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, however, been impeded by the ubiquitous presence of nontopological 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, a semiconducting core fully wrapped by a superconducting shell, allows to clearly identify subgap levels as Andreev bound states. Specifically, 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 field induces quantum phase transitions, subgap level crossings at zero energy. Apart from the Zeeman effect, the crossings also depend on the Little-Parks modulation of the gap which, in some cases, results in robust zero bias peaks in tunneling conductance near one flux quantum, a feature that could be easily misinterpreted as Majoranas. Our understanding of the complex interplay of different physical effects on the same device, fully supported by theory, offers a starting point for systematic experiments towards an unambiguous topological classification of zero modes in hybrid systems.