Topological classification of the single-wall carbon nanotube

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 presen...

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Bibliographic Details
Published in:Physical review. B 2019-03, Vol.99 (11), Article 115409
Main Authors: Okuyama, Rin, Izumida, Wataru, Eto, Mikio
Format: Article
Language:English
Subjects:
Magnetic fields
Phase transitions
Single wall carbon nanotubes
Topological insulators
Topology
Tube ends
Winding
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Summary: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.
ISSN:2469-9950
2469-9969
DOI:10.1103/PhysRevB.99.115409