We study the exciton effect of twisted single-walled carbon nanotubes (SWNTs) within the tight-binding approximation and including the electron-electron Coulomb interaction. We obtain an approximate relationship that can describe the variation of the band gap of SWNTs with the torsion angle. Based on this relationship, we can divide SWNTs into three kinds according to the different behaviors of band gap at the small torsion angle.
Furthermore, specially for metallic SWNTs, the exciton binding energies can rapidly increase to 0.2 eV under small torsion angle, like a switch on the control of generation of exciton in metallic SWNTs. (© 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)