DFT+DMFT Investigation of Strongly Correlated Topological Materials

强相关拓扑相结合了由电子-电子相互作用驱动的自发对称性破缺的涌现现象和量子波函数的非平凡拓扑。承载这种相的材料是广泛应用的有希望的候选者。然而，基于密度泛函理论（DFT）之外的方法获得的精确相关电子结构的拓扑性质表征，以及适当的相关性处理，在实际材料中仍然缺乏。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意义，并将指导新材料的进一步设计。本项目的目的是基于DFT和动态平均场理论（DMFT）方法实现可用于表征相关拓扑材料的有效理论方法，重点关注局部电子相关性重要的系统。我们旨在扩展和应用现有的DFT+DMFT方法来一致处理自旋轨道耦合和局部电子相关，以获得准确的电子结构，然后根据简化的相互作用拓扑理论评估各种拓扑不变量。虽然特别关注相关绝缘材料的拓扑特征，以及通过在板几何中执行计算对其表面状态的明确探索，但我们也特别关注具有非平凡拓扑性质的半金属系统，以及对基准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.