Peierls instability in (5,5) and (9,0) carbon nanotubes: Effect of torsional strain on band gap

Abstract

Effect of Peierls instability on the electronic band structure of carbon nanotubes (CNTs) under torsional strain is studied by tight-binding approximation. When Kekule structure with two different bond lengths is introduced, armchair (5,5) and zigzag (9,0) CNTs become semiconducting indicating by a small band gap opening at the Fermi level. Numerical calculations show that the increasing of shear strain leads to reduce the band gap of armchair (5,5) carbon nanotube. Shear strain threshold for a semiconductor–metal phase transition depends on the difference in the bond lengths. In the metal state, the torsional strain induces the Fermi wavenumber of (5,5) carbon nanotube deviated from the center of the first Brillouin zone. Under the torsional strain, a semiconductor–metal–semiconductor phase transition appears for (9,0) CNT with Kekule structure as well.