A theoretical investigation of electronic and optical properties of (6,1) single-wall carbon nanotube (SWCNT)

We report the comparative study of electronic and optical properties of (6,1) SWCNT from GGA and DFT-1/2 methods. (6,1) SWCNT is a low-bandgap semiconductor, which falls within ( $$n_1-n_2$$ )/3 $$\ne \,$$ integer. The calculated bandgaps are 0.371 eV and 0.462 eV from GGA and DFT-1/2, respectively. Thus, DFT-1/2 enhanced the electronic bandgap by 24.52%. From both GGA and DFT-1/2 approaches (6,1) SWCNT exhibits an indirect bandgap along $$\Gamma -\Delta$$ symmetry. However, the percentage change in direct–indirect bandgap is negligibly small, i.e., 4.1% and 3.7% from GGA and DFT-1/2, respectively. The refractive index measured along x-axis ( $$n_{x}$$ ) approaches unity, indicating transparent behaviour, while that along z-axis ( $$n_{z}$$ ) goes as high as $$\sim$$ 3.82 for photon energy $$0.0-0.15$$ eV, exhibiting opaque behaviour. Again, the value of $$n_z$$ drops below unity at photon energy $$\sim$$ 0.18 eV and again approaches $$\sim$$ 1 for higher energy ranges. The optical absorption is highly anisotropic and active within the infrared region.