In this paper we use symmetry of Single Walled Carbon Nanotubes (SWCNTs) to generate some types of virtual sub-bands that are lower in number than the real sub-bands obtained through conventional-TB. It is shown that the virtual sub-bands maintain the value of band gap. In obtaining the sub bands, the interactions of the nearest and the second and third-nearest neighbors are taken into account. As the consequence of lower number of sub-bands, a significant reduction in computational effort has occurred and made the approach useful.
Analytical derivation of electronic band gap of Single Walled Carbon Nanotube (SWCNT) under a small percent of uniaxial and torsional strains is in this paper. Our approach is based on a kind of π-Tight Binding (π-TB) approximation which includes interactions of the second and the third neighbors of each carbon atom in addition to the nearest ones. Implementing the approach of this paper, yields more precise results than those of other researches.
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