Multifractal analysis of electronic states on random Voronoi-Delaunay lattices

TL;DR

This study investigates electron transport on random Voronoi-Delaunay lattices, revealing localized states in 2D and two Anderson transitions in 3D, with results aligning with the orthogonal universality class.

Contribution

It demonstrates how topological disorder and anticorrelations in Voronoi-Delaunay lattices affect Anderson localization and phase transitions.

Findings

Localized states in 2D for all energies

Two Anderson transitions in 3D near band edges

Critical exponent of about 1.6 for localization length

Abstract

We consider the transport of non-interacting electrons on two- and three-dimensional random Voronoi-Delaunay lattices. It was recently shown that these topologically disordered lattices feature strong disorder anticorrelations between the coordination numbers that qualitatively change the properties of continuous and first-order phase transitions. To determine whether or not these unusual features also influence Anderson localization, we study the electronic wave functions by multifractal analysis and finite-size scaling. We observe only localized states for all energies in the two-dimensional system. In three dimensions, we find two Anderson transitions between localized and extended states very close to the band edges. The critical exponent of the localization length is about 1.6. All these results agree with the usual orthogonal universality class. Additional generic energetic randomness introduced via random potentials does not lead to qualitative changes but allows us to obtain a phase diagram by varying the strength of these potentials.