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 doublewell site potential, a nonlinear friction, and a multiplicative whitenoise term satisfying the fluctuationdissipation theorem. The nonlinear friction terms agree with those proposed by Eichler [Nature Nanotech.1748338710.1038/nnano.2011.71 6, 339 (2011)] to explain their experiments with a graphene resonator. The site doublewell 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 longlived metastable states for any temperature. Numerical solutions confirm this picture.
 Publication:

Physical Review B
 Pub Date:
 November 2012
 DOI:
 10.1103/PhysRevB.86.195402
 arXiv:
 arXiv:1211.0527
 Bibcode:
 2012PhRvB..86s5402B
 Keywords:

 61.48.Gh;
 68.65.Pq;
 64.70.p;
 Specific phase transitions;
 Condensed Matter  Mesoscale and Nanoscale Physics
 EPrint:
 16 pages, 4 figures, revtex