Spin-orbit coupling induced two-electron relaxation in coupled silicon donors

We discovered theoretically the unexpected important role of intrinsic donor spin-orbit coupling (SOC) in driving the relaxation of coupled-donor electron states in isotopically enriched silicon 28, which is a promising host material for semiconductor qubits, despite the commonly perceived weak strength of atomic SOC in this material. The only existing spin-relaxation mechanism considered in this context before our work is the relaxation of two-electron states induced by hyperfine interaction with the donor nuclear spins. The new intrinsic SOC mechanism has a parametrically strong dependence on exchange coupling (~J⁵), and becomes important when the donors are closely spaced as in the case of singlet-triplet spin qubits. Our analytical study drew on the symmetry analysis over combined band, donor envelope and valley configurations, and unraveled naturally the anisotropic dependence on the donor-alignment direction and triplet spin orientation and the associated phonon modes. This mechanism may also shed important new light on the well-studied problem of electron spin resonance in highly doped silicon.