Rippling of Graphene

TL;DR

This paper explains the spontaneous ripples in free-standing graphene sheets as resulting from adsorbed molecules causing bond lengthening, offering a new mechanism distinct from thermal fluctuations.

Contribution

It introduces a novel explanation for graphene ripples based on adsorbate-induced bond lengthening, contrasting with previous thermal fluctuation theories.

Findings

Ripples caused by adsorbates match experimental observations

Approximately 20% adsorbate coverage induces buckling

Mechanism is more plausible than thermal fluctuation explanations

Abstract

Meyer et al (2007) found that free-standing graphene sheets, just one atom thick, display spontaneous ripples. The ripples are of order 2-20 {\AA} high and 20-200 {\AA} wide. The sheets in which they appear are only one atom thick, and extend for around 5000 {\AA} through vacuum between metal struts that support them. Other groups have since created free-standing graphene as well (Garcia-Sanchez 2008 ; Bolotin et al. 2008), and similar ripples have been found for graphene on a glass substrate (Geringer et al. 2008). Here we show that these ripples can be explained as a consequence of adsorbed molecules sitting on random sites. The adsorbates cause the bonds between carbon atoms to lengthen slightly. Static buckles then result from a mechanism like the one that leads to buckling of leaves; buckles caused by roughly 20% coverage of adsorbates are consistent with experimental observations. We explain why this mechanism is more likely to explain rippled than thermal fluctuations or the Mermin-Wagner theorem, which have previously been invoked.