Interactions and valley-orbit coupling in Si quantum dots

The valley-orbit coupling in a few-electron Si quantum dot is a function of its occupation number N, and for N \textgreater 1 is in principle renormalized by the electron-electron Coulomb interaction, which is known to be strong. We study the interaction renormalization of the valley-orbit coupling for 2 $\le $ N $\le $ 4, showing that, counterintuitively, interaction effects on the valley-orbit coupling are weak. For N $=$ 2 the renormalization is suppressed by valley interference, while for N $=$ 3 all renormalization terms are zero due to spinor overlaps, and for N $=$ 4 interaction renormalization terms cancel between different pairs of electrons. Experimental observations reveal no evidence of interaction effects on the valley-orbit coupling, consistent with these findings.