g-Factors of Discrete Levels in Nanoparticles

Spin-orbit scattering suppresses Zeeman splitting of individual energy levels in small metal particles. This suppression becomes significant when the spin-orbit scattering rate ${\tau }_{\mathrm{so}}^{-1\mathrm{}}$ is comparable to the quantum level spacing $\delta$. At small $\delta {\tau }_{\mathrm{so}}$ the $g$-factor exhibits strong mesoscopic fluctuations. We find the shape of their distribution function using the random matrix theory, and express its parameters in terms of physical characteristics: ${\tau }_{\mathrm{so}}$, $\delta$, the electron mean free path $l$, and the particle size $L$. At $\delta {\tau }_{\mathrm{so}}\to 0$ the average $g$-factor levels off at a small value $g\sim (l/L{)}^{1/2}$. However, in 2D quantum dots the $g$-factor is strongly enhanced by spin-orbit coupling.