Anderson mobility edge as a percolation transition

TL;DR

This paper proposes that the Anderson localization transition in 3D systems can be understood as a percolation transition of the potential landscape derived from localization landscape theory, providing a new perspective on the mobility edge.

Contribution

It introduces a percolation-based interpretation of the Anderson transition using the localization landscape potential, applicable to different disorder types.

Findings

The localization landscape potential predicts delocalization onset in 3D models.

Eigenstates are confined within potential basins near the spectrum edge.

The mobility edge corresponds to a percolation transition of these basins.

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. 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.