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

P. Markos·L. Schweitzer
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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 $σ_c=1/[2π(2-D(1))] e^2/h$ 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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P. Markos, L. Schweitzer. 2006-03-15. Critical regime of two dimensional Ando model: relation between critical conductance and fractal dimension of electronic eigenstates. https://doi.org/10.1088/0305-4470%2F39%2F13%2F003

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