Buckling in a rotationally invariant spin-elastic model

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.

18 pages, 8 figures

References in corpus (22)

• Electric Field Effect in Atomically Thin Carbon Films
• The electronic properties of graphene
• The structure of suspended graphene sheets
• Electron-induced rippling in graphene
• Thermal mirror buckling in freestanding graphene locally controlled by scanning tunneling microscopy
• Rippling, buckling and melting of single- and multi-layer MoS${}_2$
• Fluctuation-induced current from freestanding graphene: toward nanoscale energy harvesting
• What is the stiffness of a bent book?
• Graphene Ripples as a Realization of a Two-Dimensional Ising Model: A Scanning Tunneling Microscope Study
• Thermalized buckling of isotropically compressed thin sheets
• Thermal control of nucleation and propagation transition stresses in discrete lattices with non-local interactions and non-convex energy
• Model of ripples in graphene
• Thermal buckling and symmetry breaking in thin ribbons under compression
• Buckling and metastability in membranes with dilation arrays
• Thermal buckling transition of crystalline membranes in a field
• Bifurcation analysis and phase diagram of a spin-string model with buckled states
• STM driven transition from rippled to buckled graphene in a spin-membrane model
• Spontaneous tilt of single-clamped thermal elastic sheets
• Anomalous thermal expansion in Ising-like puckered sheets
• Spin-oscillator model for DNA/RNA unzipping by mechanical force
• Derivation of a Langevin equation in a system with multiple scales: the case of negative temperatures
• A numerical study of the rippling instability driven by electron-phonon coupling in graphene