Abstract
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, $\ensuremath{\omega}\ensuremath{\propto}{q}^{2}$, the density of states $dq/d\ensuremath{\omega}\ensuremath{\propto}{\ensuremath{\omega}}^{\ensuremath{-}1/2}$ diverges as $\ensuremath{\omega}\ensuremath{\rightarrow}0$. 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 ${T}_{1}$ near an avoided crossing between spin-orbit split levels in both the high- and low-temperature limits. This provides a mechanism that supports the identification of the observed ${T}_{1}$ minimum with an avoided crossing in the single-particle spectrum by Churchill et al. [Phys. Rev. Lett. 102, 166802 (2009)].
Highlights
Due to their outstanding mechanical properties and versatile electrical characteristics, carbon nanotubes offer an exciting platform both for studies of fundamental physical phenomena and for a variety of potential applications
The relatively small nuclear charge of carbon and the low natural abundance of carbon isotopes with nonzero nuclear spin suggest that the spin-orbit and hyperfine interactions, which are the main sources of electron-spin relaxation in GaAs,[1,2] should be weak in carbon nanotubes
The availability of isotopically purified starting materials opens the possibility of growing 12Cnuclear spin I = 0͒ and 13Cnuclear spin I = 1 / 2͒ nanotubes to study the behavior of electron spins in the presence or absence of a nuclear-spin bath.[3]
Summary
Due to their outstanding mechanical properties and versatile electrical characteristics, carbon nanotubes offer an exciting platform both for studies of fundamental physical phenomena and for a variety of potential applications. Bulaev et al.[12] considered spin-orbit coupling to the bending mode deformation potential, and used the singularity in the density of states to predict a spectacular enhancement of 1 / T1 κ 1 / ͱ near the upper anticrossing point of Fig. 1͑ain the high-temperature regime. To make connection to the Gedanken experiment depicted in Fig. 1͑cwhere the spin follows the direction of the tube axis, we note that the electron-flexon coupling Hamiltonian Hs-phsee Eq ͑5͒ and accompanying discussion belowused throughout this paper depends only on the instantaneous deflection of the nanotube. V, we discuss how this picture is modified in “dirty” tubes where a substrate or coating may lead to flexon localization
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