Electronic spectra of GaAs/GaxAl1−xAs superlattice with impurities arranged according to a Fibonacci sequence

AbstractWe study the electronic density of states (DOS) of a GaAs/Ga x Al 1 x As superlattice with impurities arranged according to theFibonacci sequence. Our theory uses a Green function method based on Dyson’s equation within the real-space renormalization-group approach in the framework of the tight-binding Hamiltonian for the Fibonacci quasiperiodic lattice. An exact decimationtransformation has been done for the physical parameters characterizing the Fibonacci chain considering the scaling factor,under which the system is self-similar, equal to the golden mean t ¼ð1 þffiffiffi5pÞ=2. The electronic energy spectrum are then usedto determine the electronic specific heat which, due to the localization of the electronic states, exhibits strong Schottkyanomalies when the temperature goes to zero together with a log-periodic oscillation.# 2004 Elsevier B.V. All rights reserved. PACS: 05.10.Cc; 61.44.Br; 65.40.Ba; 68.65.Cd; 71.20.NrKeywords: Electronic density of states; Tight-binding Hamiltonian; Dyson’s equation; Real-space renormalization-group approach; Electronicspecific heat