Regensburg 2004 – wissenschaftliches Programm
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HL: Halbleiterphysik
HL 53: Elektronentheorie
HL 53.1: Vortrag
Freitag, 12. März 2004, 12:00–12:15, H13
A renormalization approach for the Anderson model in d=1 and d=2 at the band edge: Scaling of the localization length — •Stefanie Russ — Institut für Theoretische Physik III, Universität Giessen, D-35392 Giessen, Germany
A renormalization procedure for the electronic wave functions of the one- and two-dimensional Anderson model with diagonal disorder is developed that applies close to the band edges. This theory leads in d=1 to a scaling form of the localization length λ∼ ⟨є2⟩−1/3 f((2−| E|)/⟨є2⟩2/3), in agreement with former works. In d=2 a similar scaling form applies for the localization volume V (participation ratio), i.e. V1/2 ∼⟨є2⟩−1/2 g((4−| E|)/⟨є2⟩). Here, ⟨є2⟩ is the variance of the site potentials, E is the energy and f(x) and g(x) are the scaling functions (f(0)=g(0)=1).
λ and V close to the band edges are studied by numerical simulations and confirm this scaling ansatz. The scaling functions f(x) and g(x) show a crossover between the two regimes x≪ 1 and x ≫ 1. It is shown that these two regimes refer to Λ ≫ λ0 and Λ ≪ λ0, respectively where Λ is the wavelength, λ0 in d=1 is the localization length at the band edge and λ0 in d=2 is the effective localization length V1/2 at the band edge.