Model of ripples in graphene

Abstract

We propose a model of ripples in suspended graphene sheets based on plate equations that are made discrete with the periodicity of the honeycomb lattice and then periodized. In addition, the equation for the displacements with respect to the planar configuration contains a double-well site potential, a nonlinear friction and a multiplicative white noise term satisfying the fluctuation-dissipation theorem. The nonlinear friction terms agree with those proposed by Eichler et al [Nature Nanotech. {\bf 6}, 339 (2011)] to explain their experiments with a graphene resonator. The site double-well potential indicates that the carbon atoms at each lattice point have equal probability to move upward or downward off-plane. For the considered parameter values, the relaxation time due to friction is much larger than the periods of membrane vibrations and the noise is quite small. Then ripples with no preferred orientation appear as long-lived metastable states for any temperature. Numerical solutions confirm this picture.

16 pages, 4 figures, revtex

References in corpus (20)

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• The structure of suspended graphene sheets
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• Ripple Texturing of Suspended Graphene Atomic Membranes
• Gauge fields in graphene
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• Graphene as an electronic membrane
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• Electron-induced rippling in graphene
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• Ripples in a string coupled to Glauber spins
• Ripples in a graphene membrane coupled to Glauber spins
• Theory of defect dynamics in graphene: defect groupings and their stability

Cited by in corpus (10)

• Graphene Ripples as a Realization of a Two-Dimensional Ising Model: A Scanning Tunneling Microscope Study
• Critical radius and temperature for buckling in graphene
• Ripples in hexagonal lattices of atoms coupled to Glauber spins
• 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
• Measuring strain and rotation fields at the dislocation core in graphene
• Thermo-electromechanical effects in relaxed shape graphene and bandstructures of graphene quantum dots
• 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
• Buckling in a rotationally invariant spin-elastic model