J. Ribeiro et al., Scaling properties of the electronic structure of quasiperiodic GaAs/AlxGa1-xAs superwires and superdots, PHYSICA B, 305(1), 2001, pp. 38-47
We investigate the scaling properties of GaAs/AlxGa1-xAs quasiperiodic supe
rwires (superdots) structures building up following the Fibonacci, Thue-Mor
se and double-period sequences of concentric cylindrical (spherical) shells
. We perform a quantitative analysis on the electronic structure of their a
llowed bands in order to find how the scaling properties are related with t
he number of generations of the sequences. We show that the total allowed b
andwidth (the Lebesgue measure of the energy spectrum) Delta scales as the
power law Delta similar to (F-n)(-delta) for the Fibonacci sequence, where
F-n is the Fibonacci number and delta is the diffusion constant of the spec
tra. For both the Thue-Morse and double-period sequences, the power law is
given by Delta similar to (2(n))(-delta), with n being the number of the ge
neration of the sequence. (C) 2001 Elsevier Science B.V. All rights reserve
d.