Spin relaxation due to deflection coupling in nanotube quantum dots

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)].Comment: Final version accepted for publication. References added

Confinement-Deconfinement Transition in 3-Dimensional QED

We argue that, at finite temperature, parity invariant non-compact electrodynamics with massive electrons in 2+1 dimensions can exist in both confined and deconfined phases. We show that an order parameter for the confinement-deconfinement phase transition is the Polyakov loop operator whose average measures the free energy of a test charge that is not an integral multiple of the electron charge. The effective field theory for the Polyakov loop operator is a 2-dimensional Euclidean scalar field theory with a global discrete symmetry $Z$, the additive group of the integers. We argue that the realization of this symmetry governs confinement and that the confinement-deconfinement phase transition is of Berezinskii-Kosterlitz-Thouless type. We compute the effective action to one-loop order and argue that when the electron mass $m$ is much greater than the temperature $T$ and dimensional coupling $e^2$, the effective field theory is the Sine-Gordon model. In this limit, we estimate the critical temperature, $T_{\rm crit.}=e^2/8\pi(1-e^2/12\pi m+\ldots)$.Comment: 11 pages, latex, no figure