Strain effects on the band gap and work function of zigzag single-walled carbon nanotubes and graphene: A comparative study

First-principles local density functional calculation of the electronic structure and work function of zigzag single-wall carbon nanotubes (SWCNTs) and graphene under strain are presented. We found that there is a small circumference strain even for unstrained zigzag SWCNTs that release the curvature energy of the tube. Therefore, we propose that there are two effects contributing to the opening of the band gap of unstrained (3q$3q$, 0) SWCNTs: the electron transfer enhancement effect and the circumference strain effect. We show that the band gap and work function of strained zigzag SWCNTs can be successfully estimated from the band structure and work function of strained graphene based on the zone folding method with circumference strain effect. The circumference strain effect is crucial to obtain a correct result. The rate of change of the band gap with respect to the strain for zigzag SWCNTs is almost independent of the value of the strain and the radius of the tube.