The Metal-semiconductor Transition In Single Wall Carbon Nanotubes

Since the carbon nanotube was discovered by Iijima in1991, tremendous progress-es have been made both experimentally and theoretically for its potential application in electronic devices. A single-wall carbon nanotube can be seen as rolled up from a graphene sheet, and this construction suggests that its electronic properties can be deduced from that of graphene under the simple zone-folding scheme. For an ideal graphene, the valence and conduction bands touch each other at Dirac points and form a gapless metal. When folding a graphene sheet into a carbon nanotube, wavevectors along the circumferential direction are quantized due to the circumferential boundary conditions. If the wavevectors pass through the Dirac points, a SWCNT is metallic, otherwise it is a semiconductor, according to which, Saito et al. arrived at a simple categorization that one-third SWCNTs are metal, and the other two-third are semicon-ductors. This categorization does not agree with the recent experiments well, in par-ticular for carbon nanotubes with small diameters. Considering the hopping integrals corrections induced by π-σ hybridization from the curvature effect on the tube, band-gaps open for most nominally metallic SWCNTs, while armchair SWCNTs remain metallic and are protected from such a curvature effect. But this conclusion contradict-s with recent experiment seriously. Band-gaps were observed for armchair SWCNTs by scanning tunneling microscopy, and those band-gaps would not vanish as external magnetic field varies. The band-gaps are call true band-gaps, and it is obviously this true band-gaps can not be explained by the popular physics mechanism. Firstly, if the Dirac points are not in the permitted quantized wavevectors by simply zone-folding method, the Dirac points would move into the quantized wavevectors by a phase sup-plied by an external magnetic field, and the band-gaps would vanish. The zone-folding theory cannot explain the true band-gaps. Secondly, the zero band-gaps for armchair SWCNTs are supposedly protected from the curvature effect, which also differs from the experiment. Deshpande et al. ascribed the true band-gaps to the strongly correlat-ed electronic correlations. At present, experimental observation of strong correlations remains a challenge since their signature is masked by charging effect for the small quantum system of carbon nanotubes.We investigate the true band-gaps opening mechanism for SWCNTs in this thesis. Before the strong correlated model was proposed, other possibilities were explored ex-tensively, especially Peierls transition and dimerization induced by lattice deformation such as the Kekule structure. Those deformation do create band-gaps, but do not create true band-gaps, for that those deformation cannot destroy the chemical identicalness of two different types of carbon atoms on the tube, and with the applied magnetic field, the band-gaps will vanish. To have the true band-gaps, the structural symmetry of the two types of carbons should be broken. Corrugated structure of carbon nanotube is a good candidate. Such a model has been proposed for carbon nanotubes in a phe-nomenological model by Viet et al., but the stability of corrugated structures has not been confirmed by ab initio calculations, and the relationship among the band-gaps, corrugation length, radius, and chirality of SWCNTs has not been investigated up to now.In this thesis, with ab initio calculations, firstly, we analyze the stability of the cor-rugated structures of armchair SWCNTs. The total energies of SWCNTs are calculated for different corrugation length and bond length with two types of carbon atoms dis-placed from each other radially. The structure do converge to corrugated structure, which verifies the stability of corrugated structure. It is especially important that the noncorrugated SWCNT structure is not stable, not even metastable, since no potential barrier exists between the structures with and without corrugation. The stability and corrugation length increase rapidly as tube’s radius decreases. When radius approaches to infinity, corrugation vanishes for flat graphene. Combined with curvature effect, the corrugation breaks the local symmetry of two types of carbon atoms, which induces the metal-semiconductor transition and true band gaps emerge for carbon nanotubes. With the corrugation length and energies from the first-principles calculation, the tight- binding Hamiltonian is constructed for corrugated SWCNTs. The two dimensional and one dimensional electronic band structures are discussed for various types of SWCNTs. We analyze the band-gaps and true band gaps for zone-folding model, pure curvature model and corrugation model, respectively. Our conclusion is that the band-gaps sen-sitively depend on the chirality, while the true band-gaps, independent of SWCNTs’ chirality, mainly depend on the corrugation and curvature effect, and increase rapidly with the decease of radius.