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

P. Markos; L. Schweitzer

doi:10.1088/0305-4470/39/13/003

paper

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

arXiv:cond-mat/0511434 · doi:10.1088/0305-4470/39/13/003

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 $σ_{c} = 1/ [2 π (2 - D (1))] e^{2} / h$ between critical conductivity $σ_{c} = g_{c} = (1.42 \pm 0.005) e^{2} / h$ 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 $ν = 2.80 \pm 0.04$ that governs the quantum phase transition.

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