Spin-orbit coupling and topological phase transitions in semiconductor heterostructures

Spintronics, or spin-based electronics, is a current field of study that seeks to enhance the operation of electronic devices at the quantum level via manipulation of the electron spin. Semiconducting materials, which form the backbone of modern electronic technology, offer a natural platform for exploring approaches towards spin-based devices. Despite the highly advanced state of the field, however, traditional theoretical paradigms describing charge transport in semiconducting systems have so far been insufficient to permit the creation of semiconductor spintronic devices. The development of theoretical concepts to describe spin transport in existing semiconductor systems, as well as those that are accessible by current experimental technology, is the subject of this thesis. Our starting point will be materials in which spin properties have been historically predicted to respond strongly to applied electric fields - an effect known as spin-orbit coupling. Quantum engineering of these systems allows for a wide range of novel physical effects to emerge. A particularly exciting possibility is the creation of artificial lattices, created via nanofabrication on semiconductor heterostructures, which are quantum simulators of two-dimensional crystals with additional tunable interactions. This thesis will present theoretical studies of charge and spin transport in one and two-dimensional conducting systems engineered in semiconductor materials. Analytical and numerical results are presented for quantum models of transport in three different systems: semiconductor quantum wells, quantum point contacts, and artificial lattices. These results are expected to lead to new experiments to control and probe spin dynamics, as well as to introduce novel physical effects that will enhance the possibilities for these systems to be used in spintronic devices