Theory of Spin Relaxation in Two-Electron Lateral Coupled Quantum Dots

We present a global picture of the phonon-induced spin relaxation of two-electron lateral double quantum dots. The analysis covers a wide range of tuning parameters, such as the magnetic field, the exchange coupling, and the electric field (detuning). Our examples cover experimentally important scenarios. Quantitative results were obtained with a highly accurate numerical technique for the two most relevant host materials--GaAs and silicon. We find that in the presence of spin-orbit coupling, the rate becomes anisotropic and its maxima and minima are generated with an in-plane magnetic field parellel or perpendicular to the dots' alignment dependent on specifics, such as spectral (anti-)crossings (spin hot spots), or the detuning strength. For all regimes, we give qualitative explanations of our observations. By understanding the spin lifetimes ($T_1$), this work marks a crucial step to the realization of two-electron semiconductor qubits.