Topological classification of the single-wall carbon nanotube

Rin Okuyama, Wataru Izumida, Mikio Eto

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


The single-wall carbon nanotube (SWNT) can be a one-dimensional topological insulator, which is characterized by a Z-topological invariant, winding number. Using the analytical expression for the winding number, we classify the topology for all possible chiralities of SWNTs in the absence and presence of a magnetic field, which belongs to the topological categories of BDI and AIII, respectively. We find that the majority of SWNTs are nontrivial topological insulators in the absence of a magnetic field. In addition, the topological phase transition takes place when the band gap is closed by applying a magnetic field along the tube axis, in all the SWNTs except armchair nanotubes. The winding number determines the number of edge states localized at the tube ends by the bulk-edge correspondence, the proof of which is given for SWNTs in general. This enables the identification of the topology in experiments.

Original languageEnglish
Article number115409
JournalPhysical Review B
Issue number11
Publication statusPublished - 2019 Mar 11

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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