非常规超导是凝聚态物理研究的重要前沿，拓扑超导更是当前的热点问题。非常规超导体系不同磁序和超导电性的竞争是科学家们最关心的问题之一，拓扑超导电性研究最大的挑战是寻找合适的体系。在近年来研究基础上，我们将继续结合解析推导，尤其是非微扰的数值技术，集中探讨非常规或拓扑超导体系的超导配对模式、超导电性和磁性的竞争，特别是拓扑超导态的理论实现。我们将从一些微观电子模型出发，研究1，非常规超导体系磁性和超导电性的竞争，理论探索高温超导体系可能的拓扑超导态；2，六角晶格体系的量子临界及可能的拓扑超导电性；3，掺杂拓扑体系的拓扑超导态，主要关注锡烯、BiX(X=H,F,Cl,Br,I)及Weyl半金属等；4，应力对非常规超导的影响。通过这些研究，探寻理论上实现拓扑超导态的体系和边界上Majorana费米子的方法，揭示超导配对模式的参数依赖，深入理解非常规超导的微观机制，完善和发展现有量子蒙特卡罗方法。

The unconventional superconducting system is among the center of the study on condensed- matter physics, and the topological superconductivity is a hot issue in recent filed of condensed-matter physics. The vicinity between magnetic order and superconductivity in unconventional superconducting systems is one of the most concerned issues for scientists. The most important challenge in topological superconductivity is to find the system to realize it. On the basis of recent research, we will continue to combine analytic derivation, especially non-perturbable numerical techniques, to focus on the superconductivity pairing mode and the vicinity between superconductivity and magnetic correlation of the unconventional or topological superconducting system, especially the theoretical realization of topological superconductivity. We will proceed from some micro-electronic models to search for: 1. The vicinity between superconductivity and magnetic in unconventional superconducting system, and to explore the possible topological superconductivity in high-temperature superconducting system theoretically; 2, the quantum critical point and possible topological superconductivity in hexagonal lattice systems; 3, the topological superconductivity in doped topological system, especially focus on the stanine film BiX (X = H, F, Cl, Br, I) and Weyl semi-metal, etc. 4. the effect of stress on unconventional superconductivity. Through these studies, we could deeply understand the microscopic mechanism of unconventional superconductivity, and explore the method of realizing topological superconductors, as well as Majorana fermion on the boundary of the topological superconducting system. These studies should also reveal the competition between magnetic correlation and superconductivity, and the parameter dependence of superconducting pairing mode, and by the way, develop and improve the existing quantum Monte Carlo method.