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

TL;DR

This paper numerically investigates the energy eigenvalue statistics at the metal-insulator transition in disordered 2D systems with spin-orbit interaction, finding a critical exponent close to that of the quantum Hall system.

Contribution

It provides a new estimate of the critical exponent for 2D disordered symplectic systems, aligning it with the quantum Hall system, using finite-size scaling of level statistics.

Findings

Critical exponent ν ≈ 2.32 ± 0.14

Level statistics consistent with quantum Hall system

Finite-size scaling method applied to energy level distributions

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.