  Understanding the interplay between individual magnetic impurities and
superconductivity is crucial for bottom-up construction of novel phases of
matter. For decades, the description by Yu, Shiba and Rusinov (YSR) of single
spins in a superconductor and its extension to include quantum effects has
proven highly successful: the pair-breaking potential of the spin generates
sub-gap electron- and hole excitations that are energetically equidistant from
zero. By tuning the energy of the sub-gap states through zero, the impurity
screening by the superconductor makes the ground state gain or lose an
electron, signalling a parity breaking quantum phase transition. Here we show
that in multi-orbital impurities, correlations between the in-gap states can
conversely lead to a quantum phase transition where more than one electron
simultaneously leave the impurity without significant effect of the screening
by the superconductor, while the parity may remain unchanged. This finding
implies that the YSR treatment is not always valid, and that intra-atomic
interactions, particularly Hund's coupling that favours high spin
configurations, are an essential ingredient for understanding the sub-gap
states. The interaction-driven quantum phase transition should be taken into
account for impurity-based band-structure engineering, and may provide a
fruitful basis in the search for novel physics.
