Mechanically changed band gap of single walled carbon nanotube: a third neighbor tight-binding approach

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.