PH-NODE：基于DFPT和有限位移超胞的拓扑声子材料节点搜索Python代码
PH-NODE: A DFPT and finite displacement supercell based python code for searching nodes in topological phononic materials
AI总结：
本文介绍PH-NODE，一个基于DFPT和有限位移超胞的Python代码，用于第一性原理搜索拓扑声子材料中的节点，并在FeSi、LiCaAs、ScZn和TiS中验证了其准确性。
摘要：
探索声子的拓扑物理对于理解各种实际应用具有根本重要性。在此，我们介绍一个基于密度泛函微扰理论和有限位移超胞的Python 3软件包，名为PH-NODE，用于通过第一性原理方法高效计算真实材料中存在的声子节点。当前版本代码与WIEN2k、Elk和ABINIT软件包接口。为了对代码进行基准测试，考虑了四种不同类型的材料，包括(i) FeSi，一个众所周知的二重Weyl点；(ii) LiCaAs，一种半Heusler单I型Weyl拓扑声子(TP)；(iii) ScZn，共存节线和节环拓扑声子；(iv) TiS，六对体Weyl节点。在FeSi中，节点位于Γ(0, 0, 0)和R(0.5, 0.5, 0.5)高对称点。此外，有21个能量值处存在节点，对应于整个布里渊区。对于LiCaAs，先前报道的文献声称在W-X高对称方向上的最高纵向声学支和最低横向光学支之间存在一个节点，而在我们的DFT计算中，发现了一个0.17 meV的能隙。此外，ScZn在布里渊区边界平面靠近M高对称点处拥有六个节环拓扑声子。除此之外，沿Γ-X和Γ-R高对称方向还发现了直线型拓扑声子。再者，对于TiS，沿H-K高对称方向发现了六个Weyl节点(WP1、WP2、WP3、WP4、WP5和WP6)。PH-NODE代码获得的结果与每种材料的实验和理论报道数据高度一致。
英文摘要：
Exploring the topological physics of phonons is fundamentally important for understanding various practical applications. Here, we present a density-functional perturbation theory and finite displacement supercell based Python 3 software package called PH-NODE for efficiently computing phonon nodes present in real material through a first-principle approach. The present version of the code is interfaced with the WIEN2k, Elk, and ABINIT packages. In order to benchmark the code, four different types of materials are considered, which include (i) FeSi, a well-known double-Weyl point; (ii) LiCaAs, a half-Heusler single-type-I Weyl topological phonon (TP); and (iii) ScZn, coexisting nodal-line and nodal-ring TPs; (iv) TiS, six pairs of bulk Weyl nodes. In FeSi, the node points are found at $Γ$(0, 0, 0) and R(0.5, 0.5, 0.5) high symmetric points. Also, there are 21 energy values at which the node points are situated, corresponding to the full Brillouin Zone. For LiCaAs, the previously reported literature claims that there is a node point along the W-X high symmetry direction between the highest longitudinal acoustic and the lowest transverse optical branch, while in our DFT calculations, a gap of 0.17 meV is found. Furthermore, ScZn hosts six nodal-ring TPs phonons at the boundary planes of the Brillouin Zone in the vicinity of the M high-symmetric point. In addition to this, straight-line TPs are also found along the $Γ$-X and $Γ$-R high symmetric directions. Moreover, for TiS, six weyl node points (WP1, WP2, WP3, WP4, WP5 and WP6) are found along H-K high-symmetric direction. The results obtained from the PH-NODE code are in good agreement with the experimentally and theoretically reported data for each material.
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