463 research outputs found

    Fluctuations of the inverse participation ratio at the Anderson transition

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    Statistics of the inverse participation ratio (IPR) at the critical point of the localization transition is studied numerically for the power-law random banded matrix model. It is shown that the IPR distribution function is scale-invariant, with a power-law asymptotic ``tail''. This scale invariance implies that the fractal dimensions DqD_q are non-fluctuating quantities, contrary to a recent claim in the literature. A recently proposed relation between D2D_2 and the spectral compressibility χ\chi is violated in the regime of strong multifractality, with χ→1\chi\to 1 in the limit D2→0D_2\to 0.Comment: 4 pages, 3 eps figure

    Quantum criticality and minimal conductivity in graphene with long-range disorder

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    We consider the conductivity σxx\sigma_{xx} of graphene with negligible intervalley scattering at half filling. We derive the effective field theory, which, for the case of a potential disorder, is a symplectic-class σ\sigma-model including a topological term with θ=π\theta=\pi. As a consequence, the system is at a quantum critical point with a universal value of the conductivity of the order of e2/he^2/h. When the effective time reversal symmetry is broken, the symmetry class becomes unitary, and σxx\sigma_{xx} acquires the value characteristic for the quantum Hall transition.Comment: 4 pages, 1 figur
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