Graphene, the first and only two-dimensional crystal in nature, is attracting great attention as a new and unique electronic material. But graphene is not a perfectly flat sheet – recent experimental observations have found ripples in suspended sheets of the material [Meyer et al., Nature (2007) 446, 60]. Simulations of graphene carried out by researchers at Radboud University Nijmegen, The Netherlands, suggest that it is the bonding between carbon atoms in graphene that may be responsible for the ripples [Fasolino et al., Nat. Mater. (2007), doi: 10.1038/nmat2011].

There is some debate surrounding the stability of two-dimensional layers and membranes. The long-range order of two-dimensional crystals is destroyed by long-wavelength fluctuations, according to the Mermin-Wagner theorem, and such two-dimensional crystals tend to ‘crumple’ in three-dimensional space. However, while soft condensed matter membranes are known to bend and form ripples, such behavior in solids like graphene is surprising.

To better understand the unusual behavior of graphene, the researchers from Radboud University undertook atomistic Monte Carlo simulations at room (300 K) and high (1000 K, 2000 K, and 3500 K) temperatures.

“[These] large-scale simulations, based on a very accurate description of the bonding in carbon, show that graphene is intrinsically rippled as a consequence of thermal fluctuations,” says coauthor Annalisa Fasolino. Even at room temperature at equilibrium, graphene shows a broad distribution of height fluctuations.

Simulations may explain the origin of ripples in graphene sheets. (Courtesy of Annalisa Fasolino.)

“However, the correlation function of the normals does not display the expected power-law behavior that would result if ripples of all sizes were present,” explains Fasolino. In fact, the ripples appear to have an average size of 80 Å. This finding is in good agreement with experimental observations of 50–100 Å ripples in graphene. The same results are found at high temperatures too.

The researchers believe that the origin of the ripples is to be found in the carbon–carbon bonding in graphene. Even at room temperature, there is likely to be an uneven mixture of long/short (single/double) bonds. This mixture of long and short bonds could give rise to the ripples in graphene sheets.

“The versatile nature of bonding in carbon and deviations from conjugated bonding characteristic of perfectly flat layers like graphene might explain this finding,” says Fasolino.

Despite this intrinsic tendency to form ripples, the amplitude of the fluctuations is much smaller than the sample size. This means that the long-range order of graphene is preserved and it can still be considered ‘flat’ rather than crumpled. But understanding the reasons for graphene's rippled structure is important.

“This fact could be of consequence for the electronic properties of graphene and represents a major source of scattering,” notes Fasolino. However, she says, many questions remain open: what determines the typical ripple size, are ripples quenched when graphene is placed on a substrate, and what are the consequences for electronic transport?