Localization Properties Of Electronic States Of One-dimensional Aperiodic Sequences

The electronic properties of one-dimensional quasicrystals are usually studied in the framework of the tight-binding model, and only the nearest neighbor interactions between atoms are taken into account. In this framework, many peculiar physical properties have been found, especially in the Fibonacci sequence. The most obvious characteristic is the self-similarity, which is clearly shown in the electronic spectra and the wave functions. Moreover, there are three kinds of wave functions: extended, localized, and intermediate states. The study on the quasiperiodic sequences fills the gap between periodic and disordered systems. The main feature of the one-dimensional disordered system is that the atomic arrangement has no long-range order, but only short-range order. Anderson has shown that the one-dimensional disordered system has a pure point spectrum and all the electronic states are localized.In this thesis, we study the electronic properties of one-dimensional Galois sequences, which are different from quasiperiodic sequences. We generate Galois sequences by the recursion relation, which is derived from the corresponding irreducible polynomial.Following the same route to study the one-dimensional quasiperiodic sequences, we first establish two kinds of tight-binding models for Galois sequence: the on-site model and the transfer model. We then numerically calculate the energy spectra for the two models. It is found that when the hopping integrals are weak, the energy spectrum consists of only two parts. With the hopping interaction increasing, the energy levels overlap each other. We also study the localization properties and the results show that the second moment and the inverse participation ratio are both in the range of the localized states. This result is also supported by the localization length. Finally, we compare the electronic properties of Galois sequence with other one-dimensional aperiodic sequences, and we come to the conclusion that the electronic properties of Galois sequence are in accordance with the Anderson localization.