Multifractal Analysis of Electronic States on Random Voronoi-Delaunay Lattices
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.
M. Puschmann et al., "Multifractal Analysis of Electronic States on Random Voronoi-Delaunay Lattices," European Physical Journal B: Condensed Matter and Complex Systems, vol. 88, no. 11, pp. 314, Springer Berlin, Nov 2015.
The definitive version is available at https://doi.org/10.1140/epjb/e2015-60698-7
Center for High Performance Computing Research
Keywords and Phrases
Fractals; Order Disorder Transitions; Phase Diagrams; Anderson Localization; Electronic Wave Functions; Finite Size Scaling; First-Order Phase Transitions; Interacting Electrons; Multifractal Analysis; Statistical and Nonlinear Physics; Two-Dimensional Systems; Wave Functions
International Standard Serial Number (ISSN)
Article - Journal
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