在一些含重元素的化合物或中心反演非对称系统中，自旋轨道耦合效应显著。这一方面改变电子能带结构并可能使其具有特殊的拓扑结构，另一方面使得关联效应因自旋SU(2)对称的破缺而改变，可以导致更为丰富的超导相，其中包括拓扑超导。后者有望作为拓扑量子计算的平台。本项目我们用自主发展的基于奇异模式分解的泛函重整化群等理论方法研究这类系统中自旋轨道耦合与关联效应的相互影响，研究其非常规超导配对机制及其对称性，探索实现拓扑超导的关键因素，揭示相关超导态的物理性质，包括电子态的微观结构、热力学性质、输运性质和拓扑性质等，为相关的实验研究提供理论参考。

In compounds with heavy elements or in noncentrosymmetric systems, a significant spin-orbital coupling reorganizes the electron band structure, possibly leading to a nontrivial topology. This also changes the effect of correlations because of the absence of spin SU(2) symmetry, leading to a richer variety of superconducting phases, some of which are topologically nontrivial and may act as the platform of topological quantum computing. In this project, by the singular-mode functional renormalization group we developed independently and related theoretical methods, we investigate the interplay between spin-orbital coupling and electron correlation, investigate the mechanism and symmetry of unconventional superconductivity, explore the key factors for topological superconductivity, and unravel the physical properties of the resulting superconducting phases, such as the microscopic electronic structure, thermodynamic, transport and topological properties, shedding light for experiments.