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Singlet-triplet relaxation in multivalley silicon single quantum dots

We investigate the singlet-triplet relaxation due to the spin-orbit coupling together with the electron-phonon scattering in two-electron multivalley silicon single quantum dots, using the exact diagonalization method and the Fermi golden rule. The electron-electron Coulomb interaction, which is crucial in the electronic structure, is explicitly included. The multivalley effect induced by the interface scattering is also taken into account. We first study the configuration with a magnetic field in the Voigt configuration and identify the relaxation channel of the experimental data by Xiao {\em et al.} [Phys. Rev. Lett. {\bf 104}, 096801 (2010)]. Good agreement with the experiment is obtained. Moreover, we predict a peak in the magnetic-field dependence of the singlet-triplet relaxation rate induced by the anticrossing of the singlet and triplet states. We then work on the system with a magnetic field in the Faraday configuration, where the different values of the valley splitting are discussed. In the case of large valley splitting, we find the transition rates can be effectively manipulated by varying the external magnetic field and the dot size. The intriguing features of the singlet-triplet relaxation in the vicinity of the anticrossing point are analyzed. In the case of small valley splitting, we find that the transition rates are much smaller than those in the case of large valley splitting, resulting from the different configurations of the triplet states.