Spin-orbit scattering in superconducting nanoparticles

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.