DFT+DMFT Investigation of Strongly Correlated Topological Materials

强关联拓扑相将电子-电子相互作用驱动的自发对称性破缺现象与量子波函数的非平凡拓扑结合在一起。这些相所在的材料具有广泛的应用前景。然而，对于真实的材料，利用超越密度泛函理论(DFT)并适当处理关联的方法获得的精确关联电子结构，仍然缺乏对其拓扑性质的表征。这种获得相关材料拓扑特征的一致方法对理解当前的实验观察结果具有重要的价值，并将指导新材料的进一步设计。这个项目的目的是实现有效的理论方法，这些方法可以应用于基于DFT和动态平均场理论(DMFT)的相关拓扑材料的表征，重点关注局部电子关联重要的系统。我们的目标是扩展和应用目前的DFT+DMFT方法，对自旋-轨道耦合和局域电子关联进行一致处理，以获得准确的电子结构，然后按照简化的相互作用拓扑理论计算各种拓扑不变量。虽然我们特别关注相关绝缘材料的拓扑特征，以及通过在平板几何中执行计算来显式探索其中的表面态，但我们也特别关注具有非平凡拓扑性质的半金属系统以及标杆输运性质的定量评估。

Strongly correlated topological phases combine the emergent phenomena of spontaneous symmetry breaking driven by electron-electron interaction with the nontrivial topology of the quantum wave functions. Materials which host such phases are promising candidates for a wide spectrum of applications. However, a characterization of their topological nature based on accurate correlated electronic structure obtained using methods beyond density functional theory (DFT) with proper treatment of correlations is still missing for real materials. Such a consistent way to obtain the topological character of correlated materials is valuable to understand the current experimental observations and will guide further design of novel materials. The purpose of this project is to implement effective theoretical methods which can be applied to characterize correlated topological materials based on DFT and dynamical mean field theory (DMFT) methods, focusing on systems where local electronic correlations are important. We aim at extending and applying the current DFT+DMFT methodology for a consistent treatment of spin-orbit coupling and local electronic correlations to obtain accurate electronic structure, and then to evaluate various topological invariants following the simplified interacting topological theory. While a particular focus falls on the topological characterization of correlated insulating materials, as well as explicit exploration of the surface states therein by performing calculations in the slab geometry, we also dedicate special attention to semimetallic systems with nontrivial topological nature together with quantitative evaluation of benchmarking transport properties.