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  • Letter
  • Open Access

Dual gauge theory formulation of planar quasicrystal elasticity and fractons

Piotr Surówka*

  • Department of Theoretical Physics, Wrocław University of Science and Technology, 50-370 Wrocław, Poland and Max Planck Institute for the Physics of Complex Systems and Würzburg-Dresden Cluster of Excellence ct.qmat, 01187 Dresden, Germany

  • *surowka@pks.mpg.de
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Phys. Rev. B 103, L201119 – Published 24 May, 2021

DOI: https://doi.org/10.1103/PhysRevB.103.L201119

Abstract

The elastic description of planar quasicrystals can be formulated as an interplay between two Goldstone fields corresponding to phonon and phason degrees of freedom. We reformulate this description as a gauge theory with one gauge field that is symmetric under an exchange of indices and one that is not. We also show that topological defects in quasicrystals can be succinctly incorporated in the dual description and interpret them as fractonic excitations. Finally, we calculate the static interaction potential between defects in a quasicrystal with fivefold symmetry. This is done in the limit of a small coupling between phonon and phason stresses.

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Phys. Rev. B 103, L201119– Published 24 May, 2021
  • Received 18 February 2021
  • Accepted 11 May 2021
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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. Open access publication funded by the Max Planck Society.

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