Optical properties of double walled carbon nanotubes

Highlights: • The dielectric function of DWCNT (4, 4) @ (8, 8) has anisotropic behavior. • The 2p_z orbitals overlapping affects the static refractive index in z axis polarization more than that x or y axis polarization. • The first optical absorption's maximum for the SWCNTs (4, 4) and SWCNTs (8, 8) happens at 2.1 eV and 1.2 eV respectively. • Compare to the inner and outer tubes, the optical absorption of the DWCNTs is higher for the x and y polarization and lower for the z polarization. Density functional theory was utilized to simulate the electronic band structure and optical spectra of double walled (4, 4) @ (8, 8) carbon nanotubes. The dielectric constants and dielectric function were calculated for the perpendicular and parallel to the tube axis polarizations. The output indicates that for the DWCNTs, the effect of the 2p_z orbitals overlapping on the static refractive index in the parallel to the tube axis polarization outweighs that of the perpendicular to the tube axis polarization. The real part of the dielectric functions shows that for the z polarization of DWCNTs (4, 4) @ (8, 8), the optical refraction (n) for the most of the allowed energies is higher compare to the n of the SWCNTs (4, 4) and SWCNTs (8, 8). E₁₁(eV), E₂₂(eV), E₁₂(eV) and E₂₁(eV) optical band gap of DWCNTs (4, 4) @ (8, 8) are equal to 1.41 eV, 1.92 eV, 1.47 eV and 0.12 eV respectively. The first optical absorption's maximum of the SWCNTs (4, 4) and SWCNTs (8, 8) also happens at 2.1 eV and 1.2 eV respectively for the x and y polarization.