Impact of the valence band structure of cuprous oxide for excitons in quantum wells

Abstract

Excitons, postulated in the 1930s, play an important role in the fundamental research of optical properties of semiconductors and insulators. While previous research at ITP1 has mainly focused on excitons in the bulk, this bachelor thesis deals with an additional spatial boundary of the crystal, the Quantum Wells. The bound states of electron and hole can be described as hydrogen-like in a first approximation. An already implemented algorithm serves as a numerical solution approach for a hydrogen-like description of the exciton, containing Quantum Wells. For a more detailed description of the exciton states, however, the crystal structure must also be taken into account. As a known ansatz to consider the band structure of cuprous oxide, the Suzuki-Hensel-Hamiltonian is chosen, where the free parameters are determined by a fit of the Hamiltonian to a simulated band structure. Since the band structure and Quantum Wells break several important symmetries and additionally create new degrees of freedom through a spin-orbit coupling a naive diagonalisation of the resulting Hamiltonian with the already known algorithm would not provide adequate computing time. Therefore both the algorithm and the Hamiltonian must first be modified. The numerical optimisation is applied simultaneously in another bachelor thesis at the ITP1. This bachelor thesis, on the other hand, deals with an analytical consideration of the Hamiltonian. The aim is to reduce the degrees of freedom of the Hamiltonian by using the remaining symmetries, and thus to minimise the required computing time for the numerical diagonalisation.