Testing the Order Parameter of the Anderson Transition

概要

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The typical value of the local density of states \rho_{\text{typ}}, known as a candidate of the order parameter of the Anderson transition, of two-dimensional disordered electron systems with spin--orbit interactions is studied for assessing the validity of \rho_{\text{typ}} as the order parameter. We show that \rho_{\text{typ}} behaves critically as \rho_{\text{typ}}\propto (E_{\text{c}}-E)^{\beta} with \beta=0.466\pm 0.095 near the transition point. It is also found that the exponent \beta satisfies the scaling relation with the Lipschitz--Hölder exponent \alpha_{0}. Furthermore, we demonstrate that fluctuations in \rho_{\text{typ}} at the Anderson transition obey the generalized Gumbel distribution, which is expected to be the universal distribution function of critical fluctuations of order parameters. These results suggest that \rho_{\text{typ}} is a suitable quantity of the order parameter of the Anderson transition.
2012-10-15