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

• Applicant: Professor Dr. Alexander Mirlin
• Subject Area: Theoretical Condensed Matter Physics
• Term: since 2017
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 320540272

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.

• DFG Programme: Research Grants