1. Buckling in a rotationally invariant spin-elastic model
- Author
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Antonio Prados, Carlos A. Plata, Gregorio García Valladares, Universidad de Sevilla. Departamento de Física Atómica, Molecular y Nuclear, Ministerio de Ciencia e Innovación (MICIN). España, and European Union (UE)
- Subjects
Condensed Matter - Mesoscale and Nanoscale Physics ,Statistical Mechanics (cond-mat.stat-mech) ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,Soft Condensed Matter (cond-mat.soft) ,FOS: Physical sciences ,Condensed Matter - Soft Condensed Matter ,74B20, 74K05, 82B26 ,Condensed Matter - Statistical Mechanics - Abstract
Scanning tunneling microscopy experiments have revealed an 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 analyse 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. Minimisation of this free energy gives rise to the emergence of different mechanical phases, whose thermodynamic stability is thoroughly analysed, both analytically and numerically. All phases are characterised 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., Comment: 18 pages, 8 figures
- Published
- 2022
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