Random Matrix Theory for Closed Quantum Dots with Weak Spin-Orbit Coupling

To lowest order in the coupling strength, the spin-orbit coupling in quantum dots results in a spin-dependent Aharonov-Bohm flux. This flux decouples the spin-up and spin-down random matrix theory ensembles of the quantum dot. We employ this ensemble and find significant changes in the distribution of the Coulomb blockade peak height, in particular, a decrease of the width of the distribution. The puzzling disagreement between standard random matrix theory and the experimental distributions by Patel et al. [Phys. Rev. Lett. 81, 5900 (1998)] might possibly be attributed to these spin-orbit effects.

Figure 1

Correlations of the level tunneling rates $C_{\Gamma }$ and the rescaled spectral diffusion correlator $C_E$ for the RMT model (2), as a function of $x\sqrt{N}$ for different matrix sizes $N$. The data collapse for different $N$ indicates the universality.

Figure 2

Width of the conductance distribution $\sigma (G)/⟨G⟩$ vs temperature. At low temperatures, the RMT ensemble for weak spin-orbit interaction [dashed line; dotted line: low temperature behavior Eq. (7)] well describes the experiment [10] (symbols correspond to slightly different quantum dots), in contrast to standard RMT (solid line) [10]. At higher temperatures, a further suppression is due to inelastic scattering processes (dot-dashed line: ${\Gamma }_{\mathrm{i}\mathrm{n}}=\infty$ high-$T$ asymptote).

Figure 3

RMT predictions with weak spin-orbit coupling (dashed line) for the probability distribution of the Coulomb blockade peak conductance for a quantum dot at $k_{B}T=0.1\Delta$ (left) and $k_{B}T=0.5\Delta$ (right), compared with the Patel et al. experiment [10] (histograms) and standard RMT theory [10] (solid line). There are no free parameters in these distributions.