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Symmetry preservation in commensurate twisted bilayers

David T. S. Perkins*

  • *Contact author: d.perkins@lboro.ac.uk
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Phys. Rev. B 112, 035410 – Published 10 July, 2025

DOI: https://doi.org/10.1103/r61z-jhrn

Abstract

Symmetry plays a key role in materials hosting Dirac electrons and underpins our ability to completely flatten the Dirac cone through the tuning of physical parameters such as twisting in van der Waals heterostructures. The emergent moiré patterns in twisted bilayers at small twist angles appear, at first glance, to be independent of the initial stacking order and hence are only shifted when one layer is translated with respect to the other. However, when the twist angle is large, differences can be seen at the level of both the lattice and electronic structure in the case of twisted bilayer graphene and twisted bilayer kagome. In this work, we show that the rotational and dihedral symmetry of high-symmetry triangular bilayers is preserved for all commensurate twist angles with a sixfold symmetric twist center. Hence, we demonstrate that the exact symmetry of small twist angle systems depends upon the initial stacking of the bilayer. We further apply the principles of our method to twisted bilayer graphene with a threefold symmetric twist center to recover the results of [E. J. Mele, Phys. Rev. B 81, 161405 (2010)]. Finally, we outline how our method can be generalized to commensurate multilayer systems.

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Outline

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Phys. Rev. B 112, 035410– Published 10 July, 2025
  • Received 6 February 2025
  • Revised 10 June 2025
  • Accepted 11 June 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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