Energy levels in carbon nanotubes
Wataru Izumida, Tohoku University
Carbon nanotubes have been intensively investigated since their discovery. Although understanding of electron spin properties is important from viewpoint on spintronics, it has been revealed in recent studies. We have theoretically studied the electronic states in finite-length carbon nanotubes. It has been shown that the discrete energy levels due to the confinement are sensitive to the chirality and the boundary shape of the nanotubes. Although the conventional picture is based on the valley degeneracy, our study reveals the lift of the degeneracy due to the valley coupling in the majority of nanotubes . For that case the electron spin states of the nanotubes are determined by the evenness or oddness of the number of electrons.
During this study, it has been recognized that evanescent modes play an important role. By studying the evanescent modes in detail, it has been shown properties of the carbon nanotubes as topological matters such as topological invariants  and topological phase transition . W. Izumida, R. Okuyama, A. Yamakage, R. Saito, Phys. Rev. B 93, 195442 (2016).
 R. Okuyama, W. Izumida, M. Eto, J. Phys. Soc. Jpn. 86, 013702 (2017).