Band-gap change of carbon nanotubes: Effect of small uniaxial and torsional strain

We use a simple picture based on the electron approximation to study the band-gap variation of carbon nanotubes with uniaxial and torsional strain. We find (i) that the magnitude of slope of band gap versus strain has an almost universal behavior that depends on the chiral angle, (ii) that the sign of slope depends on the value of (n-m) mod3, and (iii) a novel change in sign of the slope of band gap versus uniaxial strain arising from a change in the value of the quantum number corresponding to the minimum band gap. Four orbital calculations are also presented to show that the orbital results are valid.