Buckling in a rotationally invariant spin-elastic model

Gregorio García-Valladares, Carlos A. Plata, and Antonio Prados
Phys. Rev. E 107, 014120 – Published 13 January 2023

Abstract

Scanning tunneling microscopy experiments have revealed a spontaneous rippled-to-buckled transition in heated graphene sheets, in absence of any mechanical load. Several models relying on a simplified picture of the interaction between elastic and internal, electronic, degrees of freedom have been proposed to understand this phenomenon. Nevertheless, these models are not fully consistent with the classical theory of elasticity, since they do not preserve rotational invariance. Herein, we develop and analyze an alternative classical spin-elastic model that preserves rotational invariance while giving a qualitative account of the rippled-to-buckled transition. By integrating over the internal degrees of freedom, an effective free energy for the elastic modes is derived, which only depends on the curvature. Minimization of this free energy gives rise to the emergence of different mechanical phases, whose thermodynamic stability is thoroughly analyzed, both analytically and numerically. All phases are characterized by a spatially homogeneous curvature, which plays the role of the order parameter for the rippled-to-buckled transition, in both the one- and two-dimensional cases. In the latter, our focus is put on the honeycomb lattice, which is representative of actual graphene.

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  • Received 27 September 2022
  • Accepted 22 December 2022

DOI:https://doi.org/10.1103/PhysRevE.107.014120

©2023 American Physical Society

Physics Subject Headings (PhySH)

  1. Physical Systems
Nonlinear DynamicsStatistical Physics & Thermodynamics

Authors & Affiliations

Gregorio García-Valladares*, Carlos A. Plata, and Antonio Prados

  • Física Teórica, Universidad de Sevilla, Apartado de Correos 1065, E-41080 Sevilla, Spain

  • *ggvalladares@us.es
  • cplata1@us.es
  • prados@us.es

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Vol. 107, Iss. 1 — January 2023

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