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

The combined effect of electron-electron interactions and spin-orbit scattering in metal nanoparticles can be studied by measuring splitting of electron levels in magnetic field $(g$ factors) in tunneling spectroscopy experiments. Using random matrix theory to describe the single-electron states in the metal particle, we find that even a relatively small electron-electron interaction strength (ratio of exchange constant J and mean level spacing $\delta \simeq 0.3)$ significantly increases g-factor fluctuations for not-too-strong spin-orbit scattering rates (spin-orbit time ${\tau }_{\mathrm{so}}\gtrsim 1/\delta ).\mathrm{}$ In particular, g factors larger than 2 could be observed. (This is a manifestation of the many-body correlation effects in nanoparticles). While so far measurements only on noble metal (Cu, Ag, Au) and Al samples have been done for which the effects of electron-electron interactions are negligible, we discuss the possibility of observing interaction effects in nanoparticles made of other metals.