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

Abstract: 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.