自2006年以来，探究新型拓扑材料和理论解释拓扑机制一直是凝聚态物理领域的研究热点之一。拓扑材料的能带具有非平庸的拓扑性质，拥有拓扑边缘态是其重要特征。另外，笼目晶格由于具有本征平带和狄拉克点等独特的能带结构而备受关注。因此，探索更多具有笼目晶格的拓扑非平庸材料以及调控它们的物性是具有重要意义的。本论文主要是通过基于密度泛函理论的第一性原理计算方法设计并研究了一种具有笼目晶格结构的拓扑半金属Pt₃P₂Te₈。

具体来说，我们从理论计算角度，系统地研究了Pt₃P₂Te₈的电子结构、拓扑性质以及压力和掺杂带来的拓扑相变规律等。Pt₃P₂Te₈的能带结构和电子态密度揭示了在考虑自旋轨道耦合时其半金属特征，且在费米能级附近的Γ-A路径上存在一个狄拉克点。Pt₃P₂Te₈的笼目晶格由Pt原子构成，不过其费米能级附近的能带受与Te-5p较大杂化影响而变得具有一定的色散。计算时间反演不变点上电子占据态的宇称发现，Pt₃P₂Te₈是拓扑非平庸的，且在Γ-A路径上存在单次能带反转现象。其（100）面的拓扑表面态展示了其拓扑绝缘态和体狄拉克点的投影的共存。（100）面上费米弧的脆弱行为进一步体现了Pt₃P₂Te₈的狄拉克半金属特征。对于加压和考虑mBJ（modified Becke-Johnson）修正的情况，Pt₃P₂Te₈表现出丰富的拓扑相变行为，mBJ修正的效果与加负压类似。由于原子轨道的展宽不同，Se与Te的相互掺杂也会驱动其拓扑性质发生改变。因此可以通过加压或掺杂的方式对其电子结构进行调控。总之，本文提出的Pt₃P₂Te₈是一个全新的研究拓扑半金属、笼目晶格以及调控拓扑性质的潜在平台。

Since 2006, exploring new topological materials and theoretically explaining topological mechanisms have been one of the hot topics in the field of condensed matter physics. The bands of topological materials exhibit non-trivial topological characteristics, and having topological edge states is one of their important features. Additionally, the Kagome lattice structure has attracted attention due to its unique band structure features such as intrinsic flat bands and Dirac points. Therefore, exploring topologically nontrivial materials with Kagome lattices and manipulating their physical properties is of great significance. This thesis designs and studies a new topological semimetal Pt₃P₂Te₈ which has Kagome lattice structure, using first-principle calculations based on Density Functional Theory.

Specifically, from theoretical calculation perspective, we systematically studied the electronic structure, topological properties, and the patterns of topological phase transitions induced by pressure and doping in Pt₃P₂Te₈. The band structure and electronic state density of Pt₃P₂Te₈ reveal semimetallic characteristics when considering spin-orbit coupling, with a Dirac point present on the Γ-A path near the Fermi level. The Kagome lattice of Pt₃P₂Te₈ is composed of Pt atoms, but the bands near the Fermi level are significantly hybridized with Te-5p, resulting in some dispersion. Calculations of the parity of electronic states at time-reversal invariant points indicate that Pt₃P₂Te₈ is topologically non-trivial, with a single band inversion occurring on the Γ-A path. Its topological surface states on the (100) surface show the coexistence of topological insulating state and the projection of the bulk Dirac point. The fragile behavior of the Fermi arcs on the (100) surface further reflects the Dirac semimetal characteristics of Pt₃P₂Te₈. Under pressure and considering the mBJ exchange potential correction, Pt₃P₂Te₈ exhibits a rich behavior of topological phase transitions, where the effects of mBJ correction are similar to applying negative pressure. Due to the different spreading of atomic orbitals, doping of Se and Te also drives topological properties. Thus, its electronic structure can be regulated by pressure or doping. In summary, Pt₃P₂Te₈ represents a new research platform for exploring topological semimetals, Kagome lattices, and the control of topological properties.