Impact of the valley orbit coupling on exchange gate for spin qubits in silicon

The mixing of conduction band valleys plays a critical role in determining electronic spectrum and dynamics in a silicon nanostructure. Here, we investigate theoretically how valley–orbit coupling affects the exchange interaction in a silicon double quantum dot. We find that exchange splitting can be strongly suppressed at finite valley phase differences between the dots because of the valley-phase-dependent dressing of the ground states and Coulomb exchange integrals, and a small valley splitting can render the exchange Hamiltonian incomplete in describing low-energy dynamics due to nearby excited valley states. The higher orbital states are also vital in calculating the exchange splitting, which is crucial for applications such as exchange gates for spin qubits.