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 $\pi$, 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.