Metal-semiconductor transition and Fermi velocity renormalization in metallic carbon nanotubes

Abstract

Angular perturbations modify the band structure of armchair (and other metallic) carbon nanotubes by breaking the tube symmetry and may induce a metal-semiconductor transition when certain selection rules are satisfied. The symmetry requirements apply for both the nanotube and the perturbation potential, as studied within a nonorthogonal π-orbital tight-binding method.Perturbations of two categories are considered: an on-site electrostatic potential and a lattice deformation which changes the off-site hopping integrals. Armchair nanotubes are proved to be robust against the metal-semiconductor transition in second-order perturbation theory due to their high symmetry, but can develop a nonzero gap by extending the perturbation series to higher orders or by combining potentials of different types. An assumption of orthogonality between π orbitals is shown to lead to an accidental electron-hole symmetry and extra selection rules that are weakly broken in the nonorthogonal theory. These results are further generalized to metallic nanotubes of arbitrary chirality.

Chirality-dependent properties of carbon nanotubes: electronic structure, optical dispersion properties, Hamaker coefficients and van der Waals–London dispersion interactions

“…The effects of structural relaxation 79 , phonons 29 , bending moments 85 , functionalization 86 , the importance of excitonic effects in the optical spectral calculation [51][52][53][54][55] and interlayer coupling 35 may in fact cause armchair tubes to lose some symmetry and regain a lowenergy spike. Furthermore a high transverse electric field may in fact cause the band gaps to open up 71,73,74,87 . These effects are well beyond the scope of this paper, but should be kept in mind in order to see if some differentiations are redundant or if new sub-classes need to be formed.…”

“…Although this technically leads to nine possible combinations, only five of them are allowed for smaller diameter SWCNTs. For instance, an armchair SWCNTs electronic structure is never semiconducting unless there are added defects, functional groups, or other influential external source such as a strong external field [71][72][73][74] . For the larger-diameter limit, the divisions may become redundant as the semimetal gap becomes so small (i.e., less than 0.01 eV) that it essentially blurs the line of the metal/semimetal division.…”

Terahertz applications of carbon nanotubes

“…The crystal structure of a SWNT is described by two integers (n, m), which completely define its physical properties [3][4][5]. SWNTs with true metallic band structure, for which the energy gap is absent for any SWNT radius, are armchair (n, n) SWNTs only [5,[27][28][29][30]. However, for armchair SWNTs the optical transitions between the first conduction and valence subbands are forbidden [31,32].…”

Spectral mixing formulations for van der Waals–London dispersion interactions between multicomponent carbon nanotubes

“…We do not expect this to be the case, although some reported theoretical examples in which large transverse electric fields can shift the electronic bands and turn metallic CNTs into semiconducting. [36][37][38][39] The next assumption to test is the accuracy of the mixing rules, keeping in mind the effects of the nonlinear coupling. Figure 7 shows the vdW-Ld spectra for a ͓16,0,s +7,0,s͔ MWCNT, a MWCNT created by mixing the ͓16,0,s͔ and ͓7,0,s͔ SWCNTs and the two SWCNT spectra.…”