Non-interacting electrons and the metal-insulator transition in 2D with correlated impurities

Abstract

While standard scaling arguments show that a system of non-interacting electrons in two dimensions and in the presence of uncorrelated disorder is insulating, in this work we discuss the case where inter-impurity correlations are included. We find that for point-like impurities and an infinite inter-impurity correlation length a mobility edge exists in 2D even if the individual impurity potentials are random. In the uncorrelated system we recover the scaling results, while in the intermediate regime for length scales comparable to the correlation length, the system behaves like a metal but with increasing fluctuations, before strong localization eventually takes over for length scales much larger than the correlation length. In the intermediate regime, the relevant length scale is not given by the elastic scattering length but by the inter-impurity correlation length, with important consequences for high mobility systems.

arXiv comment4 pages

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• Seeing Anderson Localization
• Simple model for a quantum wire III. Transmission of finite samples with correlated disorder
• Ensemble Averaged Conductance Fluctuations in Anderson Localized Systems
• Localization properties of a two-channel 3D Anderson model
• One Dimensional Localization for Arbitrary Disorder Correlations
• Density wave propagation in a two-dimensional random dimer potential: from a single to a bipartite square lattice
• Density of states of disordered systems with a finite correlation length