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 ¹³C 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 10.3em0exs in carbon nanotubes is still much longer than those found in conventional semiconductor structures. Moreover, it is found that the curvature effect and subsequent rehybridization of s and p orbitals in ultrathin nanotubes may significantly impact the electron spin relaxation leading to its further suppression at certain dimensions.