Critical regime of two-dimensional Ando model: relation between critical conductance and fractal dimension of electronic eigenstates

The critical two-terminal conductance g(c) and the spatial fluctuations of critical eigenstates are investigated for a disordered two-dimensional model of non-interacting electrons subject to spin-orbit scattering (Ando model). For square samples, we verify numerically the relation sigma(c) = 1/[2 pi(2 - D(1))]e(2)/h between critical conductivity sigma(c) = g(c) = (1.42 +/- 0.005)e(2)/h and the fractal information dimension of the electron wave function., D(1) = 1.889 +/- 0.001. Through a detailed numerical scaling analysis of the two-terminal conductance we also estimate the critical exponent v = 2.80 +/- 0.04 that governs the quantum phase transition.