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

We use a simple picture based on the π electron approximation to study the bandgap variation of carbon nanotubes with tensile 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) mod 3 and (iii) a novel change in sign of the slope of bandgap versus tensile strain arising from a change in the value of the quantum number corresponding to the minimum bandgap. π and four orbital results are compared. Typeset using REVTEX 1-1