Mateo Uldemolins

Understanding the interplay between individual magnetic impurities and superconductivity is crucial for the bottom-up construction of exotic phases of matter. The pair-breaking potential of the spin leads to the emergence of particle-hole symmetric in-gap excitations [known as Yu-Shiba-Rusinov (YSR) states] whose energy depends on the impurity’s local coupling to the environment. At a certain critical exchange interaction, the YSR states cross zero energy, signifying a quantum phase transition where the ground state of the system changes parity and total spin by 1/2. In transition-metal impurities such as Fe or Mn typically probed in scanning tunneling microscope (STM) experiments, the reduced symmetry of the atomic site lifts the degeneracy among the d-orbitals, and Hund’s occupation rule enforces a high-spin configuration that results in multiple in-gap states. The YSR picture can be readily extended by treating the singly occupied d-orbitals as independent scatterers, thereby accounting for the effect of Hund’s coupling in an implicit manner only. A key question is whether the inter-orbital interaction responsible for the high-spin configuration leads to any other distinct phenomenology that cannot be captured using independent scattering channels.
Motivated by recent STM experiments showcasing multiple, highly tunable impurity-bound states in superconducting Fe(Se, Te), we study the role of the inter-orbital interactions in the YSR quantum phase transition [1]. By considering a minimal Anderson impurity model that crucially includes Hund’s coupling, we show that in multi-orbital impurities, electronic correlations can lead to a quantum phase transition where the impurity's mean occupation and total spin changes dramatically, without a significant role of the screening by the superconductor. Spectroscopically, this quantum phase transition is signaled by the correlated behavior of in-gap states, consistent with STM observations. Our study belongs to a renewed effort to characterize the quantum behavior of magnetic impurities in superconductors by employing toy models that incorporate many-body correlations [2,3], and it suggests that inter-orbital interactions are an essential ingredient harboring novel physics.

[1] M. Uldemolins et al. arXiv:2310.06030.
[2] F. von Oppen and K. J. Franke, Phys. Rev. B, 103, 205424, 2021.
[3] S. Trivini et al. Phys. Rev. Lett. 130, 136004, 2023.