Theory of silicon spin qubit relaxation in a synthetic spin-orbit field

We develop the theory of single-electron silicon spin qubit relaxation in the presence of a magnetic field gradient. Such field gradients are routinely generated by on-chip micromagnets to allow for electrically controlled quantum gates on spin qubits. We build on a valley-dependent envelope function theory that enables the analysis of the electron wave function in a silicon quantum dot with an arbitrary roughness at the interface. We assume the presence of single-layer atomic steps at a Si/SiGe interface and study how the presence of a gradient field modifies the spin-mixing mechanisms. We show that our theoretical modeling can quantitatively reproduce results of experimental measurements of qubit relaxation in silicon in the presence of a micromagnet. We further study in detail how a field gradient can modify the EDSR Rabi frequency of a silicon spin qubit. While this strongly depends on the details of the interface roughness, interestingly, we find that adding a micromagnet on top of a spin qubit with an ideal interface can even reduce the EDSR frequency within some interval of the external magnetic field strength.