Spin relaxation due to deflection coupling in nanotube quantum dots

TL;DR

This paper introduces a new spin relaxation mechanism in nanotube quantum dots caused by deflection coupling to flexural phonons, which dominates at low energy transfers and explains observed spin lifetime minima.

Contribution

It identifies a novel spin-orbit mediated deflection coupling mechanism that influences spin relaxation in nanotube quantum dots, especially near avoided level crossings.

Findings

Deflection coupling dominates other mechanisms at low energy transfers.

A minimum in spin lifetime T1 occurs near avoided crossings due to this mechanism.

The mechanism explains experimental observations of T1 minima in nanotube quantum dots.

Abstract

We consider relaxation of an 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, $\omega \propto q^2$, the density of states $dq/d\omega \propto \omega^{-1/2}$ diverges as $\omega \to 0$. 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. {\bf 102}, 166802 (2009)].