Electronic and optical properties of double-walled armchair carbon nanotubes

A Review of Double-Walled and Triple-Walled Carbon Nanotube Synthesis and Applications

“…Moreover, the effectiveness of this mixing is directly related to the van der Waals forces mediating the interlayer interactions. In other words, for weak IL interactions, the tubes composing the multi-walled systems would behave independently of each other [30][31][32][33][34][35][36][37][38]54,55]. In fact, DWNTs can show up in four different flavors (inner tube@outer tube), as shown in Figure 3a, while TWNTs present eight different flavors (inner tube@middle tube@outer tube), as depicted in Figure 3b.…”

“…The magnitude of these IL interactions will change according to the chirality combinations between the pairs (n, m)@(n , m ) in a DWNT or among the set (n, m)@(n , m )@(n , m ) in a TWNT [30][31][32][33][34][35][36][37][38]. Namely, Saito et al predicted that the IL interactions would play different roles in the DWNT structure and showed that the stability of the double-walled structure does not strongly depend on the (n, m) pairs of the tubes constituting the DWNT, but the van der Waals-related barrier potential for the relative motion of the inner and outer tubes depends strongly on the (n, m) pairs [38].…”

“…It had been common sense that incommensurate systems would not present IL interactions capable of changing the electronic and vibrational properties of the individual SWNT constituting the multi-walled carbon nanotubes [30][31][32][33][34][35][36][37][38]54,55]. On the other hand, commensurate systems would present IL interactions strong enough to perturb the electronic and vibrational structures of the SWNTs constituting the multi-walled tubes [30][31][32][33][34][35][36][37][38]54,55]. However, as discussed below, incommensurate tubes may present Moiré patterns, and in these cases, the IL interactions cannot be neglected [54,55].…”

Electronic structures of finite double‐walled carbon nanotubes

“…The intertube hopping integrals are taken into account only when the interatom distance on the projection is smaller than the C-C bond length b = 1.42Å. They are in exponential decay form scaled with the interatom distance d kl ; the intertube distance is a = 3.39Å, and δ = 0.45Å [4,9]. From fitting the evaluated results with those of ab initio studies and experimental data, the strength of the intertube interactions W is determined to be 1/16.…”

“…Double-walled carbon nanotubes (DWCNs) are the simplest multiwalled systems that provide a good platform for studying the effects of the intertube atomic overlaps on electronic properties [2]. Both electronic structures and optical properties have been reported previously [3,4].…”