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The Anderson-Mott transition

D. Belitz and T. R. Kirkpatrick

D. Belitz

  • Department of Physics, and Materials Science Institute, University of Oregon, Eugene, Oregon 97403

T. R. Kirkpatrick

  • Institute for Physical Science and Technology, and Department of Physics, University of Maryland, College Park, Maryland 20742

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Rev. Mod. Phys. 66, 261 – Published 1 April, 1994

DOI: https://doi.org/10.1103/RevModPhys.66.261

Abstract

The interacting disordered electron problem is reviewed with emphasis on the quantum phase transitions that occur in a model system and on the field-theoretic methods used to describe them. An elementary discussion of conservation laws and diffusive dynamics is followed by a detailed derivation of the extended nonlinear sigma model, which serves as an effective field theory for the problem. A general scaling theory of metal-insulator and related transitions is developed, and explicit renormalization-group calculations for the various universality classes are reviewed and compared with experimental results. A discussion of pertinent physical ideas and phenomenological approaches to the metal-insulator transition not contained in the sigma-model approach is given, and phase-transition aspects of related problems, like disordered superconductors and the quantum Hall effect, are discussed. The review concludes with a list of open problems.

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