The anomalous velocity in its ultrafast regime

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Carriers in solids have fundamentally different properties than in free-space. One of the most intriguing differences is the anomalous velocity constituting carriers moving perpendicular to an electrical bias. This velocity is at the origin of fascinating physical phenomena such as the spin Hall and anomalous Hall effect and has direct impact on spintronics, topological insulators, and novel quantum computers.Our previous experimental and theoretical work on the anomalous velocity and related phenomena has led to a better understanding of light-matter interaction. Yet, it also produced fascinating results, which give rise to additional fundamental questions on anomalous velocity effects. In this proposal we would like to experimentally and theoretically investigate these so far unexplored effects in gallium arsenide (GaAs) nanostructures on ultrafast time scales:(i) We will experimentally probe the anomalous velocity in different GaAs nanostructures locally in the momentum and energy space. This work is expected to produce energy-resolved maps of intrinsic (Berry curvature) and extrinsic (scattering) contributions to the anomalous velocity, being important for future time-resolved studies of different Hall effects.(ii) We will experimentally investigate the influence of coherent interband effects on the anomalous velocity with the aim to establish the existence of new anomalous velocity components. These new velocity components are expected to appear in time-resolved studies and complement the description of the anomalous velocity.(iii) We will experimentally explore the non-Abelian Berry curvature, resulting from degenerate bands. Time-resolved experiments are an essential prerequisite for accessing the non-Abelian Berry curvature. Additionally, the experiments might also reveal new information on the Zitterbewegung, being a trembling motion first postulated by Schrödinger.Due to the complexity of the proposed work its success relies on the analysis of experimental results using elaborate microscopic calculations:(iv) We will extend the Semiconductor Bloch Equations to provide a transparent theoretical description of the generation and the coherent dynamics of the intrinsic anomalous velocity. This includes the influence of the coherent interband polarization, the non-Abelian Berry curvature, and the Zitterbewegung.(v) We will incorporate many-body effects into the theoretical description. The resulting dynamic equations will enable analysis of excitonic effects, extrinsic anomalous velocities arising from scattering effects, and also the scattering-induced damping of the intrinsic anomalous velocity.Our studies are expected to yield fundamentally novel insights into intrinsic and extrinsic contributions to the anomalous velocity. We are confident that the work will substantially improve the understanding of the anomalous velocity in its coherent and ultrafast regime and trigger additional theoretical and experimental work.