Abstract
It is shown that the band structure of single‐wall semiconducting carbon nanotubes (CNT) is analogous to relativistic description of electrons in vacuum, with the maximum velocity u= 108cm/s replacing the light velocity. One‐dimensional semirelativistic kinematics and dynamics of electrons in CNT is formulated. In particular, a relation between the effective mass and the energy is derived that is in direct analogy to the Einstein relation for electrons in vacuum. Two‐band kp Hamiltonian is employed to demonstrate that electrons in CNT experience a Zitterbewegung (trembling motion) in absence of external fields. An effect of an external magnetic field parallel to the CNT axis is considered. The amplitude of ZB in CNT can be as large as tens of nanometers.
Published Version
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