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

Andreas Theiler1,*, Christian R. Ast2, and Annica M. Black-Schaffer1

  • *Contact author: andreas.theiler@physics.uu.se
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Phys. Rev. B 112, 134505 – Published 6 October, 2025

DOI: https://doi.org/10.1103/k8qc-3cs6

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 ground state of the system 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.

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Phys. Rev. B 112, 134505– Published 6 October, 2025
  • Received 7 February 2025
  • Revised 5 September 2025
  • Accepted 9 September 2025
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