Spin coherence of carbon nanotubes

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Electronic states in the carbon nanotubes have been investigated by numerical and analytical methods which take into account the curvature of tube surface and the spin-orbit interaction. Velocity difference between the left- and right-going waves in the same valley, vernier-like spectrum and spin-orbit splitting in finite-length carbon nanotubes have been shown. These features uncover the electronic states in low temperature which are not able to be captured by the conventional picture of the valley degeneracy. The knowledge given in this research will give important aspect to understand the dynamics of spin, relaxation of spin, effect of spin in transport properties, and the controling of the spin in the carbon nanotubes.