节线圈具有Hopf连接型拓扑半金属理论研究

Nodal-loop topological semimetals are hot spots in condensed matter physics. What this project concerns is a new kind of gapless topological quantum states. These semimetal states have several nodal loops which are Hopf linked with each other. This project will study in one same framework all nodel-loop semimetal states including Hopf-link,unlink, nodal-chain as well as nodal-net states, and compare their drumhead surface states and identify their relevant characteristic properties. We also study the connection of the Hopf-link semimetal states with Hopf insulators. We also investigate some linear responses related to experiments, including Landau levels, Floquet states and transport properties, which may help experimentalists identify or distinguish those semimetal states. We also study some related important questions, including topological stability of nodal lines and nodal loops and the relevant symmetries; topological stability against disorder and interaction;possibility of realizing superconductivity on the surface of materials. We expect these work can help us better understand the topological quantum behaviors of this kind of gapless materials.

具有节线圈的拓扑半金属态是近年凝聚态物理中的热点问题。本课题关注的是一类新型具有节线圈的三维拓扑半金属量子态。这类无能隙量子态具有多个节线圈，线圈彼此不相交而且互相非平凡的缠绕，称为Hopf连接型节线圈半金属态。本课题旨在在统一的的模型或框架下研究所有类型的节线圈态（包括Hopf连接与非连接态，节线链态，节线网态），比较不同节线圈态的drumhead表面态的异同以及和每种节线圈态相关的本征属性。研究Hopf连接的节线圈态和Hopf绝缘体的联系。此外也研究一些和实验相关的线性响应，包括体系的Landau能级，有效Floquet态以及简单的输运性质，期望得到和Hopf连接态与非连接态相对应的特征拓扑属性，便于实验上辨识和区分这些半金属态。同时还探讨节线圈的拓扑稳定性以及与之相关的对称以及在表面实现超导及拓扑超导电性的可能。期望通过这些工作能更深入的理解此类无能隙半金属的拓扑量子现象。

本课题关注的是近年来凝聚态物理中的热点问题：节线圈的拓扑半金属态。具体地我们探讨一类新型具有节线圈的三维拓扑半金属量子态。这类无能隙量子态具有多个节线圈，线圈彼此不相交而且互相非平凡的缠绕，称为Hopf连接型节线圈半金属态。本课题旨在在统一的的模型或框架下研究所有类型的节线圈态，比较不同节线圈态的drumhead表面态的异同以及和每种节线圈态相关的本征属性以及在量子输运中的自旋和电荷输运现象。我们发现了节线圈半金属相关输运中存在半透射，全反射，自旋完全极化共振透射的输运现象，这些现象和节线圈半金属的拓扑属性密切相关。同时我们还探讨节线圈的拓扑稳定性以及与此问题相关的拓扑超导配对对称性的问题以及在相关冷原子体系中涡旋激发等问题。我们期望通过这些工作能更深入的理解此类无能隙半金属的拓扑量子现象。