Impact of valley phases on exchange interaction in silicon double 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. Within the Heitler-London approximation limited to the ground orbital states, exchange splitting is suppressed at a finite value of valley phase difference between the two dots and reaches its minimum value (~0) when the phase difference is π. Such a suppression can be explained using the Hubbard model and the absence of difference in double occupation. The contributions of the higher orbital states thus play a vital role in determining the value of the exchange energy in general.