Dresden 2009 – wissenschaftliches Programm

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HL: Fachverband Halbleiterphysik

HL 9: Poster 1

HL 9.73: Poster

Montag, 23. März 2009, 14:30–17:00, P2

Energy Level Statistics for the Anderson Model and in Small World Networks — •Oliver Böhm, Philipp Cain, and Michael Schreiber — Institut für Physik, Technische Universität, D-09107 Chemnitz

The Anderson model of localization (AML) describes the behavior of a single electron in a disordered solid. In three dimensions this model shows a localization-delocalization (LD) transition of the electronic wave function. For our investigation we evaluate the statistics of energy level spacings which allows us to characterize the LD transition and to distinguish between localized and delocalized behavior. First, we study the discrete AML on a three-dimensional cubic lattice where disorder is described by a variation of the on-site potential and each site is connected to its six neighbor sites. Then we extend the AML by modifying the links between sites similar to a small-world network (SWN) where the six links of each site can connect to any other site in the system independent of the distance between the sites. The particularity of these networks is, that the average path length is much shorter as in regular networks. It is not obvious whether an LD transition can be observed. Since we transform links to SWN links with a given probability we can trace the critical behavior starting from the known case of AML. We show that an increase of the critical disorder results already from a small percentage of SWN links.