A semiclassical theory of the Anderson transition

Abstract

We study analytically the metal-insulator transition in a disordered conductor by combining the self-consistent theory of localization with the one parameter scaling theory. We provide explicit expressions of the critical exponents and the critical disorder as a function of the spatial dimensionality, $d$. The critical exponent $\nu$ controlling the divergence of the localization length at the transition is found to be $\nu =\frac{1}{2}+\frac{1}{d-2}$. This result confirms that the upper critical dimension is infinity. Level statistics are investigated in detail. We show that the two level correlation function decays exponentially and the number variance is linear with a slope which is an increasing function of the spatial dimensionality.

4 pages, journal version

References in corpus (3)

• Anderson Localization of Expanding Bose-Einstein Condensates in Random Potentials
• Dimensional dependence of the metal-insulator transition
• Multifractality of Hamiltonians with power-law transfer terms

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• Character of eigenstates of the 3D disordered Anderson Hamiltonian
• Renormalization group for Anderson localization on high-dimensional lattices
• Interpretation of high-dimensional numerical results for Anderson transition
• Presence and Absence of Delocalization-localization Transition in Coherently Perturbed Disordered Lattices
• Critical behavior of Anderson transitions in higher dimensional Bogoliubov-de Gennes symmetry classes
• Disorder and Interactions in Graphene and other Quantum Systems