Band Gap Mechanism for Armchair Single Walled Carbon Nanotubes and Metal Semiconductor Transition for Symmetry Breaking

Abstract

We have studied structures of single walled carbon nanotubes and metal semiconductor transition for the symmetric breaking. It was found that band gap existed for metallic armchair single walled carbon nanotubes. Calculations were made to analyse the meta-stability of the corrugated structures of armchair single walled carbon nanotubes. The corrugated single walled carbon nanotube structures are always lower in energy than the non corrugated nanotubes. The curvature effect was that the corrugated structure breaks the local symmetry between different carbon atoms. A true gap is created which does not vanish even when an external magnetic field is swept. The corrugation length and band gap gaps are decaying functions of the nanotubes radius and approached zero for carbon nanotube such as graphene. This was also true for zigzag and chiral single wall carbon nanotubes. The obtained results were found in good agreement with previously obtained results.