08 Fakultät Mathematik und Physik
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Item Open Access Classical and semiclassical approaches to excitons in cuprous oxide(2024) Ertl, Jan; Main, Jörg (Prof. Dr.)When an electron is excited from the valence into the conduction band it leaves behind a positively charged hole in the valence band to which it can couple through the Coulomb interaction. Bound states of electrons and holes, the excitons, are the solid state analogue of the hydrogen atom. As such they follow a Rydberg series. T. Kazimierczuk et al. [Nature 514, 343 (2014)] were able to show the existence of Rydberg excitons in cuprous oxide up to principle quantum number n=25. These states then have extensions in the µm range and thus lie in a region where the correspondence principle is applicable and quantum mechanics turns into classical mechanics. A more precise study of experimental spectra reveals significant deviations from a purely hydrogen-like behavior. These deviations can be traced to the complex valence band structure of cuprous oxide which inherits the cubic symmetry of the system. A theoretical description of the band structure introduces new degrees of freedom, i.e., a quasispin I=1 describing the three-fold degenerate valence band. Due to the coupling of quasispin and hole spin the valence band splits resulting in a yellow exciton series and two green exciton series with light and heavy holes. In this thesis we provide a semiclassical interpretation for excitons in cuprous oxide beyond the hydrogen-like model. To this end we introduce an adiabatic approach diagonalizing the band structure part of the Hamiltonian in a basis for quasi- and hole spin. This leads to a description via energy surfaces in momentum space, which correspond to the different exciton series. Classical dynamics can be calculated by choosing the energy surface of the series under interest and integrating Hamilton's equations of motion. Due to the energy surfaces the symmetry is drastically reduced compared to the hydrogen-like problem now allowing for the existence of fully three-dimensional orbits as well as the possibility of chaotic dynamics. For the yellow exciton series we find mostly regular phase space regions with quasi-periodic motion on near-integrable tori and small chaotic phase space regions. To demonstrate the existence of classical exciton orbits in the quantum spectra we show that the quantum mechanical recurrence spectra exhibit peaks, which, by application of semiclassical theories and a scaling transformation, can be directly related to classical periodic exciton orbits. An analysis of the energy dependence reveals that the dynamics deviations' from a purely hydrogen-like behavior increase with decreasing energy. Starting from the full Hamiltonian we develop a spherical model from which we are able to derive the quantum defects of the yellow exciton series using a semiclassical torus quantization. A comparison with quantum mechanical calculations show good agreement with our semiclassical results, thus allowing to identify individual quantum states by a corresponding classical exciton orbit in analogy to Bohr's atomic model. Finally, we provide a comparison of yellow exciton series with the two distinct green exciton series. The phase space is analyzed by application of Poincaré surfaces of section and Lagrangian descriptors. In addition, we investigate the Lyapunov stability of individual orbits. The analysis reveals the existence of a classically chaotic exciton dynamics for both yellow and green excitons, however, the chaotic regions are more pronounced for the green than for the yellow excitons. Excitons in cuprous oxide thus provide an example of a two-particle system with chaos even without the application of external fields.Item Open Access Polaritontransformation der gelben Magnetoexzitonen in Kupferoxydul(2017) Ertl, JanWird im Halbleiter ein Elektron aus dem Valenzband in das Leitungsband angeregt, so bleibt ein Loch im Valenzband zurück. Gebundene Elektronen-Loch-Paare, die sogenannten Exzitonen, können im Festkörper durch Absorption eines Photons angeregt werden. Trifft Licht auf den Festkörper so kann es mit den Exzitonen in Wechselwirkung treten. Diese Kopplung von Licht und Exzitonen wird durch ein neues Quasiteilchen, das Exziton-Polariton, beschrieben. Zur Beschreibung der Exziton-Polaritonen wird dann ein Basiswechsel, die Polaritontransformation, durchgeführt. In dieser Arbeit wird zur Beschreibung der Exzitonen ein wasserstoffartiges Modell angenommen. Damit wird die gelbe Exzitonenserie in Kupferoxydul für verschiedene Magnetfelder in der Coulomb-Sturm'schen Basis ausgewertet. Anschließend wird die Polaritontransformation durchgeführt und der Einfluss von verschiedenen Parametern auf die Polaritondispersion untersucht.Item Open Access Adiabatic approximation for the dynamics of magnetoexcitons in Cu2O(2019) Ertl, JanWhen exciting an electron in a semiconductor from the valence to the conduction band, the missing electron in the valence band can be treated as a positively charged quasi particle, the hole. As a bound state of electron and hole the exciton is the solid state analogon to the hydrogen atom. The most important difference when comparing exctions to hydrogen-like systems is the influence of the band structure in the solid state system. The band structure breaks the full rotational symmetry of the hydrogen-like system leading to additional features in the absorption spectra of cuprous oxide. Absorption spectra for magnetoexcitons in cuprous oxide can be calculated in a quantum mechanical framework with good accordance to the experimental spectra. However those calculations are limited to low principal quantum numbers. On the other hand experimental data is available for higher energies. In the range of the gap energy one can observe quasi-Landau resonances. In atomic physics these features can be explained within a semiclassical theory. This connects properties of classical orbits to the observed absorption spectra. This thesis aims to lay down the foundations for the calculation of classical orbits for magentoexcitons in cuprous oxide as well as their parameters to provide the tools to apply semiclassical theory.