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

分数阶量子霍尔（FQH）系统为研究基本量子现象提供了一个非常好的平台，例如干涉和退相干、拓扑量子化、纠缠、电荷分数化以及分数阶和非阿贝尔统计。FQH系统的低洼激励位于边缘。特别是具有反传播模式的FQH边显示了丰富的物理特性。边缘处的库仑相互作用和无序发挥了突出的作用，导致了模态分数化，出现了“上游”传播的中性模和“下游”传播的带电模。在前面的项目中，我们已经证明有两种不同的传输机制——连贯的和不连贯的。这两种模式的特点是电荷模式和中性模式的分离，后者携带能量。然而，中性模式的性质和由此产生的输运性质是非常不同的。我们已经证明，两种状态下的输运观测值都反映了体拓扑结构，并且几乎所有先前的实验都是在非相干状态下进行的。我们与WIS实验组的合作已经允许设计一个基于工程边缘的实验设置，该边缘展示了我们理论预测的从相干到非相干的交叉。这些新颖的实验发现为工程和控制各种复杂的FQH边缘以及探索其在各种制度下的输运特性提供了有前途的平台。这是当前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。这样的制度应该出现在参数广泛的参数范围内的各种实验相关设置。我们的初步结果表明，部分平衡机制导致定性新颖的拓扑物理。我们将分析电荷和热传导、散粒噪声和能量分辨输运光谱，并将研究扩展到非阿贝尔边缘和具有量子点接触的几何形状。其次，我们将研究由非平凡重整化不动点描述的边缘上人工设计的新相位。这样的相位可以设计在以模间耦合层次为特征的工程边缘上。最后，我们将探讨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干涉测量。这种非平凡准粒子的量子干涉不仅具有重要的基础意义，而且具有潜在的技术重要性。这项工作将与M. Heiblum （WIS）和A. Das （IISc）的实验小组密切合作，分别探索半导体和石墨烯结构。

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.