Structural and Electronic Properties of Small-Diameter Carbon NanoTubes: A DFT Study

One of the crucial properties of Carbon NanoTubes (CNTs) is their conductivity. They can be metallic, semiconducting or insulating in nature [6]. Therefore, their conducting properties are closely related to the existence and width of CNTs energy band gap – quantity which is (relatively) easily calculable. From a theoretical point of view, CNTs have been studied by various methods. Many results have been obtained; however, their status is quite diverse. The widespread rule claims that (n,m) CNT is metallic if \(n-m = 0\) mod 3 [2, 6]. This rule was based on ‘gluing’ of graphene sheets into tubes (or the ‘zone folding’ method). Moreover, the geometry of all hexagons has been assumed to be identical – the structure optimization hasn’t been performed. Such an approach can be reliable for large-diameter CNTs, where curvature effects are small. However, it is at least disputable for its applicability to small-diameter CNTs. For these reasons, we undertook a systematic exploration of small-diameter CNTs to examine the significance of the ‘deviation’ effects (i.e. the deviation from planar regular hexagon geometry) on properties of CNTs. In particular, we wanted to check explicitly the validity of the claim that ‘CNTs (n,m), where \(n-m\) = 0 mod 3, possess zero energy gap’.

In our paper, we present the results of calculations for (2, m) and (3, m) series of CNTs. These are optimized geometries, densities of states, energy gaps, and electronic band structures. The general conclusion is that the ‘zone-folding’ based rule predicting metallicity for those CNTs where \(n-m=0\) mod 3 is fulfilled, besides the find that hexagons forming CNTs are not planar and possess non-equal bond lengths. So this ‘zone-folding’ based law describes conductivity aspects of CNTs amazingly well.