Scaling properties of the electronic structure of quasiperiodic GaAs/AlxGa1-xAs superwires and superdots

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.