# Magic angle for barrier-controlled double quantum dots. (arXiv:1707.07929v2 [cond-mat.mes-hall] UPDATED)

We show that the exchange interaction of a singlet-triplet spin qubit

confined in double quantum dots, when being controlled by the barrier method,

is insensitive to a charged impurity lying along certain directions away from

the center of the double-dot system. These directions differ from the polar

axis of the double dots by the magic angle, equaling

$\arccos\left(1/\sqrt{3}\right)\approx 54.7^\circ$, a value previously found in

atomic physics and nuclear magnetic resonance. This phenomenon can be

understood from an expansion of the additional Coulomb interaction created by

the impurity, but also relies on the fact that the exchange interaction solely

depends on the tunnel coupling in the barrier-control scheme. Our results

suggest that for a scaled-up qubit array, when all pairs of double dots rotate

their respective polar axes from the same reference line by the magic angle,

cross-talks between qubits can be eliminated, allowing clean single-qubit

operations. While our model is a rather simplified version of actual

experiments, our results suggest that it is possible to minimize unwanted

couplings by judiciously designing the layout of the qubits.