The anomalous velocity in its ultrafast regime

固体中的载体与自由空间中的载体具有根本不同的性质。最耐人寻味的区别之一是构成载流子垂直于电偏置运动的异常速度。这一速度是自旋霍尔和反常霍尔效应等令人着迷的物理现象的起源，并直接影响到自旋电子学、拓扑绝缘体和新型量子计算机。我们之前对反常速度和相关现象的实验和理论工作使我们对光-物质相互作用有了更好的理解。然而，它也产生了令人着迷的结果，这引发了关于反常速度效应的其他基本问题。在这个方案中，我们想要在超快时间尺度上从实验和理论上研究砷化镓(GaAs)纳米结构中这些迄今未被探索的效应：(I)我们将在动量和能量空间中对不同的GaAs纳米结构中的反常速度进行实验探索。这项工作有望产生内部(Berry曲率)和外部(散射)对反常速度的贡献的能量分辨图，这对未来不同霍尔效应的时间分辨研究很重要。(Ii)我们将通过实验研究相干带间效应对反常速度的影响，目的是建立新的反常速度分量的存在。这些新的速度分量有望出现在时间分辨研究中，并补充对反常速度的描述。(Iii)我们将从实验上探索由简并带产生的非阿贝尔Berry曲率。时间分辨实验是获得非阿贝尔Berry曲率的基本前提。此外，这些实验还可能揭示关于Zitterbewegung的新信息，Zitterbewegung首先是由Schrödinger假设的一种颤动运动。由于拟议的工作的复杂性，它的成功依赖于使用精细的微观计算对实验结果的分析：(Iv)我们将扩展半导体Bloch方程，以提供本征异常速度的产生和相干动力学的透明理论描述。这包括相干带间极化、非阿贝尔Berry曲率和Zitterbewegung的影响。(V)我们将多体效应纳入到理论描述中。由此得到的动力学方程将能够分析激子效应、由散射效应引起的外在反常速度，以及由散射引起的本征反常速度的衰减。我们的研究有望从根本上对反常速度的内在和外在贡献产生新的见解。我们相信，这项工作将大大提高对相干和超快区域中的反常速度的理解，并引发更多的理论和实验工作。

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.