Oscillatory metallic behaviour of carbon nanotube superlattices—an ab initiostudy

Abstract

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 principlespseudo-potential method within density functional theory (DFT) in the generalized gradientapproximation (GGA). There occur pentagon–heptagon defects along the circumference ofthe heterojunction of these superlattices. The role of the length of the superlattice unit cellon the electronic and optical properties has been investigated. The curvature effects on thevarious properties are also discussed. The heterojunctions of the small diametern(3,3)/n(6,0) superlattices which possess a threefold rotational symmetry exhibit an oscillatorybehaviour in terms of the fundamental energy bandgaps which vanish whenever the integern is a multiple of 3. These results indicate that a similar oscillatory behaviour in the fundamentalgap energy having a periodicity of 6 may be observed in the case of the large diametern(6,6)/n(12,0) superlattices whose heterojunctions reveal a sixfold symmetry. The system energy of the3(6,6)/3(12,0) superlattice shows a minimum. The electronic structure and optical absorption of asuperlattice are quite different from those of its constituent carbon nanotubes. The presentresults obtained after employing all the s-, p- and d-orbitals of the atoms (although thed-orbital contributions are quite small) are quite different from the findings of earlier workerswho have employed a phenomenological tight-binding formulation considering only oneπ orbital or four orbitals. We find that most of the states are extended resonance statesand are quite delocalized in contrast to the earlier finding of the occurrence ofthe completely localized states in sections of the constituent nanotubes. Themetallic superlattices exhibit a high density of states (DOS) at the Fermi level(EF). For thelarge diameter n(6,6)/n(12,0) superlattices, the electron energy gap vanishes forn = 1 and 2 but increases up to a maximum value of 0.344 eV forn = 3 and decreasesthereafter for larger n, a result which is in disagreement with earlier workers. These new facts have not beenreported in the literature so far.