Quantum Mechanical Conduction of Electrons in 1D Fibonacci Quasicrystals

Abstract

Abstract In this report we model and study the propagation of electrons in one-dimensional (1D) Fibonacci quasicrystals. The quasicrystals are modeled with delta function potentials and created by either arranging their strengths or their spacings as a 2 letter Fibonacci word. The transmission and reflection amplitudes are calculated using an iterative method. A comparison is made against an ordinary crystal and a semi-random setup. The transmission of electrons are investigated and related to the electrical conduction in the different types of materials. We also investigate how sensitive the quasicrystals are to perturbations, compared to crystals. Finally, a quasicrystal modeled with a 3 letter Fibonacci word is discussed. We find that the Fibonacci structure increases the resistance by a relatively large factor, which makes the quasicrystals act like semiconductors. We also find tendencies that the quasicrystals are more sensitive to perturbations compared to ordinary crystals. The results are in good agreement with similar, earlier studies, both theoretical and experimental

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