Abstract
This work considers the $g$-tensor anisotropy induced by the flexural thermal vibrations in one-dimensional structures and its role on electron spin relaxation. In particular, the mechanism of spin-lattice relaxation via flexural modes is theoretically studied for localized and delocalized electronic states in semiconducting carbon nanotubes in the presence of a magnetic field. The calculation of a one-phonon spin-flip process predicts distinctive dependencies of the relaxation rate on temperature, magnetic field, and nanotube diameter. A comparison to the spin relaxation caused by the hyperfine interaction clearly suggests the relative efficiency of the proposed mechanism at sufficiently high temperatures. Specifically, the longitudinal spin relaxation time in the semiconducting carbon nanotubes is estimated to be as short as $30\text{ }\ensuremath{\mu}\text{s}$ at room temperature.
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