Multifractal properties of critical eigenstates in two-dimensional systems with symplectic symmetry

The multifractal properties of electronic eigenstates at the metal-insulator transition of a two-dimensional disordered tight-binding model with spin-orbit interaction are investigated numerically. The correlation dimensions of the spectral measure $\widetilde{D}_{2}$ and of the fractal eigenstate $D_{2}$ are calculated and shown to be related by $D_{2}=2\widetilde{D}_{2}$. The exponent $\eta=0.35\pm 0.05$ describing the energy correlations of the critical eigenstates is found to satisfy the relation $\eta=2-D_{2}$.