Spin relaxation of a donor electron coupled to interface states

An electron spin qubit in a silicon donor atom is a promising candidate for quantum information processing because of its long coherence time. To be sensed with a single-electron transistor, the donor atom is usually located near an interface, where the donor states can be coupled with interface states. Here we study the phonon-assisted spin-relaxation mechanisms when a donor is coupled to confined (quantum-dot-like) interface states. We find that both Zeeman interaction and spin-orbit interaction can hybridize spin and orbital states, each contributing to phonon-assisted spin relaxation in addition to the spin relaxation for a bulk donor or a quantum dot. When the applied magnetic field $B$ is weak (compared to orbital spacing), the phonon assisted spin relaxation shows the $B^5$ dependence. We find that there are peaks (hot spots) in the $B$ -dependent and detuning dependent spin relaxation due to strong hybridization of orbital states with opposite spin. We also find spin relaxation dips (cool spots) due to the interference of different relaxation channels. Qubit operations near spin relaxation hot spots can be useful for the fast spin initialization and near cool spots for the preservation of quantum information during the transfer of spin qubits.