Model of ripples in graphene
arXiv:1211.0527 · doi:10.1103/PhysRevB.86.195402
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 (11)
- The electronic properties of graphene
- The structure of suspended graphene sheets
- Ripple Texturing of Suspended Graphene Atomic Membranes
- Electron scattering on microscopic corrugations in graphene
- Finite temperature lattice properties of graphene beyond the quasiharmonic approximation
- Graphene as an electronic membrane
- Electron-induced rippling in graphene
- Dislocations in graphene
- Roughness of undoped graphene and its short-range induced gauge field
- Periodized discrete elasticity models for defects in graphene
- Ripples in a graphene membrane coupled to Glauber spins