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205. Multifractality and metal-insulator transition
This is a guest blog post by Matthew Foster from Rutgers about his recent paper arXiv:0901.0284v1 [cond-mat.dis-nn]. Dmitry.
In most electronic materials, impurities and other defects (“quenched disorder”) play a dominant role in shaping transport phenomena. Of particular interest has been the interplay between multiple impurity scattering and quantum interference effects. The scaling theory of localization, developed nearly 30 years ago by Abrahams, Anderson, Licciardello, and Ramakrishnan, predicts that sufficiently strong impurity scattering can exponentially localize electronic wavefunctions; when all states at the Fermi energy become localized, the material is an insulator, incapable of conducting electric current at zero temperature. This effect is especially pronounced in low dimensions, where the scaling theory in fact predicts that all wavefunctions localize for arbitrarily weak disorder (in the conventional symmetry classes of disordered metals). By contrast, in three and higher dimensions, a continuous metal-insulator transition (MIT) is predicted to occur at a critical value of the sample conductance.
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