Quantum interference and entanglement of helical supercurrents in Dirac materials

目前，人们正在努力理解具有节点Dirac类费米子的材料中的超导现象，例如石墨烯，拓扑绝缘体，硅烯，二硫化钼，仅举几例。在这些材料中，电子过程受到由载流子自旋（或赝自旋）和动量方向（也称为螺旋度）耦合引起的几何（Berry）相位的影响。它是狄拉克材料相当奇特的性质，从抑制弹性背散射和弱反定域到预测的p波超导性和拓扑简并与马约拉纳零模式。虽然后一个主题已经得到了相当大的关注，超导狄拉克系统的许多相关问题仍然很少探索。该项目解决了其中一个问题，即狄拉克材料中螺旋超电流的检测和量子控制。在这个方向上的一个重要步骤已经在最近的实验中完成了二维拓扑绝缘体实现为两个超导体之间的约瑟夫森弱链接。这种混合结构充当纳米级超导量子干涉器件（纳米SQUID），其中干涉发生在螺旋边缘电流之间，并且通过外部磁通量以高精度控制。这些发现可能为超小物体的磁力测量和使用纠缠螺旋电流的新量子比特系统的工程中的潜在应用铺平道路。除了可能的应用，超导量子干涉可以提供一个工具，用于检测拓扑零模式的运输测量。该项目旨在通过开发不同纳米SQUID结构中螺旋超电流的量子干涉和纠缠的微观描述，从理论上评估这些前景。

There is currently much effort being put into understanding superconducting phenomena in materials with nodal Dirac-like fermions such as graphene, topological insulators, silicene, molybdenum disulfide, just to name a few. In these materials, electronic processes are influenced by geometric (Berry) phases caused by the coupling of the carrier spin (or pseudospin) and momentum directions, also referred to as helicity. It is responsible for rather peculiar properties of Dirac materials, from the suppression of elastic backscattering and weak antilocalization to the predicted p-wave superconductivity and topological degeneracies associated with Majorana zero modes. While the latter topic has already received considerable attention, many related issues of superconducting Dirac systems still remain barely explored. This project addresses one of such issues, namely the detection and quantum control of helical supercurrents in Dirac materials. An important step in that direction has been done in recent experiments on two-dimensional topological insulators implemented as Josephson weak links between two superconductors. Such hybrid structures act as nanoscale superconducting quantum interference devices (nano-SQUIDs) in which the interference occurs between helical edge currents and is controlled with high precision by an external magnetic flux. These findings may pave the way towards potential applications in magnetometry of ultra-small objects and in engineering of new qubit systems using entangled helical currents. Apart from possible applications, superconducting quantum interference may provide a tool for detecting topological zero modes in transport measurements. The project aims to assess these prospects theoretically by developing a microscopic description of quantum interference and entanglement for helical supercurrents in different nano-SQUID structures.