Rippling of Graphene*

Experiments found that free standing single-layer graphene sheets display ripples (see ref. Meyer et al. Nature 446, 60 2007). Here we show that these ripples can be a consequence of adsorbed molecules sitting on random sites. The adsorbates cause the bonds between the carbon atom to lengthen slightly. Static buckles caused by roughly 20 \% coverage of adsorbates are consistent with experimental observations. We explain why this mechanism is more likely to explain ripples than are thermal fluctuations or the Mermin-Wagner theorem (previously invoked).