Spin orbit interaction in dynamics of silicon double quantum dots*

We present a theoretical study of the role of spin-orbit interactions in a silicon double quantum dot. We propose that an accurate estimate of the strength of this interaction can be obtained through the study of the return probability of the double occupation singlet state in a magnetic field, as the system is gated dynamically across the relevant states in the low energy two-electron manifold. Landau-Zener-Stückelberg (LZS) type of processes involving appropriate control of voltage pulses across neighboring avoided crossings in the energy spectrum of the system are utilized to explore the system dynamics. Our description takes into account Zeeman splitting, intervalley mixing and spin-orbit interaction present in the structure. Using a density matrix equation of motion approach, we carry out numerical calculations of the return probability of the double occupation singlet state. The analysis in terms of LZS theory allows the determination of the spin-orbit coupling strength for different Zeeman splitting regimes.