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

TL;DR

This paper provides detailed numerical analysis of phonon-induced two-electron spin relaxation in silicon quantum dots, highlighting the dominant role of spin-orbit coupling and the conditions affecting relaxation rates.

Contribution

It offers the first comprehensive numerical study of spin relaxation in silicon double quantum dots considering realistic experimental parameters.

Findings

Relaxation rates are significantly lower in silicon than in GaAs.

Anisotropic switch of the spin lifetime axis with detuning is confirmed.

Spin-orbit coupling dominates over hyperfine interactions in typical regimes.

Abstract

Highly accurate numerical results of phonon-induced two-electron spin relaxation in silicon double quantum dots are presented. The relaxation, enabled by spin-orbit coupling and the nuclei of $^{29}$Si (natural or purified abundance), are investigated for experimentally relevant parameters, the interdot coupling, the magnetic field magnitude and orientation, and the detuning. We calculate relaxation rates for zero and finite temperatures (100 mK), concluding that our findings for zero temperature remain qualitatively valid also for 100 mK. We confirm the same anisotropic switch of the axis of prolonged spin lifetime with varying detuning as recently predicted in GaAs. Conditions for possibly hyperfine-dominated relaxation are much more stringent in Si than in GaAs. For experimentally relevant regimes, the spin-orbit coupling, although weak, is the dominant contribution, yielding anisotropic relaxation rates of at least two order of magnitude lower than in GaAs.