基于高阶外尔半金属的Josephson效应的理论研究

高阶外尔半金属是2020年提出的一种高阶拓扑相，具有新型体-边对应关系：同时存在外尔点型体态、二维费米弧型表面态和一维棱态（铰链态）。该物相兼具外尔半金属与高阶拓扑相的特征，可以呈现出丰富的物理现象，具有重要的理论意义和应用价值。高阶外尔半金属目前已在基于超材料的声学系统中被实验证实，但尚未在晶体中实现；理论研究则集中于磁性电子系统。本项目即关注高阶外尔半金属的电子输运性质，具体包括：（1）构造一种非磁性的高阶外尔半金属模型哈密顿量并研究其低能电子性质，揭示不同模型参数对应的相图、尺寸效应以及门电压的调控效应；（2）研究其与超导耦合体系的电子输运性质，主要关注直流Josephson效应，考察超导临界电流随弱磁场的演化图样，厘清尺寸效应、退相干、安德森无序等的影响。通过以上工作，将对高阶外尔半金属的研究推广到非磁性电子系统，并提出一种基于Josephson效应检测高阶外尔半金属的方案。

Higher-order Weyl semimetal is a new higher-order topological phase proposed in 2020. It has a new bulk-boundary correspondence that Weyl nodes (bulk states), two-dimensional Fermi-arc surface states and one-dimensional hinge states coexist. Since it links Weyl semimetal with higher-order topology, it can present rich phenomena and is very important in theory and applications. For the time being, higher-order Weyl semimetals have been realized experimentally in metamaterials for phonons, but not yet in crystalline solids for electrons. Besides, the theoretical study has focused in magnetic electronic system only. This project is to study the electronic transport properties of higher-order Weyl semimetals. At first, we propose a model Hamiltonian of the non-magnetic higher-order Weyl semimetal. We study its low-energy electronic properties, including: the phase diagram for various parameters, size effect and the effect of gate voltages. Then, we study electronic transports of a higher-order Weyl semimetal coupled to superconductors. We focus mainly on dc Josephson effect. We study the relation between the critical superconducting current and weak magnetic field to uncover the effect of geometrical size, dephasing and Anderson disorder. This project can extend the study of higher-order Weyl semimetals from magnetic to non-magnetic system of electrons. And it will design an experimental scheme to measure higher-order Weyl semimetals by Josephson effect.