%0 Book Section %1 statphys23_0659 %A Fasolino, A. %A Katsnelson, M.I. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K Graphene Membranes %T Ripples in graphene: Monte Carlo simulations compared to theory of tethered membranes %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=659 %X Graphene, the strictly two-dimensional hexagonal carbon crystal formed by just one graphitic plane has been recently shown to be stable and to be a gapless semiconductor with high mobility, with great potential for new applications for electronic devices. The experimental demonstration of its Dirac spectrum and anomalous Quantum Hall effect has initiated a very strong interest in this material. The very existence of graphene challenges the well known belief that two-dimensional crystals should be thermodynamically unstable. However, following the seminal work of Nelson and Peliti ( J. Physique, 48, 1085 (1987)), it is by now accepted that a flat two-dimensional layer can be stabilized by anharmonic interactions between bending and stretching modes. Recent experiments (J.C. Meyer et al,Nature 445 (2007)) have found that freely hanged graphene is overall flat but rippled, i.e. it presents finite height fluctuations. We address the question of the stability of graphene and the possibility of stabilization due to anharmonic coupling between stretching and bending by means of atomistic Monte Carlo simulations based on the very accurate interactomic potential for carbon LCBOPII that we have developped in the past J.Los et al. Phys. Rev B 72, 214102 (2005). We perform simulations for samples up to 20000 particles, or about 25 nm X 25nm with periodic boundary conditions. We monitor height fluctutations and normal-normal correlations so as to be able to compare with existing results for models of membranes with fixed connectivity in the continuum. We find several qualitative features that support the idea that ripples are an intrinsic mechanism of stabilization for two-dimensional membranes. In particular we find clear evidence of anharmonic coupling between bending and stretching phonons for long wavelength fluctuations, as well as softening of the elastic constants at high temperature. However, a detailed comparison shows deviations from the expected scaling.

@incollection{statphys23_0659, abstract = {Graphene, the strictly two-dimensional hexagonal carbon crystal formed by just one graphitic plane has been recently shown to be stable and to be a gapless semiconductor with high mobility, with great potential for new applications for electronic devices. The experimental demonstration of its Dirac spectrum and anomalous Quantum Hall effect has initiated a very strong interest in this material. The very existence of graphene challenges the well known belief that two-dimensional crystals should be thermodynamically unstable. However, following the seminal work of Nelson and Peliti ( J. Physique, 48, 1085 (1987)), it is by now accepted that a flat two-dimensional layer can be stabilized by anharmonic interactions between bending and stretching modes. Recent experiments (J.C. Meyer et al,Nature 445 (2007)) have found that freely hanged graphene is overall flat but rippled, i.e. it presents finite height fluctuations. We address the question of the stability of graphene and the possibility of stabilization due to anharmonic coupling between stretching and bending by means of atomistic Monte Carlo simulations based on the very accurate interactomic potential for carbon LCBOPII that we have developped in the past [J.Los et al. Phys. Rev B 72, 214102 (2005)]. We perform simulations for samples up to 20000 particles, or about 25 nm X 25nm with periodic boundary conditions. We monitor height fluctutations and normal-normal correlations so as to be able to compare with existing results for models of membranes with fixed connectivity in the continuum. We find several qualitative features that support the idea that ripples are an intrinsic mechanism of stabilization for two-dimensional membranes. In particular we find clear evidence of anharmonic coupling between bending and stretching phonons for long wavelength fluctuations, as well as softening of the elastic constants at high temperature. However, a detailed comparison shows deviations from the expected scaling.}, added-at = {2009-04-20T22:38:08.000+0200}, address = {Genova, Italy}, author = {Fasolino, A. and Katsnelson, M.I.}, biburl = {https://www.bibsonomy.org/bibtex/21e32d0eaca4cafc6e1796bdd89c12c09/mimetics}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {2f9d1bca1514cbfac922cc0a92d1a7d6}, intrahash = {1e32d0eaca4cafc6e1796bdd89c12c09}, keywords = {Graphene Membranes}, month = {9-13 July}, timestamp = {2009-04-25T12:14:09.000+0200}, title = {Ripples in graphene: Monte Carlo simulations compared to theory of tethered membranes}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=659}, year = 2007 }