Lattice Instability in Metallic Carbon Nanotubes

A lattice instability toward in-plane Kekulé and out-of-plane distortions is studied in metallic carbon nanotubes in both k · p approximation and tight-binding model. The k · p model Hamiltonian is given by Dirac's relativistic equation in the presence of distortion. The resulting gap equation is solved analytically in the presence of an Aharonov-Bohm magnetic flux through the cross section of nanotube, leading to the conclusion that the in-plane and out-of-plane distortions cannot coexist. A tight-binding model gives results in excellent agreement with k · p results and justifies the k · p model Hamiltonian.