Rippling of Graphene

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 Å high and 20-200 Å wide. The sheets in which they appear are only one atom thick, and extend for around 5000 Å 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.

5 pages and 5 figures

References in corpus (11)

• Ultrahigh electron mobility in suspended graphene
• The structure of suspended graphene sheets
• Intrinsic ripples in graphene
• Atomic Structure of Graphene on SiO2
• Temperature dependent transport in suspended graphene
• Imaging mechanical vibrations in suspended graphene sheets
• Self-Consistent Theory of Polymerized Membranes
• Graphene as an electronic membrane
• The environment of graphene probed by electrostatic force microscopy
• Roughness of undoped graphene and its short-range induced gauge field
• A graphene-based electrochemical switch

Cited by in corpus (28)

• Electronic transport in two dimensional graphene
• Novel effects of strains in graphene and other two dimensional materials
• Mermin-Wagner fluctuations in 2D amorphous solids
• Effects of Mismatch Strain and Substrate Surface Corrugation on Morphology of Supported Monolayer Graphene
• High-fidelity conformation of graphene to SiO2 topographic features
• Scaling behavior and strain dependence of in-plane elastic properties of graphene
• Approximate Modeling of Spherical Membrane
• Electron density distribution and screening in rippled graphene sheets
• Excess energy and deformation along free edges of graphene nanoribbons
• On the structure and topography of free-standing chemically modified graphene
• Low Energy Electron Point Projection Microscopy of Suspended Graphene, the Ultimate "Microscope Slide"
• Ripple edge engineering of graphene nanoribbons
• Correlation between Charge Inhomogeneities and Structure in Graphene and Other Electronic Crystalline Membranes
• Anharmonic effects in the optical and acoustic bending modes of graphene
• Tearing of Free-Standing Graphene
• Anamolous reduction of magnetic coercivity of graphene oxide and reduced graphene oxide upon cooling
• Gap opening in topological-defect lattices in graphene
• Irreversibility in response to forces acting on graphene sheets
• Ripples in a graphene membrane coupled to Glauber spins
• Optically Forged Diffraction-Unlimited Ripples in Graphene
• Graphene edge structures: Folding, scrolling, tubing, rippling and twisting
• Thermo-electromechanical effects in relaxed shape graphene and bandstructures of graphene quantum dots
• Rippling of two-dimensional materials by line defects
• Limits of Lateral Expansion in Two-Dimensional Materials with Line Defects
• The Structure of Fluctuating Thin Sheets Under Random Forcing
• Thermally driven elastic membranes are quasi-linear across all scales
• Dynamics of Fluctuating Thin Sheets Under Random Forcing
• Ultraclean suspended graphene by radiolysis of adsorbed water