The diamagnetic Kepler problem in a semiconductor environment

This thesis focuses on the classically chaotic motion of a Rydberg electron in an external magnetic field, known as the diamagnetic Kepler problem. This area has been studied extensively in atomic systems since the first experimental observation of oscillations in atomic spectra in 1969 by Garton and Tomkins. In subsequent investigations, both theoretical and experimental, these oscillations were linked the closed classical orbits of Rydberg electrons excited at energies close to the ionization threshold. Under these excitation conditions, the electron goes into an sphericallysymmetric, near-zero energy radially outgoing Coulomb wave, sections of which are turned back towards the nucleus by the external magnetic field, thereby causing interference between the outgoing and returning waves resulting in the oscillations observed in the experimental atomic spectra. This can be efficiently modelled using classical mechanics by considering small sections of the electron wave as classical electrons where the length of time taken for the classical electron to traverse a closed orbit back to the nucleus is related to the experimental oscillation period. Due to its relative simplicity, hydrogen was predominately chosen to investigate this phenomenon. However, the recent detection of associated effects in the n-type hydrogenic doping centres of silicon have provided a new testing ground for these effects. In the course of the work presented here, we discuss how the semiconductor environment provides new classical effects not available in atomic systems. We investigate the effects associated with anisotropy leading to the so-called anisotropic diamagnetic Kepler problem, and also what effect the position of the oscillations in the spectrum have on the underlying classical mechanics. We then explore effects related to the addition of an external electric field in the special-case geometries of parallel and perpendicular to the external magnetic field. A new simplified theoretical framework for the general case of arbitrary external-field geometry is also developed.