High-Resolution Spectroscopy of the Intermediate Impurity States near a Quantum Phase Transition.

The intermediate behavior near a quantum phase transition is crucial for understanding the quantum criticality of various competing phases and their separate origins, yet it remains unexplored for the multiple Yu-Shiba-Rusinov (YSR) states. Here, we investigated the detailed spectroscopic change of the exchange-coupling-dependent YSR states near a quantum phase transition. The initially developed one pair of YSR states, induced by the Fe vacancy in monolayer Fe(Te,Se) superconductor, are clearly resolved with high resolution showing an evolution into two pairs of YSR peaks yet with dichotomy in their spectral features as they enter the quantum phase transition region. Spectral-weight analysis suggests that the double YSR pairs occur as a result of field splitting by the magnetic anisotropy. Our findings unveil the intermediate region of a quantum phase transition with a magnetic anisotropy-induced splitting of the YSR resonance, and highlight a prospect for developing functional electronics based on the flexibly controllable multiple quantum states.