Topological phase transition in metallic single-wall carbon Nanotube

The topological phase transition is theoretically studied in a metallic single-wall carbon nanotube (SWNT) by applying a magnetic field B parallel to the tube. The Z topological invariant, winding number, is changed discontinuously when a small band gap is closed at a critical value of B, which can be observed as a change in the number of edge states owing to the bulk-edge correspondence. This is confirmed by numerical calculations for finite SWNTs of ∼1 μm length, using a one-dimensional lattice model to effectively describe the mixing between σ and Π orbitals and spin-orbit interaction, which are relevant to the formation of the band gap in metallic SWNTs.