Interplay between Majorana and Shiba states in a minimal Kitaev chain coupled to a superconductor

Two semiconducting quantum dots (QDs) coupled through a superconductor constitute a minimal realization of a Kitaev chain with Majorana zero modes (MZMs). Such MZMs can be detected, e.g., by tunneling conductance between each QD and normal leads [Dvir et al., Nature (London) 614, 445 (2023)]. We here discuss how the seemingly trivial substitution of one of the normal leads by a superconducting (SC) one gives rise to a plethora of unique effects. In particular, the coupling to the SC lead induces nonlocal Majorana effects upon variations of the QDs' energies. Furthermore, the lowest excitation of the chain is no longer determined by the bulk gap but rather by the energy of an emergent subgap Yu-Shiba-Rusinov (YSR) state coexisting with the MZMs. The YSR state hybridizes with the MZMs when the coupling between the SC and the QD is larger than the spin splitting, spoiling the Majorana properties, including the quantized conductance.