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Spin–curvature interaction from curved Dirac equation: Application to single-wall carbon nanotubes

Kai Zhang

Department of Applied Physics, School of Science, Xi’an Jiaotong University, Xi’an 710049, P. R. China

School of Science, Xi’an Technological University, Xi’an 710021, P. R. China

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Erhu Zhang

Department of Applied Physics, School of Science, Xi’an Jiaotong University, Xi’an 710049, P. R. China

E-mail Address: gnahz@mail.xjtu.edu.cn

Corresponding authors.

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Huawei Chen

Department of Applied Physics, School of Science, Xi’an Jiaotong University, Xi’an 710049, P. R. China

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, and

Shengli Zhang

Department of Applied Physics, School of Science, Xi’an Jiaotong University, Xi’an 710049, P. R. China

E-mail Address: zhangsl@mail.xjtu.edu.cn

Corresponding authors.

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https://doi.org/10.1142/S021797921750120XCited by:0 (Source: Crossref)

Abstract

The spin–curvature interaction (SCI) and its effects are investigated based on curved Dirac equation. Through the low-energy approximation of curved Dirac equation, the Hamiltonian of SCI is obtained and depends on the geometry and spinor structure of manifold. We find that the curvature can be considered as field strength and couples with spin through Zeeman-like term. Then, we use dimension reduction to derive the local Hamiltonian of SCI for cylinder surface, which implies that the effective Hamiltonian of single-wall carbon nanotubes results from the geometry and spinor structure of lattice and includes two types of interactions: one does not break any symmetries of the lattice and only shifts the Dirac points for all nanotubes, while the other one does and opens the gaps except for armchair nanotubes. At last, analytical expressions of the band gaps and the shifts of their positions induced by curvature are given for metallic nanotubes. These results agree well with experiments and can be verified experimentally.

Keywords:

PACS: 04.62.+v, 04.20.Gz, 71.70.Ej, 73.22.-f

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