Scaling of level-statistics and critical exponent of disordered two-dimensional symplectic systems

Abstract

The statistics of the energy eigenvalues at the metal-insulator-transition of a two-dimensional disordered system with spin-orbit interaction is investigated numerically. The critical exponent $\nu$ is obtained from the finite-size scaling of the number $J_0$ which is related to the probability $Q_{n}(s)$ of having $n$ energy levels within an interval of width $s$. In contrast to previous estimates, we find $\nu=2.32\pm 0.14$ close to the value of the two-dimensional quantum Hall system.