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Chirality in the Solid State: Chiral Crystal Structures in Chiral and Achiral Space Groups

Fecher, Gerhard H. ; Kübler, Jürgen ; Felser, Claudia (2022)
Chirality in the Solid State: Chiral Crystal Structures in Chiral and Achiral Space Groups.
In: Materials, 2022, 15 (17)
doi: 10.26083/tuprints-00022324
Article, Secondary publication, Publisher's Version

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Item Type: Article
Type of entry: Secondary publication
Title: Chirality in the Solid State: Chiral Crystal Structures in Chiral and Achiral Space Groups
Language: English
Date: 12 September 2022
Place of Publication: Darmstadt
Year of primary publication: 2022
Publisher: MDPI
Journal or Publication Title: Materials
Volume of the journal: 15
Issue Number: 17
Collation: 32 Seiten
DOI: 10.26083/tuprints-00022324
Corresponding Links:
Origin: Secondary publication DeepGreen

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.

Uncontrolled Keywords: chirality, chirality measure, chiral space groups, chiral elements, compounds, and surfaces, electronic structure, dichroism
Status: Publisher's Version
URN: urn:nbn:de:tuda-tuprints-223241
Classification DDC: 500 Science and mathematics > 530 Physics
500 Science and mathematics > 540 Chemistry
Divisions: 05 Department of Physics > Institute for Condensed Matter Physics
Date Deposited: 12 Sep 2022 13:18
Last Modified: 14 Nov 2023 19:05
SWORD Depositor: Deep Green
URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/22324
PPN: 499597095
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