Interaction-driven quantum phase transition of a single magnetic impurity in Fe(Se,Te)

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.