Eur. Phys. J. B (2015) 88: 314
https://doi.org/10.1140/epjb/e2015-60698-7

Regular Article

Multifractal analysis of electronic states on random Voronoi-Delaunay lattices

¹ Institute of Physics, Technische Universität Chemnitz, 09107 Chemnitz, Germany
² Department of Physics, Missouri University of Science and Technology, Rolla, Missouri 65409, USA

^a e-mail: martin.puschmann@physik.tu-chemnitz.de

Received: 26 August 2015
Received in final form: 12 October 2015
Published online: 26 November 2015

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.