In this study, a previously published continuum model for a stretched sheet was adapted to the case of a compressed sheet to understand the geometry of graphene nanoripples. The validity of the model is tested by comparing with experimental data. Furthermore, the existence of an intrinsic wavelength is revealed based on a simple mechanical analysis, and is confirmed by the quantized feature of the experimental data. Although only graphene nanoripples are investigated in this study, it is believed that such quantized phenomena could exist in other two-dimensional (2D) materials and even in superthin films. Thus, it is believed that the model proposed in this study can help develop the control of nanoripples as an engineering method for future applications.

http://dx.doi.org/10.1016/j.carbon.2015.10.070

This study was supported by the National Natural Science Foundation of China (Grant Nos. 11021262 and 11172303) and the National Basic Research Program of China ("973" Project) (Grant No. 2012CB937500).

Liu F,Wang ZQ. Quantized phenomena in graphene nanoripples[J]. CARBON,2016,96:1175-1180.