Vortex-induced pairing suppression and near-zero modes in quantum dots coupled to full-shell nanowires

We analyze the subgap excitations and phase diagram of a quantum dot (QD) coupled to a semiconducting nanowire fully wrapped by a superconducting (S) shell. We take into account how a Little-Parks (LP) pairing vortex in the shell influences the proximity effect on the dot. We find that under axially symmetric QD-S coupling, shell vortices cause the induced pairing to vanish, producing instead a level renormalization that pushes subgap levels closer to zero energy and flattens parity crossings as the coupling strength increases. This vortex-induced stabilization mechanism has analogues in symmetric S-QD-S Josephson junctions at phase π, and can naturally lead to patterns of near-zero modes weakly dispersing with parameters in all but the zero-th lobe of the LP spectrum. We also show that, under certain conditions, this mechanism could give rise to states that mimic some of the features of Majorana bound states in full-shell wires, despite of the fact that they are topologically trivial.