  Recently, exciting progress has been made in using the superconducting
nanowires coupled to gate-defined quantum dots (QDs) to mimic the Kiteav chain
and realize the Majorana-bound states via a poor man's route. The essential
ingredient is to balance the interdot elastic-cotunneling (ECT) and crossed
Andreev reflection (CAR). As theoretically proposed, this can be mediated by
the Andreev bound states (ABSs) formed in the superconducting nanowires.
However, most of the gate-tuning asymmetric features observed in experiments
can not be captured using the current theoretical models. To address this
insufficiency, here, we consider a full model that explicitly includes all the
details of both the QD states and the ABSs. Remarkable agreement is found with
the recent experimental observations, where our model correctly reveals the
gate-tuning asymmetry in ECTs and by which the average QD state energy can also
be extracted. In contrast, CARs do not depend on the tuning of QD states.
Moreover, armed with the tunability of ECTs and CARs with QD states, we also
predict a controllable anisotropic superexchange interaction between electron
spins in the two separated QDs.
