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The presence of degenerate conduction band valleys and how they are mixed byinterfaces play critical roles in determining electron interaction and spectrumin a silicon nanostructure. Here we investigate how the valley phases affectthe exchange interaction in a symmetric two-electron silicon double quantumdot. Through a configuration interaction calculation, we find that exchangesplitting is suppressed at a finite value of valley phase difference betweenthe two dots, and reaches its minimum value ({\sim} 0) when the phasedifference is {\pi}. Such a suppression can be explained using the Hubbardmodel, through the valley-phase-dependent dressing by the doubly occupiedstates on the ground singlet and triplet states. The contributions of thehigher orbital states also play a vital role in determining the value of theexchange energy in general, which is a crucial parameter for applications suchas exchange gates for spin qubits.

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