Phonon Mediated Spin Relaxation

Experimental Signature of Phonon Mediated Spin Relaxation in a Two-Electron Quantum Dot

T. Meunier, I.T. Vink, L.H. Willems van Beveren, K.J. Tielrooij, R. Hanson, F.H.L. Koppens, H.P. Tranitz, W. Wegscheider, L.P. Kouwenhoven, and L.M.K. Vandersypen

PRL 98, 126601 (2007)

URL: http://link.aps.org/abstract/PRL/v98/e126601


The authors measured the singlet-triplet relaxation time in a two electron quantum dot. They vary the splitting of the two levels using an applied magnetic field. They find a minimum relaxation time between zero field and the field at which the singlet and triplet states become degenerate. This would not be expected if the only mechanism at work was Zeeman splitting.

The only relevant pathway for energy dissipation in the setup is coupling with acoustic phonons. This coupling is indirect, as phonons cannot couple states with different spin. The phonons can couple different atomic levels, and spin-orbit coupling provides a pathway for phonons to carry away the spin-flip energy.

To explore whether this model of phonon-assisted spin flips could explain the minimum in the spin relaxation time, the authors developed a simple but elegant model. It reproduces the qualitative features of the data quite well. The phonon coupling is strongest --- and the relaxation time shortest --- when the energy splitting of the singlet and triplet states corresponds to a phonon whose wavelength is twice the size of the dot. I.e., there is a resonant acoustic mode at this energy, which maximizes the rate of phonon assisted spin-flips.

When the phonon wavelength is large compared to the dot size, couplings to the singlet and triplet states are roughly equal, and their respective contributions to the electron-phonon interaction cancel. When the phonon wavelength is small, the coupling to both states is small individually, and the overall coupling is small. It is the resonant phonon energy that maximizes the coupling and leads to the observed minimum in decay time.

I've made some notes on the model.