Atomically sharp non-classical ripples in graphene

Abstract

A fundamental property of a material is the measure of its deformation under applied stress. After studying the mechanical properties of bulk materials for the past several centuries, with the discovery of graphene and other two-dimensional materials, we are now poised to study the mechanical properties of single atom thick materials at the nanoscale. Despite a large number of theoretical investigations of the mechanical properties and rippling of single layer graphene, direct controlled experimental measurements of the same have been limited, due in part to the difficulty of engineering reproducible ripples such that relevant physical parameters like wavelength, amplitude, sheet length and curvature can be systematically varied. Here we report extreme (>10%) strain engineering of monolayer graphene by a novel technique of draping it over large Cu step edges. Nanoscale periodic ripples are formed as graphene is pinned and pulled by substrate contact forces. We use a scanning tunneling microscope to study these ripples to find that classical scaling laws fail to explain their shape. Unlike a classical fabric that forms sinusoidal ripples in the transverse direction when stressed in the longitudinal direction, graphene forms triangular ripples, where bending is limited to a narrow region on the order of unit cell dimensions at the apex of each ripple. This non-classical bending profile results in graphene behaving like a bizarre fabric, which regardless of how it is pulled, always buckles at the same angle. Using a phenomenological model, we argue that our observations can be accounted for by assuming that unlike a thin classical fabric, graphene undergoes significant stretching when bent. Our results provide insights into the atomic-scale bending mechanisms of 2D materials under traditionally inaccessible strain magnitudes and demonstrate a path forward for their strain engineering.Comment: 22 pages, 4 figure