High resolution transmission electron microscope Imaging and first-principles simulations of atomic-scale features in graphene membrane

Ultra-thin membranes such as graphene[1] are of great importance for basic science and technology applications. Graphene sets the ultimate limit of thinness, demonstrating that a free-standing single atomic layer not only exists but can be extremely stable and strong [2--4]. However, both theory [5, 6] and experiments [3, 7] suggest that the existence of graphene relies on intrinsic ripples that suppress the long-wavelength thermal fluctuations which otherwise spontaneously destroy long range order in a two dimensional system. Here we show direct imaging of the atomic features in graphene including the ripples resolved using monochromatic aberration-corrected transmission electron microscopy (TEM). We compare the images observed in TEM with simulated images based on an accurate first-principles total potential. We show that these atomic scale features can be mapped through accurate first-principles simulations into high resolution TEM contrast. [1] Geim, A. K. {\&} Novoselov, K. S. \textit{Nat. Mater. }\textbf{6}, 183-191, (2007). [2] Novoselov, K. S.\textit{et al. Science }\textbf{306}, 666-669, (2004). [3] Meyer, J. C. \textit{et al. Nature }\textbf{446}, 60-63, (2007). [4] Lee, C., Wei, X. D., Kysar, J. W. {\&} Hone, J. \textit{Science }\textbf{321}, 385-388, (2008). [5] Nelson, D. R. {\&} Peliti, L. \textit{J Phys-Paris }\textbf{48}, 1085-1092, (1987). [6] Fasolino, A., Los, J. H. {\&} Katsnelson, M. I. \textit{Nat. Mater. }\textbf{6}, 858-861, (2007). [7] Meyer, J. C. \textit{et al. Solid State Commun. }\textbf{143}, 101-109, (2007).