Curvature effects in the band structure of carbon nanotubes including spin

article Curvature effects in the band structure of carbon nanotubes including spin–orbit coupling published Hong Liu author Dirk Florian Heinze author 10904 Huynh Thanh Duc author Stefan Schumacher author 272710000-0003-4042-4951 Torsten Meier author 3440000-0001-8864-2072 15 department 170 department 293 department 297 department 230 department 35 department 27 department Computing Resources Provided by the Paderborn Center for Parallel Computing project PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing project The Kane–Mele model was previously used to describe effective spin–orbit couplings (SOCs) in graphene. Here we extend this model and also incorporate curvature effects to analyze the combined influence of SOC and curvature on the band structure of carbon nanotubes (CNTs). The extended model then reproduces the chirality-dependent asymmetric electron-hole splitting for semiconducting CNTs and in the band structure for metallic CNTs shows an opening of the band gap and a change of the Fermi wave vector with spin. For chiral semiconducting CNTs with large chiral angle we show that the spin-splitting configuration of bands near the Fermi energy depends on the value of $\text{mod}(2n+m,3)$ . 2015 eng Journal of Physics: Condensed Matter 0953-8984 1361-648X10.1088/0953-8984/27/44/445501 2744 Liu, Hong, et al. “Curvature Effects in the Band Structure of Carbon Nanotubes Including Spin–Orbit Coupling.” Journal of Physics: Condensed Matter, vol. 27, no. 44, 445501, 2015, doi:<a href="https://doi.org/10.1088/0953-8984/27/44/445501">10.1088/0953-8984/27/44/445501</a>. @article{Liu_Heinze_Thanh Duc_Schumacher_Meier_2015, title={Curvature effects in the band structure of carbon nanotubes including spin–orbit coupling}, volume={27}, DOI={<a href="https://doi.org/10.1088/0953-8984/27/44/445501">10.1088/0953-8984/27/44/445501</a>}, number={44445501}, journal={Journal of Physics: Condensed Matter}, author={Liu, Hong and Heinze, Dirk Florian and Thanh Duc, Huynh and Schumacher, Stefan and Meier, Torsten}, year={2015} } Liu H, Heinze DF, Thanh Duc H, Schumacher S, Meier T. Curvature effects in the band structure of carbon nanotubes including spin–orbit coupling. Journal of Physics: Condensed Matter. 2015;27(44). doi:<a href="https://doi.org/10.1088/0953-8984/27/44/445501">10.1088/0953-8984/27/44/445501</a> H. Liu, D. F. Heinze, H. Thanh Duc, S. Schumacher, and T. Meier, “Curvature effects in the band structure of carbon nanotubes including spin–orbit coupling,” Journal of Physics: Condensed Matter, vol. 27, no. 44, Art. no. 445501, 2015, doi: <a href="https://doi.org/10.1088/0953-8984/27/44/445501">10.1088/0953-8984/27/44/445501</a>. Liu, H., Heinze, D. F., Thanh Duc, H., Schumacher, S., & Meier, T. (2015). Curvature effects in the band structure of carbon nanotubes including spin–orbit coupling. Journal of Physics: Condensed Matter, 27(44), Article 445501. <a href="https://doi.org/10.1088/0953-8984/27/44/445501">https://doi.org/10.1088/0953-8984/27/44/445501</a> H. Liu, D.F. Heinze, H. Thanh Duc, S. Schumacher, T. Meier, Journal of Physics: Condensed Matter 27 (2015). Liu, Hong, Dirk Florian Heinze, Huynh Thanh Duc, Stefan Schumacher, and Torsten Meier. “Curvature Effects in the Band Structure of Carbon Nanotubes Including Spin–Orbit Coupling.” Journal of Physics: Condensed Matter 27, no. 44 (2015). <a href="https://doi.org/10.1088/0953-8984/27/44/445501">https://doi.org/10.1088/0953-8984/27/44/445501</a>. 229462021-08-06T08:49:10Z2025-12-05T14:48:46Z