Bandgap Change of Carbon Nanotubes: Effect of Small Tensile and Torsional Strain

TL;DR

This paper investigates how small tensile and torsional strains affect the bandgap of carbon nanotubes, revealing universal behaviors and sign changes linked to chiral angles and quantum numbers, supported by orbital calculations.

Contribution

It introduces a simple $\pi$ electron model to analyze bandgap variations under strain, highlighting universal behaviors and a novel sign change phenomenon.

Findings

Bandgap slope depends on chiral angle.

Sign of bandgap slope depends on $(n-m) mod 3$.

Sign change of slope due to quantum number shift.

Abstract

We use a simple picture based on the $\pi$ electron approximation to study the bandgap variation of carbon nanotubes with uniaxial and torsional strain. We find (i) that the magnitude of slope of bandgap versus strain has an almost universal behaviour that depends on the chiral angle, (ii) that the sign of slope depends on the value of $(n-m) \bmod 3$ and (iii) a novel change in sign of the slope of bandgap versus uniaxial strain arising from a change in the value of the quantum number corresponding to the minimum bandgap. Four orbital calculations are also presented to show that the $\pi$ orbital results are valid.