Electron-nuclei spin relaxation through phonon-assisted hyperfine interaction in a quantum dot

TL;DR

This paper studies how phonon-assisted hyperfine interactions cause spin relaxation in quantum dots, revealing a suppression at long wavelengths and providing numerical estimates for realistic systems.

Contribution

It introduces a novel spin-phonon coupling mechanism derived from hyperfine interaction considering nuclear motion, differing from previous models.

Findings

Relaxation rate suppressed at long phonon wavelengths due to interference effects.

At higher frequencies, the rate scales linearly with phonon frequency.

Mechanism is less efficient than piezoelectric electron-phonon coupling in GaAs quantum dots.

Abstract

We investigate the inelastic spin-flip rate for electrons in a quantum dot due to their contact hyperfine interaction with lattice nuclei. In contrast to other works, we obtain a spin-phonon coupling term from this interaction by taking directly into account the motion of nuclei in the vibrating lattice. In the calculation of the transition rate the interference of first and second orders of perturbation theory turns out to be essential. It leads to a suppression of relaxation at long phonon wavelengths, when the confining potential moves together with the nuclei embedded in the lattice. At higher frequencies (or for a fixed confining potential), the zero-temperature rate is proportional to the frequency of the emitted phonon. We address both the transition between Zeeman sublevels of a single electron ground state as well as the triplet-singlet transition, and we provide numerical estimates for realistic system parameters. The mechanism turns out to be less efficient than electron-nuclei spin relaxation involving piezoelectric electron-phonon coupling in a GaAs quantum dot.