Topological Phase Transition in Metallic Single-Wall Carbon Nanotube

TL;DR

This paper theoretically investigates a topological phase transition in metallic single-wall carbon nanotubes induced by a magnetic field, showing a change in topological invariant and edge states, confirmed through numerical simulations.

Contribution

It introduces a model demonstrating a magnetic-field-induced topological phase transition in metallic SWNTs, linking band gap closure to changes in topological invariants and edge states.

Findings

Discontinuous change in winding number at critical magnetic field

Observation of edge state variation due to bulk-edge correspondence

Numerical confirmation using finite-length SWNT models

Abstract

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 $\mathbb{Z}$ 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 $\sim$ 1 $\mu$m length, using a one-dimensional lattice model to effectively describe the mixing between $\sigma$ and $\pi$ orbitals and spin-orbit interaction, which are relevant to the formation of the band gap in metallic SWNTs.