Revealing THz optical signatures of Shiba-state-induced gapped and gapless superconductivity

TL;DR

This paper presents a comprehensive theoretical study of how magnetic impurities induce gapless superconductivity and alter optical responses, highlighting the potential of THz spectroscopy to detect Shiba states.

Contribution

It provides a self-consistent calculation of the phase diagram and optical properties of magnetic impurity-doped superconductors, revealing new signatures of Shiba states in THz spectra.

Findings

Magnetic disorder can induce a gapless superconducting phase.

Optical conductivity shows finite absorption below the gap energy.

The nonlinear response is dominated by Higgs-mode dynamics.

Abstract

We report a fully self-consistent calculation of the complex renormalization by exchange interactions and hence the complete phase diagram of conventional $s$-wave superconductors with magnetic impurities as well as the related physical properties including the optical response. We show that a small amount of magnetic disorder can drive the system into a gapless superconducting state, where the single-particle excitation gap vanishes whereas the superconducting order parameter $\Delta_0$ remains finite. In this phase, the linear optical conductivity exhibits a finite absorption over the low-frequency regime, particularly for photon energies below the conventional threshold $2|\Delta_0|$, even at low temperatures, in sharp contrast to the gapped state. The nonlinear response, however, remains coherent and is dominated by the Higgs-mode dynamics rather than gapless quasiparticle background. These findings reveal a fundamental distinction between dissipative single-particle excitations and coherent collective dynamics of the condensate, a feature likely general to other gapless superconductors, and introduces a fundamentally different detection scheme, using THz spectroscopy to probe the signatures of Shiba states.