Critical radius and temperature for buckling in graphene

Abstract

In this work, we find an analytical flat-membrane solution to the saddle point equations, derived by Guinea et al. [Phys. Rev. B 89, 125428 (2014)], for the case of a suspended graphene membrane of circular shape. We also find how different buckled membrane solutions bifurcate from the flat membrane at critical temperatures and membrane radii. The saddle point equations take into account electron-phonon coupling and this coupling provides a residual stress even for a flat graphene layer. Below a critical temperature (which is exceedingly high for an infinite layer) or above a critical size that depend on boundary conditions, different buckling modes that may be the germ of rippling appear. Our results provide the opportunity to develop new feasible experiments dealing with buckling in small suspended graphene membranes that could verify them. These experiments may also be used to fit the phonon-electron coupling constant or the bending energy.

21 pages, 2 figures

References in corpus (14)

• The structure of suspended graphene sheets
• Ripple Texturing of Suspended Graphene Atomic Membranes
• Graphene as an electronic membrane
• Morphogenesis of growing soft tissues
• Unusual ultralow frequency fluctuations in freestanding graphene
• Electron-induced rippling in graphene
• Roughness of undoped graphene and its short-range induced gauge field
• Differential growth of wrinkled biofilms
• Atomic structure and energetics of large vacancies in graphene
• Graphene Ripples as a Realization of a Two-Dimensional Ising Model: A Scanning Tunneling Microscope Study
• Theory of the spontaneous buckling of doped graphene
• Model of ripples in graphene
• Ripples in a graphene membrane coupled to Glauber spins
• Rippling transition from electron-induced condensation of curvature field in graphene

Cited by in corpus (11)

• Fluctuation-induced current from freestanding graphene: toward nanoscale energy harvesting
• Buckling of thermalized elastic sheets
• Thermalized buckling of isotropically compressed thin sheets
• Snap-through transition of graphene membranes for memcapacitor applications: A combined study using MD, DFT and elasticity theory
• Thermal stiffening of clamped elastic ribbons
• Bifurcation analysis and phase diagram of a spin-string model with buckled states
• Bending rigidity, sound propagation and ripples in flat graphene
• STM driven transition from rippled to buckled graphene in a spin-membrane model
• Anomalous thermal expansion in Ising-like puckered sheets
• A numerical study of the rippling instability driven by electron-phonon coupling in graphene
• Large-scale critical behavior of the rippling phase transition for graphene membranes