Crossed Andreev reflection and elastic co-tunneling optimization using magnetic field

A short superconducting segment can mediate two peculiar interactions between attached quantum dots: elastic co-tunneling (ECT) and crossed Andreev reflection (CAR). Such interacting quantum dots can realize a minimal Kitaev chain hosting Majorana bound states, provided that the interaction is strong and the ratio between the two processes can be controlled. In our device, CAR and ECT are mediated by Andreev bound states formed in a hybrid semiconductor-superconductor heterostructure. We show that the combination of the intrinsic InSb nanowire spin-orbit coupling and an applied magnetic field provides an efficient knob to tune the ratio between CAR and ECT as well as their strength. By rotating the magnetic field, we show how to deterministically reach a ratio equal to 1, the so-called poor man's Majorana sweet-spot. If the field is rotated in 3D, then the sweet-spot becomes a manifold, in which we can locate a sweetest-spot: the point where CAR equals ECT and their value is maximal.