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# A new technique to calculate the electronic structure of disordered and quasicrystal systems in two-dimensions.

thesis

posted on 2015-11-19, 09:18 authored by Abdulkadir. YildizThe purpose of this work is to investigate the electronic structure of two-dimensional structurally disordered solids and quasicrystals by means of the Beeby and Hayes method which is based on multiple scattering theory. Using this method, the formal expressions for a two-dimensional system, such as the dynamical matrix and the spectral density, are determined in terms of a self-consistent function. The expressions are then applied to two-dimensional models to evaluate the densities of electronic states. Two principal issues are investigated in the calculations of the density of states. One is to illustrate the convergence of the method through the results of calculations. The other issue is to observe the variation of densities of electronic states with- respect to varying the disorder in the structure. For the first case, different sizes of the dynamical matrix, which correspond to the atomic structure of the system, are solved, and for each matrix the density of states is calculated. It is found that the densities of states for a disordered system do not change after the matrix size (NxN) exceeds 101x101. In the second case, some particular models are chosen, such as 3-fold, 4-fold, 5-fold and 6-fold coordinated sites, and the densities of states are calculated for each model. It is shown that the densities of states vary significantly with increasing disorder in the structure. The electronic structure of a two-dimensional quasicrystal, i.e. a Penrose lattice, has also been investigated in the tight binding limit using this approach. We have in particular studied the vertex model of the lattice and calculated the density of electronic states and integrated density of electronic states. The method used is effectively for an infinite structure and produces no distortions from edge effects or periodic continuation. The vertex model, which is based on fat and thin rhombi, has three nearest interatomic distances, the short diagonal of a thin rhombus, the edge of a rhombus, and the short diagonal of a fat rhombus. We have found the effect of interactions involving these various distances in the DOS. For example, there exists a very high central peak at zero energy if only the shortest is taken, the peak disappears if the first and second shortest distances are taken, and when all three distances are included there are no gaps and no central peak. The density of electronic states is asymmetric in all three cases.

## History

## Date of award

1995-01-01## Author affiliation

Physics and Astronomy## Awarding institution

University of Leicester## Qualification level

- Doctoral

## Qualification name

- PhD

## Language

en## Administrator link

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