Bound states in the continuum in cuprous oxide quantum wells

Abstract

Excitons were first introduced in the 1930s by J. A. Frenkel, as the quanta of the excitation of an electron in a semiconductor. When an electron in a semiconductor is excited, it leaves behind a positively charged electron hole. The electron and hole, bound by the Coulomb force, form a quasi-particle known as an exciton. This exciton, made up of both a negative and a positive charge, can be thought of as the solid-state analog of a hydrogen atom. The first experimental observation of excitons was made by Gross and Karryev in Cu2O in 1952. This thesis specifically explores Wannier-Mott excitons. Due to different bandgaps of the adjoint materials, the exciton can be considered trapped in a quantum potential well. Moreover, the higher quantum-confinement subbands couple with the continuum of the lower ones, resulting in resonance states above the scattering threshold. Under certain circumstances, some resonance states appear to have an infinite lifetime, which means these states are bound. These so-called bound states in the continuum (BIC) are the main subject of this thesis. They will be further investigated by approximating an exciton trapped in a cuprous oxide quantum well through quantum defect theory (QDT) and comparing it with numerically precise calculations based on a large B-spline basis. First, there will be a theoretical introduction to excitons in general. Further, the QDT will be explained, and the method of approximating the system will be detailed. After that, the method of approximating the wavefunctions in a B-spline basis together with the complex-coordinate-rotation method will be explained. Lastly, the results of both methods will be compared and discussed.