Fluctuations of $g$ Factors in Metal Nanoparticles: Effects of Electron-Electron Interaction and Spin-Orbit Scattering

We investigate the combined effect of spin-orbit scattering and electron-electron interactions on the probability distribution of $g$ factors of metal nanoparticles. Using random matrix theory, we find that even a relatively small interaction strength significantly increases $g$-factor fluctuations for not-too-strong spin-orbit scattering (ratio of spin-orbit rate and single-electron level spacing $1/{\tau }_{\mathrm{s}\mathrm{o}}\delta \lesssim 1$), and leads to the possibility to observe $g$ factors larger than 2.

Figure 1

Ensemble averaged $g$ factors for $J/\delta =0$, $0.1$, $0.2$, $0.3$, $0.4$, $0.5$, and $0.6$. Note that the limit $\lambda \to 0$ is singular. The figure shows $⟨g⟩$ for $\lambda >0$. For $\lambda =0$ one has $⟨g⟩=2$.

Figure 2

Cumulative $g$-factor distribution for $\lambda =0.70$, $J=0$ (solid curve), $\lambda =0.85$, $J=0.2\delta$ (points), $\lambda =0.90$, $J=0.3\delta$ (dotted line), $\lambda =1.0$, $J=0.4\delta$ (dash-dotted line), and $\lambda =1.15$, $J=0.6\delta$ (dashed line). The values of $\lambda$ are chosen such that $⟨g⟩=1.58$ in all cases. Inset: Probability for a level to have a $g$ factor larger than two, for $J/\delta =0.1–0.6$, versus $\lambda$.