EAGER: Braiding of Majorana Zero Modes in the Quantum Hall - Superconductor Hybrids

摘要：半导体电子学目前依赖于电子和空穴的流动，但其他类型的类粒子“激发”可以人为地创造和控制。这些激发态，包括所谓的马约拉纳费米子和非阿贝尔任意子，具有保护它们免受外部扰动的特性。由于这种鲁棒性，对这种“拓扑激发”的控制将彻底改变电子学，使量子计算更接近现实。在过去的几年中，凝聚态研究团体在拓扑激励的实际实现方面取得了巨大的进展。人们确实意识到，它们可以通过将超导性诱导到某些低维材料（如半导体纳米线）中来人工制造。PI提出了另一种方法来制造基于高磁场和超导电极耦合的拓扑激发的石墨烯。单个拓扑激励通过可选链接连接起来，允许人们可控地耦合和操纵它们。宿主材料的平面特性应该有助于制造这些器件的多个副本，从而实现未来的缩放和与传统电子器件的集成。该项目非常强调指导和教育：涉及两名博士生，本科生和一名高中生。将招募北卡罗来纳大学科学与数学学院的高中生参加实验室活动，感受物理研究。这项研究将培养研究生和本科生在测量和纳米制造方法相关的工业和学术事业。技术摘要：研究基于II型超导体接触石墨烯的约瑟夫森结，首席研究员小组去年报告了在量子霍尔效应下第一次观察到通过二维区域的超电流。这一结果证明了超导体电极与量子霍尔边缘态相干耦合的能力。这使得首席研究小组能够接近具有更复杂几何形状的超导体-量子霍尔界面，这些界面有望承载马约拉纳费米子。具体目标是在量子霍尔台面上蚀刻出准一维“沟槽”形状的超导电极，边缘状态在接触的相反两侧反向传播。据预测，在自旋极化量子霍尔态中（例如，在填充因子等于1时），马约拉纳零模式在堑壕的两端形成。实现这些器件需要对量子霍尔态和超导体之间耦合的基本理解，以及在超导触点和量子霍尔主体材料之间设计极其干净的界面的制造技术的发展。石墨烯在这方面有很多优点：可调谐的能带结构和卓越的电子质量，这导致在相对较低的磁场下出现自旋极化量子霍尔态。一旦形成，马约拉纳零模式可以通过可选的边态链路连接起来，允许人们控制地融合（杂化）它们。这些激发的多个副本可以在同一个平台上制造，使它们能够编织。宿主材料的平面特性应该有助于制造这些器件的多个副本，从而实现未来的缩放和与传统读出电子器件的集成。最后但并非最不重要的是，这些测量有望揭示非阿贝尔任意子的迷人物理特性，它们具有与任何传统准粒子明显不同的特性。这些拓扑激发与一整类混合拓扑器件相关，并可能导致有助于使量子计算成为现实的突破。

Non-technical Abstract:Semiconductor electronics currently relies on the flow of electrons and holes, but other types of particle-like "excitations" can be artificially created and controlled. These excitations, which include so-called Majorana fermions and non-abelian anyons, have properties that protect them against external perturbations. As a result of this robustness, control over such "topological excitations" would revolutionize electronics and bring quantum computing closer to reality. Over the past few years, the condensed matter research community achieved dramatic progress in the practical implementation of topological excitations. It was indeed realized that they could be artificially created by inducing superconductivity into certain types of low-dimensional materials such as semiconducting nanowires. The PI proposes an alternative approach to create the topological excitations based graphene subject to high magnetic fields and coupled to superconducting electrodes. The individual topological excitations are connected by gateable links, allowing one to controllably couple and manipulate them. The planar nature of the host material should facilitate making multiple copies of these devices, enabling future scaling and integration with conventional electronics. The project strongly emphasizes mentoring and education: it involves two PhD students, and undergraduate and a high school student. High school students from the NC School of Science and Math will be recruited to participate in the laboratory activities and get a feel for physics research. This research will train the graduate and undergraduate students in the measurement and nanofabrication methods relevant for both industrial and academic careers.Technical Abstract:Working with Josephson junctions based on graphene contacted by type II superconductor, the principal investigator's group reported last year on the first observation of supercurrent through a two-dimensional region in the regime of the quantum Hall effect. This result proves the capability to coherently couple the superconductor electrodes to the quantum Hall edge states. It allows the principal investigator's group to approach superconductor-quantum Hall interfaces with more complex geometries, which are expected to host Majorana fermions. The specific goals are the superconducting electrodes in a shape of quasi-1D "trenches" etched in a quantum Hall mesa, with the edge states counter-propagating on the opposite sides of the contact. It has been predicted that in the spin-polarized quantum Hall regime (for example, at the filling factor equal to one), Majorana zero modes are formed at the ends of the trenches. Realizing these devices requires fundamental understanding of the coupling between the quantum Hall states and superconductor, as well as the development of fabrication techniques to design extremely clean interfaces between the superconducting contacts and the quantum Hall host material. Graphene has much to offer in that regard: a tunable band-structure and a remarkable electronic quality, which results in the appearance of the spin-polarized quantum Hall states at relatively low magnetic fields. Once formed, the Majoranas zero modes could be connected by gateable edge-state links, allowing one to controllably fuse (hybridize) them. Multiple copies of these excitations could be fabricated on the same mesa, enabling their braiding. The planar nature of the host material should facilitate making multiple copies of these devices, enabling future scaling and integration with conventional read-out electronics. Last but not least, the measurements are expected to reveal the fascinating physics of non-abelian anyons, which have properties distinctly different from any conventional quasiparticles. These topological excitations are relevant to a whole class of hybrid topological devices and could lead to breakthroughs that help make quantum computing a reality.