Quantum interference and entanglement of helical supercurrents in Dirac materials

目前，人们正致力于理解具有类狄拉克节点费米子的材料中的超导现象，如石墨烯、拓扑绝缘体、硅烯、二硫化钼等，仅举几例。在这些材料中，电子过程受到几何(Berry)相的影响，几何(Berry)相是由载流子自旋(或伪自旋)和动量方向(也称为螺旋度)耦合引起的。它导致了狄拉克材料相当特殊的性质，从抑制弹性后向散射和微弱的反局域化到预测的p波超导电性和与Majorana零模相关的拓扑简并。虽然后一个主题已经得到了相当大的关注，但超导狄拉克系统的许多相关问题仍然很少被探索。该项目解决了其中的一个问题，即狄拉克材料中螺旋超流的检测和量子控制。最近在两个超导体之间实现约瑟夫森弱连接的二维拓扑绝缘体上的实验中，朝着这个方向迈出了重要的一步。这种混合结构作为纳米级超导量子干涉器件(Nano-SQUID)，其中的干涉发生在螺旋边缘电流之间，并由外部磁通高精度地控制。这些发现可能为超微小物体的磁测量和利用纠缠螺旋电流设计新的量子比特系统的潜在应用铺平道路。除了可能的应用外，超导量子干涉还可能提供一种在输运测量中检测拓扑零模的工具。该项目旨在通过开发不同纳米鱿鱼结构中螺旋超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.