Multifractal analysis of electronic states on random Voronoi-Delaunay lattices

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.

References in corpus (6)

• Anderson Transitions
• Critical exponent for the Anderson transition in the three dimensional orthogonal universality class
• Multifractal analysis of the metal-insulator transition in the 3D Anderson model I: Symmetry relation under typical averaging
• Multifractal analysis of the metal-insulator transition in the 3D Anderson model II: Symmetry relation under ensemble averaging
• Contact process on a Voronoi triangulation
• Phase Transitions on Random Lattices: How Random is Topological Disorder?

Cited by in corpus (6)

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• Mobility edges and fractal states in quasiperiodic Gross-Pitaevskii chains
• Amplitude mode at the superfluid-insulator transition on a random lattice
• Critical Behavior and Collective Modes at the Superfluid Transition in Amorphous Systems