The effects of disorder on the electronic structure
Disorder and randomness lead to new phenomena in the electronic structure, the most prominent of which is Anderson localization. It describes the localization of wave functions in a small region of space as opposed to the extended Bloch waves found in perfect crystals. Recently, we have found a system with which we can correlate theory and experiment on an atomic scale. Interestingly, calculations to compare experiment with theory can be done on an undergraduate level giving much conceptual insight. The project involves calculating the electronic structure for different disordered two-dimensional lattices within a real space tight-binding model (e.g. graphene, surface alloys). The idea is to find out how the fundamental parameters used to describe the model can be extracted from experimental data.
The project involves programming in MatLab, which is a high-level, easy to learn programming language highly suitable for matrix manipulation. As three generations of coop students have worked so far on this project, it has already evolved into a small package with a number of functionalities, such as the capability to calculate different kinds of disorder and defects in graphene or trigonal lattices. It can now be applied, for example, to better understand the effects of defects on the graphene band structure. From a student's perspective, the project offers deep insight into the understanding of band structures. It nicely illustrates the difference between the idealized band structure of a perfect lattice and the imperfect band structure in the real world as well as why the perfect model works in most cases anyway.