We plan to employ quantum transport characteristics, such as weak (anti-)localization, conductance fluctuations and the Aharonov-Bohm effect, as a probe of spin dynamics and associated geometrical phases in confined conductors with complex band topologies. On the one hand, we will consider quantum wires and rings with Rashba- and Dresselhaus spin-orbit coupling and investigate the interplay between confinement and spin relaxation, focusing in the role of the cubic Dresselhaus term. Based on recent work on all-electrical detection of the spin-orbit ratio α/β, we will study α/β-effects on spin coherence, in particular on Aharonov-Casher phases in transport through rings. On the other hand, we propose to develop a semiclassical path-integral approach to the quantum conductance in diffusive and ballistic hole systems, based on four-band models and invoking Berry curvature effects, with the longterm aim to devise semiclassics for topological quantum states in mesoscopic geometries. Both interrelated research lines furthermore aim at making predictions for corresponding experiments to be pursued in the Nitta and Weiss groups. We will use a powerful numerical transport code to check the analytical predictions and to employ realistic models to compare with experiment.
