Anderson localization problem: an exact solution for 2-D anisotropic systems
V.N. Kuzovkov, W. von Niessen
TL;DR
This paper provides an exact analytical solution for the 2-D anisotropic Anderson localization problem, revealing the nature of the metal-insulator transition and the emergence of two localization lengths in such systems.
Contribution
It generalizes previous 2-D Anderson localization solutions to anisotropic systems with different hopping elements, analyzing the phase transition and localization lengths.
Findings
Identification of two localization lengths in anisotropic systems
Mathematical characterization of the metal-insulator transition in 2-D
Contrast with the 1-D case where no phase transition occurs
Abstract
Our previous results [J.Phys.: Condens. Matter 14 (2002) 13777] dealing with the analytical solution of the two-dimensional (2-D) Anderson localization problem due to disorder is generalized for anisotropic systems (two different hopping matrix elements in transverse directions). We discuss the mathematical nature of the metal-insulator phase transition which occurs in the 2-D case, in contrast to the 1-D case, where such a phase transition does not occur. In anisotropic systems two localization lengths arise instead of one length only.
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