First-principles study of electronic structure of double-walled and single-walled carbon nanotubes

The density functional theory (DFT) is adopt to study the electronic structure of 56 double-walled carbon nanotubes (DWCNTs) and 25 corresponding single-walled carbon nanotubes (SWCNTs) with GGA-PBE. The band gap of SWCNTs is given by the formula E-g = 6.084/d + c and E-g = 8.168/d + c (E-g and c in eV, d in angstrom) for the n = 3p+1 and n = 3p+2 respectively when n > 8 (d > 7 angstrom), where d represents the diameter of tubes and c is the correction for band gap. The band gap and charge transfer of DWCNTs have also been studied. We found that the band gap of DWCNTs is always smaller than the mean value of the sum of corresponding SWCNTs, which qualitatively explains the metallization tendency. Due to the interaction between the tubes, all DWCNTs always transfer electrons from the outer tubes to the inside of inner tubes except for the DWCNTs with an inner tube of (4, 0).