Engineered Complex Edges of Fractional Quantum Hall Phases: Coherence, Topology, and Non-Equilibrium

分数量子霍尔(FQH)系统是研究基本量子现象的理想场所，如干涉和退相干、拓扑量子化、纠缠、电荷分数以及分数和非阿贝尔统计等。FQH系统的低能级激发位于边缘。特别丰富的物理是通过具有反向传播模式的FQH边缘显示的。边缘的库仑相互作用和无序起着重要的作用，导致模的分馏化和中性模的出现，中性模在“上游”传播，带电模式在“下游”传播。在前面的项目中，我们证明了有两种截然不同的运输制度--连贯和不连贯。这两个体系的特点是电荷模式和中性模式分离，而中性模式携带能量。然而，中性模式的特性以及由此产生的传输特性是非常不同的。我们已经证明，在这两个区域中的输运观测数据反映了整体的拓扑结构，并且几乎所有以前的实验都是在非相干区域中进行的。我们与WIS实验小组的合作使我们能够设计一种基于工程边缘的实验装置，该装置已经展示了我们理论预测的从相干到非相干区域的交叉。这些新颖的实验发现为设计和控制各种复杂的FQH边缘和探索它们在不同区域的输运特性提供了很有前途的平台。这是本项目的主要动机之一。首先，我们将探索以边缘部分平衡为特征的部分相干输运机制。在各种与实验相关的环境中，这种制度应该出现在参数范围广泛的参数范围内。我们的初步结果表明，部分平衡态导致了定性新颖的拓扑物理。我们将分析电荷和热导、散粒噪声和能量分辨输运光谱，将研究扩展到具有量子点接触的非阿贝尔边缘和几何图形。其次，我们将研究由非平凡重整化不动点描述的边缘上的新的人工设计的相。这样的阶段可以设计在以内模耦合的层次为特征的工程边缘上。最后，我们将探索涉及边缘新工程相的基本激发的量子干涉现象，包括Mach-Zehnder、Hanbury-Brown-Twiss和Hong-ou-Mandel干涉计量学。这种非平凡准粒子的量子干涉既具有基本意义，也具有潜在的技术重要性。这项工作将与M.Heiblum(Wis)和A.Das(IISc)分别探索半导体和石墨烯结构的实验小组密切合作进行。

Fractional quantum Hall (FQH) systems represent a remarkable playground to study fundamental quantum phenomena, such as interference and decoherence, topological quantization, entanglement, charge fractionalization, and fractional and non-abelian statistics. Low-lying excitations of FQH systems are located at the edge. Especially rich physics is displayed by FQH edges with counterpropagating modes. Coulomb interaction and disorder at the edge play a prominent role, leading to mode fractionalization and to the emergence of neutral modes propagating “upstream”, along with charged modes propagating “downstream”. Within the preceding project we have demonstrated that there are two distinct transport regimes—coherent and incoherent. Both regimes are characterized by a separation of charge and neutral modes, with the latter carrying energy. However, properties of the neutral modes, and the resulting transport properties, are very different. We have shown that transport observables in both regimes reflect bulk topology and that nearly all previous experiments were done in the incoherent regime. Our collaboration with WIS experimental group has permitted to devise an experimental setup based on an engineered edge that has demonstrated the crossover from the coherent to incoherent regime predicted by our theory. These novel experimental discoveries lead to promising platforms for engineering and controlling a variety of complex FQH edges and exploring their transport properties in various regimes. This serves as one of key motivations for the present project. First, we will explore partially coherent regimes of transport which are characterized by partial equilibration at the edge. Such regimes should emerge in parametrically broad range of parameters for a variety of experimentally relevant settings. Our preliminary results show that partially equilibrated regimes lead to qualitatively novel topological physics. We will analyze charge and heat conductances, shot noise, and energy-resolved transport spectroscopy, extending the study also to non-abelian edges and geometries with quantum point contacts. Second, we will investigate novel artificially designed phases on the edge described by non-trivial renormalization fixed points. Such phases may be designed on engineered edges that are characterized a hierarchy of inter-mode couplings. Finally, we will explore quantum interference phenomena involving elementary excitations of the new engineered phases on the edge, including Mach-Zehnder, Hanbury-Brown-Twiss, and Hong-Ou-Mandel interferometry. Such quantum interference of non-trivial quasi-particles is of fundamental as well as of potential technological importance. The work will be carried out in close cooperation with experimental groups of M. Heiblum (WIS) and A. Das (IISc) exploring semiconductor and graphene structures, respectively.