Intrinsic
ripples in graphene
Fasolino, A., Los, J. H., Katsnelson, M. I.
NATURE MATERIALS 6 (11): 858-861 NOV 2007
Abstract: The stability of
two-dimensional (2D) layers and membranes is the subject of a
long-standing theoretical debate. According to the so-called
Mermin-Wagner theorem(1), long-wavelength fluctuations destroy the
long-range order of 2D crystals. Similarly, 2D membranes embedded in a
3D space have a tendency to be crumpled(2). These fluctuations can,
however, be suppressed by anharmonic coupling between bending and
stretching modes meaning that a 2D membrane can exist but will exhibit
strong height fluctuations(2-4). The discovery of graphene, the first
truly 2D crystal(5,6), and the recent experimental observation of
ripples in suspended graphene(7) make these issues especially
important. Besides the academic interest, understanding the mechanisms
of the stability of graphene is crucial for understanding electronic
transport in this material that is attracting so much interest owing to
its unusual Dirac spectrum and electronic properties(8-11). We address
the nature of these height fluctuations by means of atomistic Monte
Carlo simulations based on a very accurate many-body interatomic
potential for carbon(12). We find that ripples spontaneously appear
owing to thermal fluctuations with a size distribution peaked around 80
A which is compatible with experimental findings(7) (50-100 angstrom ).
This unexpected result might be due to the multiplicity of chemical
bonding in carbon.