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

The presence of degenerate conduction band valleys and how they are mixed by interfaces play critical roles in determining electron interaction and spectrum in a silicon nanostructure. Here we investigate how the valley phases affect the exchange interaction in a symmetric two-electron silicon double quantum dot. Through a configuration interaction calculation, we find that exchange splitting is suppressed at a finite value of valley phase difference between the two dots, and reaches its minimum value ({\sim} 0) when the phase difference is {\pi}. Such a suppression can be explained using the Hubbard model, through the valley-phase-dependent dressing by the doubly occupied states on the ground singlet and triplet states. The contributions of the higher orbital states also play a vital role in determining the value of the exchange energy in general, which is a crucial parameter for applications such as exchange gates for spin qubits.