Temperature dependent energy gap for Yu-Shiba-Rusinov states at the quantum phase transition

Abstract

Motivated by recent experiments, which allow for fine tuning of the effective magnetic interaction between the impurity and the superconductor, we investigate the regime around the quantum phase transition where the system's ground state changes from a weakly coupled free spin to a screened spin regime. At this transition we find that the Yu-Shiba-Rusinov (YSR) states remain at finite energies at low temperatures, thereby generating a gap in the spectrum, which is inconsistent with predictions of the original YSR theory. We investigate various gap-generating scenarios and determine that the local suppression of the order parameter, only captured by self-consistent calculations, generates the gap.