Fecher Gerhard H, Kübler Jürgen, Felser Claudia
Max Planck Institute for Chemical Physics of Solids, D-01187 Dresden, Germany.
Institute of Solid State Physics, Technical University Darmstadt, D-64289 Darmstadt, Germany.
Materials (Basel). 2022 Aug 23;15(17):5812. doi: 10.3390/ma15175812.
Chirality depends on particular symmetries. For crystal structures it describes the absence of mirror planes and inversion centers, and in addition to translations, only rotations are allowed as symmetry elements. However, chiral space groups have additional restrictions on the allowed screw rotations as a symmetry element, because they always appear in enantiomorphous pairs. This study classifies and distinguishes the chiral structures and space groups. Chirality is quantified using Hausdorff distances and continuous chirality measures and selected crystal structures are reported. Chirality is discussed for bulk solids and their surfaces. Moreover, the band structure, and thus, the density of states, is found to be affected by the same crystal parameters as chirality. However, it is independent of handedness. The Berry curvature, as a topological measure of the electronic structure, depends on the handedness but is not proof of chirality because it responds to the inversion of a structure. For molecules, optical circular dichroism is one of the most important measures for chirality. Thus, it is proposed in this study that the circular dichroism in the angular distribution of photoelectrons in high symmetry configurations can be used to distinguish the handedness of chiral solids and their surfaces.
手性取决于特定的对称性。对于晶体结构而言，它描述的是不存在镜面和反演中心的情况，并且除了平移之外，仅允许旋转作为对称元素。然而，手性空间群对作为对称元素的允许螺旋旋转有额外限制，因为它们总是以对映体对的形式出现。本研究对手性结构和空间群进行了分类和区分。使用豪斯多夫距离和连续手性度量对手性进行了量化，并报告了选定的晶体结构。讨论了块体固体及其表面的手性。此外，发现能带结构以及态密度受与手性相同的晶体参数影响。然而，它与手性无关。贝里曲率作为电子结构的一种拓扑度量，取决于手性，但并不是手性的证明，因为它会对结构的反演做出响应。对于分子而言，圆二色性是手性最重要的度量之一。因此，本研究提出，在高对称构型下光电子角分布中的圆二色性可用于区分手性固体及其表面的手性。
