Anderson mobility edge as a percolation transition
arxiv(2023)
摘要
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. Near the edge of the spectrum, the eigenstates are
confined inside the basins of the LL-based potential. The delocalization
transition corresponds to the progressive merging of these basins resulting in
the percolation of this classically-allowed region throughout the system. 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.
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