Empirical prediction of bandgap in semiconducting single-wall carbon nanotubes

Necessity for improved calculation of bandgap energies of semiconducting single wall carbon nanotubes is discussed. An effective empirical equation for nearest neighbor hopping parameter (γ₀) in tight binding model of carbon nanotube is proposed in terms of nanotube diameter and chiral index combination. Bandgap energies of all semiconducting single-wall carbon nanotubes in between theoretical minimum and maximum diameter range are calculated from simplest tight binding model using this empirical γ₀. Calculated bandgap values excellently match with experimental results over the full diameter range. The proposed hopping parameter greatly improves tight binding model, and remove its quantitative failure in predicting bandgap energy of nanotube.