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

TL;DR

This paper studies how the energy gap of Yu-Shiba-Rusinov states varies with temperature near the quantum phase transition, revealing a finite-energy gap caused by local suppression of the order parameter.

Contribution

It demonstrates that self-consistent calculations are necessary to explain the temperature-dependent energy gap in YSR states at the quantum phase transition.

Findings

YSR states remain at finite energies at low temperatures.

Local suppression of the order parameter generates the energy gap.

Self-consistent calculations are essential for accurate modeling.

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.