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

Abstract

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 ${\sigma }_c=g_c=(1.42\pm 0.005)e^2/h$ and the fractal information dimension of the electron wave function, $D(1)=1.889\pm 0.001$. Through a detailed numerical scaling analysis of the two-terminal conductance we also estimate the critical exponent $\nu =2.80\pm 0.04$ that governs the quantum phase transition.

IOP Latex, 7 figures

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