Breakdown of continuum mechanics for nanometer-wavelength rippling of graphene

TL;DR

This study investigates nanometer-wavelength rippling in suspended graphene, revealing deviations from continuum mechanics predictions and highlighting the importance of quantum mechanical effects at the nanoscale.

Contribution

It demonstrates the breakdown of continuum models for graphene ripples at nanometer wavelengths and shows how quantum simulations can accurately describe these phenomena.

Findings

Nanorippling wavelengths comparable to lattice constants.

Continuum models fail to predict observed rippling modes.

Nanoripples significantly influence local electronic properties.

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. 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, and evidences the breakdown of the plate idealization 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 one-dimensional electronic superlattices.