Coupling of quantum-dot states via elastic cotunneling and crossed Andreev reflection in a minimal Kitaev chain

We consider a quantum-dot (QD) based minimal Kitaev chain model and study the effects of modulation of QD states on the elastic cotunneling (ECT) and crossed Andreev reflection (CAR) processes. We demonstrate that the ECT amplitudes are strongly dependent on the energies of the QD states and are generally asymmetric, even in the absence of magnetic field, with respect to the chemical potential in the proximitized superconducting nanowire. We calculate the phase diagram of the total electron-number parity of the two QDs in terms of the spin-quantization axis direction in the QDs and the chemical potential in the superconducting nanowire, and also evaluate the precondition to attain a balance between ECT and CAR towards realizing the poor man's Majorana bound states. When the QDs are tuned into the deep Coulomb blockade regime, we predict a controllable anisotropic superexchange interaction between electrons in the two QDs under the combined effect of high-order interdot ECT and CAR processes.