Monte Carlo study of disorder in electronic tight-binding models

Sammanfattning: Oftentimes solids are described by uniform, periodic lattices. In reality, however, there is often some disorder on some of the sites in the lattice. This disorder may come from, for example, there being a different type of atom or tightly bound electrons resulting in a larger on-site potential, affecting the electronic properties of the lattice. In this thesis the electronic properties of square, periodic lattices with a number of these impurity sites are studied. The main electronic properties that are studied are the electronic energies of the lattice, and the density of states. Several properties of the impurity sites are also studied. The Hamiltonians that describe the different lattices were created with the tight-binding model. Two models for the placements of impurities were considered. The binary mixture model which considers random placements of disorders and the Falicov-Kimball model which considers thermodynamic placements of disorder. The results from these models were discussed and compared. For the Falicov-Kimball model a Monte Carlo algorithm was developed to examine the system and provide accurate results. Some papers that had previously looked at approximate solutions to the Falicov-Kimball model were examined and some of the results were recreated in the hope that the developed program could be used as a benchmark for approximate solutions. Recreations of works with similar algorithms were very accurate and for the more approximate solutions my simulations shared all of the important characteristics. The efficiency of the Monte Carlo algorithm was evaluated by first studying a benchmark smaller system that could be calculated and verified by hand and then using a benchmark of a previous paper that solved the systems in a similar way. It was determined that the Monte Carlo algorithm worked as expected.