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Abstract
Interest in semiconductor heterostructures remains strong today, twelve years after the Nobel Prize in physics was awarded to Alferov and Kroemer for the invention of the heterotransistor. In the present day, the focus is on the quantum properties of heterostructures at low temperatures, and the high rate of experimental progress which has been made in recent years has allowed the characterization of devices with high mobility and purity to be studied at low density, low temperature and high magnetic fields. A new branch of the field has only recently emerged from the study of holes which are positively charged carriers possessing spin equal to 3/2 in conventional semiconductors, which are known to exhibit strikingly different quantum behaviour to systems composed of electrons. In this work, the theoretical framework for describing holes in 1D and 2D systems is both critically reviewed and expanded, with the common underlying being the role of the spin-orbit interaction in the formation of highly non-trivial structure which can be directly observed in transport measurements. We present three major results: 1) calculation of the anomalous 1D and 2D dispersions arising from valence band mixing, and the physical effects arising from the anomalous masses, 2) the study of the spin structure of 1D and 2D hole systems, and an analytical expression for the g-factors based on the Luttinger model, and 3) both numerical and analytical results for the spin-resolved conductance of a quantum wire in the presence of non-adiabatic dynamics arising from local spin-orbit interactions.