Optical properties of semiconductor nanostructures in magnetic field

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In this work, the near bandgap linear optical properties of semiconductor quantum structures under applied magnetic field are investigated. These properties are determined mainly by a quasi-particle consisting of one electron and one hole called exciton. First, the exciton theory is developed starting with the one-electron Hamiltonian in a crystal, continuing with the Luttinger and Bir-Pikus Hamiltonian, and ending with the exciton Hamiltonian in the envelope function approximation. Further, concentrating on the quantum well and thus assuming strong confinement in the growth (z-) direction, the motion parallel and perpendicular to the xy-plane is factorized leading to the well-known single sublevel approximation. A magnetic field perpendicular to the xyplane is applied, and a general theorem describing the behavior of the energy eigenvalues is derived. This theorem is generally valid for any many-particle system. Last but not least, the strain calculation within the isotropic elasticity approach is described in detail. Second, disorder is taken into account. After discussing its properties, the standard ansatz of factorizing exciton relative and center-of-mass motion is introduced. The Schrödinger equation is solved numerically for both the full model and the factorization with artificially generated disorder potentials showing that the differences between them are pronounced especially for tail states. From the physical point of view it is shown that (i) the diamagnetic shift, i. e. energy change with magnetic field, is inversionally proportional to the localization of the wave function, (ii) the distribution of the diamagnetic shifts of individual exciton states exists and these shifts are non-monotonic in energy, (iii) the average value of the diamagnetic shift increases with energy, and (iv) absorption and consequently photoluminescence spectra become wider with increasing magnetic field. Furthermore, having structural information from the cross-sectional scanning tunneling microscopy of a given sample avaible, the statistical properties of the disorder in a real quantum well have been analyzed. This analysis enabled the numerical generation of new lateral disorder potentials which served as input in the simulation of exciton optical properties. In particular, temperature dependent photoluminescence spectra and diamagnetic shift statistics, have been compared with the experimental ones and very good agreement has been found. The second part of this thesis deals predominantly with highly symmetrical structures embedded in the quantum well: namely quantum rings and dots. First, adopting an ansatz for the wave function, the Hamiltonian matrix is derived discussing which matrix elements are non-zero according to the symmetry of the potential. Additionally, the expectation values of the current and magnetization operators are evaluated. Then, concentrating on the case of the highest (circular) symmetry, the model of zero width ring is introduced. Within this model the close relation between the oscillatory component of the exciton energy (exciton Aharonov-Bohm effect) and the persistent current is revealed. Examples for different material systems follow revealing the importance of the relation between exciton Bohr radius and ring diameter for oscillations and persistent current to be observed. The circular quantum dot is treated briefly. Finally, a case of the non-circular ring is discussed and it is shown that oscillations can be observed although with lower amplitude compared to circular case. Finally, the exciton emission kinetics is calculated, too. The limitations of the experimental observability of energy oscillations, photoluminescence quenching, caused by non-zero non-radiative channels are disclosed.