Effects of spin-orbit interactions on tunneling via discrete energy levels in metal nanoparticles

The presence of spin-orbit scattering within an aluminum nanoparticle affects measurements of the discrete energy levels within the particle by (1) reducing the effective g factor below the free-electron value of 2, (2) causing avoided crossings as a function of magnetic field between predominantly spin-up and predominantly spin-down levels, and (3) introducing magnetic-field-dependent changes in the amount of current transported by the tunneling resonances. All three effects can be understood in a unified fashion by considering a simple Hamiltonian. Spin-orbit scattering from 4% gold impurities in superconducting aluminum nanoparticles produces no dramatic effect on the superconducting gap at zero magnetic field, but we argue that it does modify the nature of the superconducting transition in a magnetic field.