Flux-tunable Andreev bound states in hybrid full-shell nanowires*

Understanding excitations of the Cooper pair condensate in a superconductor is crucial for many applications in quantum information processing. A remarkable example is the possibility of creating topologically-protected non-local qubits based on quasiparticle excitations at no energy cost, so-called Majorana zero modes. Their unambiguous detection has been impeded by the ubiquitous presence of non-topological Andreev bound states pinned to zero energy. It has thus become of utmost importance to find ways to experimentally establish the physical origin of subgap states in a controlled way. Here we show that the magnetic flux tunability of full-shell nanowires allows to clearly identify subgap levels as Andreev bound states. Transport spectroscopy reveals them as Yu-Shiba-Rusinov bound states, resulting from a quantum spin impurity --a quantum dot forming within the tunneling region-- that forms Kondo-like singlets with quasiparticles in the superconductor. The magnetic flux, both through the Little-Parks modulation of the gap and the Zeeman effect, induces quantum phase transitions between physically-different ground states, resulting in subgap level crossings at zero energy -zero bias peaks in tunneling conductance- unrelated to Majoranas. Our understanding of the complex interplay of different physical effects, fully supported by theory, offers a starting point for systematic experiments towards an unambiguous topological classification of zero modes.