Figure 4: Valley-controlled quantum gates of a spin qubit.
(a) The Zeeman splitting of the spin qubit has different magnitude in valley K and –K in presence of both static electric (Ez) and magnetic (Bz) fields. A pulse of oscillating magnetic field Bx in resonance with the splitting at −K rotates the spin qubit only if the valley bit is on state −K, as illustrated on the spin Bloch sphere. (b) When a static Bx splits the spin qubit, both oscillating Ez and Bz can drive the spin resonance, and the two fields constructively (destructively) interfere in valley −K (K), which realize valley-controlled rotation of the spin qubit about the z axis.
