Theory of Phonon-Induced Spin Relaxation in Laterally Coupled Quantum Dots

Phonon-induced spin relaxation in coupled lateral quantum dots in the presence of spin-orbit coupling is calculated. The calculation for single dots is consistent with experiment. Spin relaxation in double dots at useful interdot couplings is dominated by spin-hot spots that are strongly anisotropic. Spin-hot spots are ineffective for a diagonal crystallographic orientation of the dots with a transverse in-plane field. This geometry is proposed for spin-based quantum information processing.

Figure 1

Calculated spin relaxation rate for a single quantum dot as a function of $B_{\parallel }$ applied along $[110]$, $[010]$, and $[\overline{1}10]$. The symbols are experimental data from Ref. 16. The calculated curves for $B_{\parallel }\gtrsim 10\mathrm{T}$ are not realistic since they do not incorporate cyclotron effects in the $z$ direction.

Figure 2

Calculated spin relaxation, in ${\mathrm{s}}^{-1}$, for a double quantum dot along $[100]$ as a function of a perpendicular magnetic field $B_{\perp }$ and tunneling energy or interdot distance. The labeled contours are equirelaxational lines. Three spin-hot spot “ridges” are visible with spin relaxation as large as ${10}^9{\mathrm{s}}^{-1}$. The granular pattern at spin-hot spots is due to the finite resolution of the graphics.

Figure 3

Calculated spin relaxation rate, in ${\mathrm{s}}^{-1}$, of a double quantum dot as a function of $\gamma$ and tunneling energy, for $B_{\parallel }=5\mathrm{T}$. The dots are oriented along $[100]$. The weakest relaxation is for $\gamma \approx 35°$. Spin-hot spots strongly influence spin relaxation at tunneling energies from 0.001 to 0.1 meV.

Figure 4

Calculated spin relaxation, in ${\mathrm{s}}^{-1}$, of a double dot as a function of $\gamma$ and the tunneling energy, for $B_{\parallel }=5\mathrm{T}$. The dots are oriented along $[110]$. The weakest spin relaxation is for $\gamma =135°$, while at $\gamma =45°$ spin-hot spots do appear.