Analysis of cooperative effects between uniaxial and torsional strains in carbon nanotubes

The analyses of the electronic properties of a Single-Wall Carbon Nanotube (SWCN) under both uniaxial and torsional strains are presented with the main intrinsic curvature taken into account. Within tight-binding mechanism, Heyd and Charlier method is extended to cover chiral types of SWCNs using a single $π−$orbital model for the nanotubes. The variations of the bond lengths and the band gap as functions of chirality and the strain parameters of carbon nanotube are discussed. An improved analytical expression for the deformed geometrical structure of a SWCN with arbitrary chiral indices has been derived, and a numerical band gap analysis of a chiral type is conducted. The existence of an interference or cooperative effect between uniaxial and torsional strains on band gap of a SWCN is found. The results of our calculations show that the cooperative effects depend strongly on the chirality of SWCNs and the strain parameters, so that, in contrast to the other works, there exists some strain parameters for which the cooperative effects are not found in the armchair SWCNs. In addition, it was found that the strain parameters can be chosen to correspond to the cooperative effects in zigzag SWCNs.