Breakdown of continuum mechanics for nanometre-wavelength rippling of graphene

Abstract

Understanding how the mechanical behavior of materials deviates at the nanoscale from the macroscopically established concepts is a key challenge of particular importance for graphene, given the complex interplay between its nanoscale morphology and electronic properties 1,2,3,4,5 . In this work, the (sub-) nanometer wavelength periodic rippling of suspended graphene nanomembranes has been realized by thermal strain-engineering and investigated using Scanning Tunneling Microscopy. This allows us to explore the rippling of a crystalline membrane with wavelengths comparable to its lattice constant. The observed nanorippling mode violates the predictions of the continuum model 6 , and evidences the breakdown of the plate idealization 7 of the graphene monolayer. Nevertheless, microscopic simulations based on a quantum mechanical description of the chemical binding accurately describe the observed rippling mode and elucidate the origin of the continuum model breakdown. Spatially resolved tunneling spectroscopy measurements indicate a substantial influence of the nanoripples on the local electronic structure of graphene and reveal the formation of onedimensional electronic superlattices.

Structure of graphene and its disorders: a review

“…As a result, the electronic structure in the vicinity of these disorders differs from that in a perfect lattice. More specifically, intrinsic ripples are expected to influence the electrical properties of graphene by changing band gap [239], creating polarized carrier puddles [240] and inducing pseudo-magnetic fields [241]. Whereas wrinkles and crumples result in several electronic phenomena, such as electron-hole puddles [189,242], carrier scattering [195,243], band gap opening [244], suppression of weak localization [245] and quantum corrections [246].…”

Generating atomically sharp p−n junctions in graphene and testing quantum electron optics on the nanoscale

“…S1), and then graphene monolayer was grown on it by the low pressure CVD method. During the high-temperature annealing process, the surface Cu atomic vacancies and adatoms emerge through migration and massive diffusion of the surface Cu atoms [21][22][23][24] , as schematically shown in Fig. 1a.…”

“…Previous studies demonstrated that reconstructions of metals, such as Cu, Ag and Au, could induce both islands and vacancy-islands on the surface [20][21][22][23][24] . In this work, monolayer-vacancy-islands on Cu surface were generated during the synthesis of the graphene.…”

Graphene as a Prototypical Model for Two-Dimensional Continuous Mechanics

“…all play a role in the mechanical behavior of graphene. The presence of wrinkles or ripples [19] introduces an additional complexity that may affect the picture [55]. In particular, thermal fluctuations in suspended graphene, in addition to requiring a statistical approach, may amplify non-linear effects [56].…”