The Anderson mobility edge as a percolation transition
Author:
Marcel Filoche, Pierre Pelletier, Dominique Delande, Svitlana Mayboroda
Keyword:
Condensed Matter, Disordered Systems and Neural Networks, Disordered Systems and Neural Networks (cond-mat.dis-nn)
journal:
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date:
2023-09-06 16:00:00
Abstract
The location of the mobility edge is a long standing problem in Anderson localization. In this paper, we show that the effective confining potential introduced in the localization landscape (LL) theory predicts the onset of delocalization in 3D tight-binding models, in a large part of the energy-disorder diagram. The delocalization transition corresponds to the percolation of the classically-allowed region of the LL-based potential throughout the system, which is very different from the percolation of the original potential. This approach, shown to be valid both in the cases of uniform and binary disorders despite their very different phase diagrams, allows us to reinterpret the Anderson transition in the tight-binding model: the mobility edge appears to be composed of two branches, one being understood as a percolation transition while the second branch, going to the critical disorder at zero energy, is a consequence of the discrete lattice.