Electron spin relaxation in semiconducting carbon nanotubes: the role of hyperfine interaction

A theory of electron spin relaxation in semiconducting carbon nanotubes is developed based on the hyperfine interaction with disordered nuclei spins I=1/2 of $^{13}$C isotopes. It is shown that strong radial confinement of electrons enhances the electron-nuclear overlap and subsequently electron spin relaxation (via the hyperfine interaction) in the carbon nanotubes. The analysis also reveals an unusual temperature dependence of longitudinal (spin-flip) and transversal (dephasing) relaxation times: the relaxation becomes weaker with the increasing temperature as a consequence of the particularities in the electron density of states inherent in one-dimensional structures. Numerical estimations indicate relatively high efficiency of this relaxation mechanism compared to the similar processes in bulk diamond. However, the anticipated spin relaxation time of the order of 1 s in CNTs is still much longer than those found in conventional semiconductor structures.