On the material geometry of continuously defective corrugated graphene sheets

TL;DR

This paper introduces a geometric framework for modeling continuously defective graphene sheets, focusing on dislocations and curvature effects within a Riemann-Cartan material space, and analyzes their influence on the material's geometry.

Contribution

It develops a variational geometric model incorporating dislocations and secondary curvature defects in graphene, including a formula linking dislocations to the material metric at a reference temperature.

Findings

Dislocations are modeled as effective edge dislocations with scalar density and Burgers vectors.

The influence of dislocations on the material's Riemannian metric is quantified.

The geometric model accounts for secondary curvature-type defects in defective graphene sheets.

Abstract

Geometrical objects describing the material geometry of continuously defective graphene sheets are introduced and their compatibility conditions are formulated. Effective edge dislocations embedded in the Riemann-Cartan material space and defined by their scalar density and by local Burgers vectors, are considered. The case of secondary curvature-type defects created by this distribution of dislocations is analysed in terms of the material space. The variational geometry of the material space closely related with the existence of a characteristic length parameter is proposed. The formula which describes, in a reference temperature, the influence of dislocations on the material Riemannian metric, is given.