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arXiv · 1812.06399

Topological classification of the single-wall carbon nanotube

Rin Okuyama·Wataru Izumida·Mikio Eto
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Abstract

The single-wall carbon nanotube (SWNT) can be a one-dimensional topological insulator, which is characterized by a $\mathbb{Z}$-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.

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Rin Okuyama, Wataru Izumida, Mikio Eto. 2019-03-12. Topological classification of the single-wall carbon nanotube. https://doi.org/10.1103/physrevb.99.115409

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