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The symmetry of a crystal structure with a three dimensional (3D) lattice can be classified by one of the 230 space group types. For some types of crystals, e.g. crystalline films, surfaces, or planar interfaces, it is more appropriate to assume a 2D lattice. With this assumption the structure can be classified by one of the 80 layer group types. We have implemented an algorithm to determine the layer group type of a 3D structure with a 2D lattice, and applied it to more than 15 000 monolayer structures in the Computational 2D Materials (C2DB) database. We compare the classification of monolayers by layer groups and space groups, respectively. The latter is defined as the space group of the 3D bulk structure obtained by repeating the monolayer periodically in the direction perpendicular to the 2D lattice (AA-stacking). By this correspondence, nine pairs of layer group types are mapped to the same space group type due to the inability of the space group to distinguish the in-plane and out-of-plane axes. In total 18% of the monolayers in the C2DB belong to one of these layer group pairs and are thus not properly classified by the space group type. Our result shows that classifying 2D materials via layer groups is more accurate and outperforms the commonly used space group classification scheme.

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• Creative Commons BY Attribution 4.0 International
  

Keyword: Layer group

Date published: 2024-07-01

Publisher: IOP Publishing

Journal:

• 2D Materials (ISSN: 20531583) vol. 11 issue. 3 035009

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Manuscript type: Publisher's version (Version of record)

MDR DOI:

First published URL: https://doi.org/10.1088/2053-1583/ad3e0c

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Updated at: 2024-08-21 16:30:34 +0900

Published on MDR: 2024-08-21 16:30:34 +0900