Abstract
We study the electronic states of different GaAs-AlAs Fibonacci, Thue-Morse and Rudin-Shapiro quasiperiodic 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 different generations of the quasiperiodic heterostructures, formed by different building blocks. We compare these results with those of the constituent quantum wells and with those of heterostructures containing the same total number of GaAs and AlAs slabs after periodic repetition of the building blocks. The states in the energy regions near the conduction- and valence-band edges of GaAs do not exhibit any spectrum fragmentation. They show a strong localization of the local density of states in the GaAs layers, and they can be traced to the states of the isolated quantum wells.
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