Band gap of carbon nanotubes under combined uniaxial–torsional strain

Within tight-binding model, the band gaps of armchair and zigzag carbon nanotubes (CNTs) under both uniaxial tensile and torsional strains have been studied. It is found that the changes in band gaps of CNTs depend strongly on the strain type. The torsional strain can induce a band gap for armchair CNTs, but it has little effect on band gap of the zigzag CNTs. While the tensile strain has great effect on band gap of zigzag CNTs, but it has no effect on that of the armchair CNTs. More importantly, when both the tensile and torsional strains are simultaneously applied to the CNTs, the band gap changes of armchair CNTs are not equal to a simple sum over those induced separately by uniaxial tensile and torsional strains. There exists a cooperative effect between two kinds of strains on band gap changes of armchair CNTs. But for zigzag CNTs, the cooperative effect was not found. Analytical expressions for the band gaps of armchair and zigzag CNTs under combined uniaxial–torsional strains have been derived, which agree well with the numerical results.