title: Curvature effects in the band structure of carbon nanotubes including spin-orbit coupling.
abstract: The Kane-Mele model was previously used to describe effective spin-orbit couplings (SOCs) in graphene. Here we extend this model and also incorporate curvature effects to analyze the combined influence of SOC and curvature on the band structure of carbon nanotubes (CNTs). The extended model then reproduces the chirality-dependent asymmetric electron-hole splitting for semiconducting CNTs and in the band structure for metallic CNTs shows an opening of the band gap and a change of the Fermi wave vector with spin. For chiral semiconducting CNTs with large chiral angle we show that the spin-splitting configuration of bands near the Fermi energy depends on the value of mod(2n + m, 3).
authors.affiliation: Department Physik and CeOPP, Universität Paderborn, D-33098 Paderborn, Germany. Physics Department, Nanjing Normal University, Nanjing 210046, People's Republic of China.
authors.forename: Hong
authors.initials: H
authors.lastname: Liu
authors.forename: Dirk
authors.initials: D
authors.lastname: Heinze
authors.forename: Huynh Thanh
authors.initials: HT
authors.lastname: Duc
authors.forename: Stefan
authors.initials: S
authors.lastname: Schumacher
authors.forename: Torsten
authors.initials: T
authors.lastname: Meier