Spin relaxation due to deflection coupling in nanotube quantum dots

We consider relaxation of a single-electron spin in a nanotube quantum dot due to its coupling to flexural phonon modes, and identify a new spin-orbit-mediated coupling between the nanotube deflection and the electron spin. This mechanism dominates other spin-relaxation mechanisms in the limit of small energy transfers. Due to the quadratic dispersion law of long-wavelength flexons, q2, the density of states dq /d −1/2 diverges as →0. Furthermore, because here the spin couples directly to the nanotube deflection, there is an additional enhancement by a factor of 1 /q compared to the deformation-potential coupling mechanism. We show that the deflection coupling robustly gives rise to a minimum in the magnetic field dependence of the spin lifetime T1 near an avoided crossing between spin-orbit split levels in both the highand low-temperature limits. This provides a mechanism that supports the identification of the observed T1 minimum with an avoided crossing in the single-particle spectrum by Churchill et al. Phys. Rev. Lett. 102, 166802 2009 .