Metal-Semiconductor Transition and Fermi Velocity Renormalization in Metallic Carbon Nanotubes

TL;DR

This paper investigates how angular perturbations affect the electronic properties of metallic carbon nanotubes, revealing conditions for metal-semiconductor transitions and the effects on Fermi velocity, with implications for nanotube electronic behavior.

Contribution

It provides a detailed analysis of symmetry-breaking perturbations in metallic nanotubes and extends the understanding of their electronic structure beyond previous models.

Findings

Armchair nanotubes are resistant to metal-semiconductor transitions at second order.

Higher-order perturbations or combined potentials can induce a gap in nanotubes.

Nonorthogonal orbital assumptions affect electron-hole symmetry and selection rules.

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 $\pi$-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 $\pi$ 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.