Effect of sigma electrons on the pi-electron behavior in single-wall carbon nanotubes

TL;DR

This paper investigates how sigma-electrons influence pi-electron behavior in single-wall carbon nanotubes, revealing that sigma-electron scattering increases the band gap and localizes pi-electrons, with implications for nanotube electronic properties.

Contribution

It introduces a model accounting for sigma-electron scattering effects on pi-electrons and calculates resulting changes in band gap and localization in specific nanotube structures.

Findings

Band gap increases with sigma-electron scattering coefficients

Sigma-electron scattering enhances pi-electron localization

Electronic hopping energies are affected by sigma-orbital interactions

Abstract

The hybrid orbitals of single-wall carbon nanotubes are given according to the structure of the nanotube. Because the energy levels of these hybrid orbitals are close to each other, the sigma-orbitals will affect the behavior of the pi-electrons, which is called the scattering of pi- electrons. This scattering effect is taken into account in the nanotube and the local wave function of pi-electrons is constructed, which is called the extended Wannier function. In the Wannier representation, the electronic hopping energies and the energy gap of the tubes (9,0) and (9,9) are calculated. Our results show that the band gap of the tubes increases in direct ratio with the scattering coefficients of sigma-orbitals and this scattering is able to enhance the localization of pi-electrons.