On the origin of non-classical ripples in draped graphene sheets

TL;DR

This paper investigates the unique non-classical ripples in draped graphene sheets, revealing triangular ripple formations, strain-locked buckling behavior, and strain-induced pseudo electric fields, advancing understanding of graphene's nanoscale mechanical properties.

Contribution

It uncovers the origin of non-classical ripples in graphene, showing the interplay of in-plane and out-of-plane deformations and their electronic effects, which differ from classical fabric models.

Findings

Graphene forms triangular ripples with localized bending regions.

Graphene buckles at a consistent angle regardless of draping.

Strain modulation in graphene creates pseudo electric fields and heterojunctions.

Abstract

Ever since the discovery of graphene and subsequent explosion of interest in single atom thick materials, studying their mechanical properties has been an active area of research. New length scales often necessitate a rethinking of physical laws, making such studies crucial for understanding and ultimately utilizing novel material properties. Here we report on the investigation of nanoscale periodic ripples in suspended, single layer graphene sheets by scanning tunneling microscopy and atomistic scale simulations. Unlike the sinusoidal ripples found in classical fabrics, we find that graphene forms triangular ripples, where bending is limited to a narrow region on the order of a few 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 draped, always buckles at the same angle. Investigating the origin of such non-classical mechanical properties, we find that unlike a thin classical fabric, both in-plane and out-of-plane deformations occur in a graphene sheet. These two modes of deformation compete with each other, resulting in a strain-locked optimal buckling configuration when draped. Electronically, we see that this in-plane deformation generates pseudo electric fields creating a ~3 nm wide pnp heterojunction purely by strain modulation.