measured in single-electron tunneling spectroscopy experiments) is affected by such pairing correlations and how it can provide a signature of pairing correlations. We also consider the spin susceptibility of the nanoparticle and discuss how spin-orbit scattering changes the signatures of pairing correlations in this observable.
It is shown that nanoparticles made of low $T_c$ superconductors have large diamagnetic response at temperatures several orders of magnitude above $T_c$. Most features of the recently observed Giant diamagnetism of Au nanorods are explained in terms of superconducting fluctuations, except for the huge magnitude of the effect.
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Spin-orbit scattering suppresses Zeeman splitting of individual energy levels in small metal particles. This suppression becomes significant when the spin-orbit scattering rate τ_{so}^{-1} is comparable with the quantum level spacing δ. The g-factor exhibits mesoscopic fluctuations; at small δτ_{so} it is distributed according to the Maxwell distribution. At δτ_{so}\to 0 the average g-factor levels off at a small value g\sim(l/L)^{1/2} given by the ratio of the electron mean free path l to the particle size L. On the contrary, in 2D quantum dots the g-factor is strongly enhanced by spin-orbit …
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