Anderson mobility edge as a percolation transition

Abstract

The location of the mobility edge is a long-standing problem in Anderson localization. In this Letter, 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 parts, one being understood as a percolation transition.

Locations

• Physical review. B./Physical review. B - View
• arXiv (Cornell University) - View - PDF
• HAL (Le Centre pour la Communication Scientifique Directe) - View