Graphene edge structures: Folding, scrolling, tubing, rippling and twisting

TL;DR

This paper explores the diverse topological structures that graphene edges can adopt, including folding, scrolling, and tube formation, driven by chemical and mechanical factors, revealing new possibilities for 2D material interfaces.

Contribution

It introduces a comprehensive analysis of graphene edge topologies, combining theoretical discussion with density functional calculations to understand their formation and stability.

Findings

Graphene edges can undergo buckling, folding, and rolling due to strain and chemical effects.

Different edge topologies depend on chemical functionalisation and local strain conditions.

Density functional calculations support the stability of various topological edge structures.

Abstract

Conventional three-dimensional crystal lattices are terminated by surfaces, which can demonstrate complex rebonding and rehybridisation, localised strain and dislocation formation. Two dimensional crystal lattices, of which graphene is the archetype, are terminated by lines. The additional available dimension at such interfaces opens up a range of new topological interface possibilities. We show that graphene sheet edges can adopt a range of topological distortions depending on their nature. Rehybridisation, local bond reordering, chemical functionalisation with bulky, charged, or multi-functional groups can lead to edge buckling to relieve strain, folding, rolling and even tube formation. We discuss the topological possibilities at a 2D graphene edge, and under what circumstances we expect different edge topologies to occur. Density functional calculations are used to explore in more depth different graphene edge types.