Volume 81, Issue 4 pp. 339-349
research papers

Symmetries of all lines in monolayer crystals

Bernard Field

Bernard Field

Lawrence Berkeley National Laboratory, Berkeley, California, USA

Lawrence Berkeley National Laboratory, Berkeley, California, USA

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Sinéad M. Griffin

Corresponding Author

Sinéad M. Griffin

Lawrence Berkeley National Laboratory, Berkeley, California, USA

Lawrence Berkeley National Laboratory, Berkeley, California, USA

Sinéad M. Griffin, e-mail: [email protected]Search for more papers by this author
First published: 13 June 2025

Abstract

As `2D' materials (i.e. materials just a few atoms thick) continue to gain prominence, understanding their symmetries is critical for unlocking their full potential. In this work, we present comprehensive tables that tabulate the rod group symmetries of all crystallographic lines in all 80 layer groups, which describe the symmetries of 2D materials. These tables are analogous to the scanning tables for space groups found in Volume E of the International Tables for Crystallography, but are specifically tailored for layer groups and their applications to 2D materials. This resource will aid in the analysis of line defects, such as domain walls, which play a crucial role in determining the properties and functionality of 2D materials.

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