多轨道关联电子系统是凝聚态物理的一个重要研究对象。轨道自由度的存在使得体系中电子相互作用和对称自发破缺的形式都变得更为丰富。以铁基超导体为代表的铁基材料是典型的多轨道关联系统，实验上观测到了很多不同寻常的量子特征，然而轨道自由度的引入也使得理论分析变得更加复杂。本文综合使用密度泛函（DFT）、动力学平均场（DMFT）、有效模型等多种理论手段，具体研究了两种铁基材料中的多轨道关联物理。（1） FeSe的电子向列序。向列序是铁基超导体中普遍存在的一种重要的序，在我们的工作之前，还没有第一性原理的描述。FeSe的向列序附近没有磁性序的干扰，是研究轨道自由度如何产生向列序的理想平台。我们使用DFT+U和杂化泛函，在顺磁条件下仔细搜寻轨道自由度的自发对称破缺，计算出了能量最低的向列态，复现了实验上能带结构和费米面的重要特征。对称性分析表明主要的序参量属于D4h点群的Eu不可约表示。与之前作为条带状反铁磁序的残余序而被广泛讨论的B1g Ising向列序不同，二分量的Eu矢量序会导致d轨道之间的混合以及空间反演对称性的破缺，进而产生引人注目的实验结果，比如一个电子口袋的消失。为了更精确地处理电子关联，更清晰透明地理解向列序的成因，我们进一步在五带模型的Hartree-Fock（HF）和三带模型的DMFT计算中重复出了Eu向列序。（2）CaFeTi2O6（CFTO）的复杂磁性。CFTO是一种罕见的A位有序双钙钛矿材料，与铁基超导体类似，它具有互相耦合的自旋、轨道和晶格自由度。通过引入轨道极化，我们的DFT计算更正了早期计算中预测它是半金属的错误结论。DFT+DMFT计算正确复现了顺磁顺轨道的Mott绝缘态。第一性原理电场梯度（EFG）计算定量解释了M?ssbauer谱的重要特性，为其中一半的Fe存在轨道极化提供了实验证据。我们还建立了包含自旋、轨道和晶格的最简模型，利用Monte Carlo（MC）模拟磁化曲线，分析实验观察到的奇异磁性的来源。这些计算不仅揭示了轨道自由度在以上两种材料中的重要作用，也旨在摸索研究多轨道关联物态具有普遍意义的方法和路径。总的来说，充分理解这些复杂的体系需要实验和理论的紧密结合。因此对于文中涉及的每项计算，我们都仔细论述了相关的实验数据。此外，由于轨道自由度带来的额外复杂性，很多计算的细节需要仔细地考虑，我们也尽可能地对相关的经验加以了梳理和总结。
Multiorbital correlated electron systems are an important subject in condensed matter physics. The presence of the orbital degree of freedom enriches electron interaction effects and possible spontaneous symmetry breaking patterns. Iron-based materials, represented by iron-based superconductors, are typical examples of multiorbital correlated systems. Many unusual quantum phenomena observed experimentally are closely related to the orbital degree of freedom of iron. However, the presence of the orbital degree of freedom also complicates theoretical analysis. In this dissertation, we combine multiple theoretical methods such as density functional theory （DFT）, dynamical mean-field theory （DMFT） and effective model analysis to perform a detailed study on the multiorbital correlated physics in two iron-based materials.（1） Electronic nematicity in FeSe. Nematicity is an important order in most iron-based superconductors. However, its first-principles description remains elusive before our work. FeSe represents an ideal platform to perform such study, in which nematicity disentangles from spin ordering. Here, we use DFT＋U and hybrid functional to search for the potential spontaneous symmetry breaking in the orbital channel under the paramagnetic condition. A nematic solution stands out with band structure and Fermi surface well comparable with experiments. Symmetry analysis assigns the dominant order parameter to the Eu irreducible representations of the D4h point group. Distinct from the B1g Ising nematicity as widely discussed in the context of vestigial stripe antiferromagnetic order, the two-component Eu vector order features mixing of the Fe d-orbitals and inversion symmetry breaking, which lead to striking experimental consequences, e.g. missing of an electron pocket. To treat the electron correlation more precisely, and for a more transparent understanding of nematicity, we further reproduce the Eu order parameter in both the Hartree-Fock （HF） calculation of a 5-band model and the dynamical mean-field theory （DMFT） calculation of a 3-band model. （2） Complicated magnetism in CaFeTi2O6 （CFTO）. CFTO is a rare A-site ordered double perovskite with intertwined spin, orbital, and lattice degrees of freedom, sharing similarity with iron-based superconductors. By introducing orbital polarization, our DFT calculations correct the half metal scenario proposed in an earlier work. DFT＋DMFT calculations well reproduce the paramagnetic and paraorbital Mott insulating state. First-principles electric field gradient （EFG） calculations quantitatively explain important features of the M＆＃246;ssbauer spectrum, providing key experimental evidence for orbital polarization in half of the Fe atoms. We also construct a minimal model with spin, orbit, and lattice ingredient and use Monte Carlo （MC） to simulate the magnetization curves, analyzing the origin of the unusual magnetism observed experimentally. Our calculations not only reveal the importance of the orbital degree of freedom in the above two materials, but also aim to explore the general methodology for studying multiorbital correlated states. Crucially, a comprehensive understanding of such complex systems requires a close combination of experiment and theory. Therefore, for each presented calculation, we also discuss the relevant experiments in detail. Furthermore, due to the additional complexity introduced by the orbital degree of freedom, many calculation details need to be treated carefully, which are also an emphasis during our writing.
