Magnetotransport of functional oxide heterostructures affected by spin-orbit coupling: a tale of two-Dimensional systems.

Oxide heterostructures allow for detailed studies of two-dimensional electronic transport phenomena. Here different facets of magnetotransport in selected spin-orbit coupled systems are analyzed and characterized by their single-band and multi-band behavior, respectively. Experimentally, temperature and magnetic field dependent measurements in the single-band system BaPbO$_3$/SrTiO$_3$ reveal strong interplay of weak antilocalization (WAL) and electron-electron interaction (EEI). Within a scheme which treats both, WAL and EEI, on an equal footing a strong contribution of EEI at low temperatures is found which suggests the emergence of a strongly correlated ground state. Furthermore, now taking multi-band effects into account as they appear, e.g., in the model system LaAlO$_3$/SrTiO$_3$, theoretical investigations predict a huge impact of filling on the topological Hall effect in systems with intermingled bands. Already weak band coupling produces striking deviations from the well-known Hall conductivity that are only explainable in a fully quantum mechanical treatment which builds upon the hybridization of intersecting Hofstadter bands.