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

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

2005-11-17

arxiv.org/abs/cond-mat/0511434v2

J. Phys. A: Math. Gen. 39 (2006) 3221-3230

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

IOP Latex, 7 figures

Scientific paper

10.1088/0305-4470/39/13/003

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.

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