A computational study of Rydberg excitons and defects in cuprous oxide

Abstract

Various theoretical and computational techniques were applied to Rydberg excitons in cuprous oxide. The techniques fall into two catagories: top down, and bottom up. In the first chapter, Floquet theory is applied to a hydrogen-like model of an exciton to model the ultrastrong driving of the exciton by a microwave field. This is the top down approach, where the exciton is considered as an atom and the effect of the crystal is considered only insofar as it alters the energy levels and dipole transition moments of the atom. This method is very successful, quantitatively reproducing the experimental results up to the highest field strengths achievable. We demonstrate how the high energy exciton states hybridise into a quasi-continuum of Floquet states, and we can also predict qualitatively the intensity of sidebands on the laser, opening avenues for microwave-to-optical conversion. However, there are places the model fails, such as in correctly predicting the dependence on the polarisation of the microwave field. This is the limit of what can be done with models that neglect the effects of the crystal. Beginning the ab initio 'bottom up' approach, in chapter 2 we study the effect of point defects on the electronic structure of CuO using density functional theory, with the aim of determining the origin of experimentally observed photoluminescence peaks. The method is very successful in determining which defects are not involved in photoemission, having accounted for many possible sources of erroneous results. However, it is difficult to make positive assignments as to exactly which peak is caused by which defect. Finally, in chapter 3, we begin to bridge the two approaches, studying ab initio the excitations of CuO with time-dependent density functional theory. We demonstrate a novel method for estimating the radius of the 1S exciton, and show the effect that a local defect on the localisation of the exciton and on the excitation energies. These results demonstrate new theoretical approaches to understanding of Rydberg excitons, especially in applying ab initio techniques, which is not currently seen in the field.