Electronic properties of Fibonacci quasi-periodic heterostructures

We study the electronic states of different GaAs-AlAs Fibonacci quasi-perodic heterostructures grown along the (001) direction. We employ an empirical tight-binding Hamiltonian including spin-orbit coupling together with the surface Green function matching method. We present results for the eighth Fibonacci generation formed from different building blocks. We compare these results with those of the constituent quantum wells and with those of heterostructures containing the same number of GaAs and AlAs slabs after periodic repetition of the building blocks. No Fibonacci spectrum is found in the energy regions near the conduction and valence band edges of GaAs. A selective localization of the local density of states in the GaAs layers is found for many electronic states.