Oscillatory metallic behaviour of carbon nanotube superlattices-an ab initio study

We study the structural, electronic and optical properties of the (n,n)/(2n,0);n = 3 and 6 superlattices of carbon nanotubes (CNs) by employing the first principles pseudo-potential method within density functional theory (DFT) in the generalized gradient approximation (GGA). There occur pentagon-heptagon defects along the circumference of the heterojunction of these superlattices. The role of the length of the superlattice unit cell on the electronic and optical properties has been investigated. The curvature effects on the various properties are also discussed. The heterojunctions of the small diameter n(3,3)/n(6,0) superlattices which possess a threefold rotational symmetry exhibit an oscillatory behaviour in terms of the fundamental energy bandgaps which vanish whenever the integer n is a multiple of 3. These results indicate that a similar oscillatory behaviour in the fundamental gap energy having a periodicity of 6 may be observed in the case of the large diameter n(6,6)/n(12,0) superlattices whose heterojunctions reveal a sixfold symmetry. The system energy of the 3(6,6)/3(12,0) superlattice shows a minimum. The electronic structure and optical absorption of a superlattice are quite different from those of its constituent carbon nanotubes. The present results obtained after employing all the s-, p- and d-orbitals of the atoms (although the d-orbital contributions are quite small) are quite different from the findings of earlier workers who have employed a phenomenological tight-binding formulation considering only one pi orbital or four orbitals. We find that most of the states are extended resonance states and are quite delocalized in contrast to the earlier finding of the occurrence of the completely localized states in sections of the constituent nanotubes. The metallic superlattices exhibit a high density of states (DOS) at the Fermi level (E(F)). For the large diameter n(6,6)/n(12,0) superlattices, the electron energy gap vanishes for n = 1 and 2 but increases up to a maximum value of 0.344 eV for n = 3 and decreases thereafter for larger n, a result which is in disagreement with earlier workers. These new facts have not been reported in the literature so far.