A systematic ab-initio study of curvature effects in carbon nanotubes

TL;DR

This paper uses first-principles calculations to analyze how curvature influences the geometry, energy, and electronic properties of zigzag carbon nanotubes, revealing deviations from classical and simplified models.

Contribution

It provides a comprehensive ab-initio analysis of curvature effects on nanotubes, highlighting differences from classical elasticity and tight-binding predictions.

Findings

Curvature energies inversely proportional to square of radius

Band gap variation differs from zone-folded graphene rules

Discrepancies between tight-binding and first-principles band gap calculations

Abstract

We investigate curvature effects on geometric parameters, energetics and electronic structure of zigzag nanotubes with fully optimized geometries from first-principle calculations. The calculated curvature energies, which are inversely proportional to the square of radius, are in good agreement with the classical elasticity theory. The variation of the band gap with radius is found to differ from simple rules based on the zone folded graphene bands. Large discrepancies between tight binding and first principles calculations of the band gap values of small nanotubes are discussed in detail.