Theoretical investigation of electronic bandgaps of semiconducting single-walled carbon nanotubes using semi-empirical self-consistent tight binding and <i>ab-inito</i> density functional methods

We perform a comprehensive theoretical study of electronic band gaps of semiconducting single-walled carbon nanotubes (SWNTs) with different sets of chiral indices using semi-empirical tight binding and density functional (DFT) based ab-initio methods. In particular, self-consistent extended Huckel (EH-SCF) and self-consistent Slater Koster (SK-SCF) tight binding models are used as semi-empirical methods, whereas the DFT based LDA-1/2 and Tran-Blaha (TB09) meta-GGA schemes are used as ab-initio methods. The calculations are performed for 1) (n,m) chiral SWNTs for which experimental optical gaps have been reported 2) (9,0), (12,0) and (15,0) "metallic" zigzag SWNTs for which small bad gaps have been reported 3) Pairs of SWNTs having same diameters but different chiral angles 4) (n,0) zigzag SWNTs with 10≤n≤30. From the comparison of bands gaps of tubes with same diameter, the electronic band gaps are found to vary with chiral angles with opposing trend as compared to that reported for experimental optical band gaps. This result may be expected to have important implications for self-energy corrections and/or exciton binding energies and their dependence on chiral angles. The hopping parameter γ0 obtained from fitting EH-SCF and SK-SCF bandgap data, is found to be in good agreement with that obtained from fitting experimental data. In general, the band gap values of SWNTs computed using semi-empirical EH-SCF and SK-SCF methods are quite close (within ~5%) to those computed using DFT-based LDA-1/2 and TB09 meta-GGA methods. The results suggest that self-consistent semi-empirical methods can be expected to provide similar accuracy in results as that expected from more computationally challenging ab-intio DFT based LDA-1/2 and TB09 meta-GGA methods