Electronic and optical properties of bundled single-walled carbon nanotubes investigated by the first-principles method

We performed first-principles calculations to investigate the energetic, electronic and optical properties of bundled armchair and zigzag carbon nanotubes (CNTs). The nanotubes are assumed to be aligned in a hexagonal closed-packed array in the bundle. The total energy and electronic band structure show stronger dependence on the orientation of the tube for the (n,n) and (n,0) bundles if n=3q(q=integer) than if n≠3q. The optical properties are also sensitive to the orientation of the tubes. For the (n,n) tubes, the calculated imaginary part of the dielectric functions of the tube bundles are similar to that of the isolated tube, except for the appearance of broadened peaks and an extra peak at low energies due to the avoided crossing of the π and π∗ bands. This extra peak is absent in the (n,n) tubes with n=3q in special orientations where the symmetry of the tube is compatible with that of the hexagonal lattice. For the (n,0) tubes, the imaginary part of the dielectric functions of tubes with larger radius are very similar to that of the isolated tube, while for the (5,0) and (6,0) tubes with smaller radii, coupling causes gaps near the Fermi level, which contribute to an extra peak at low energies.