Signature of the Leggett mode in the A1g Raman response: from MgB2 to iron-based superconductors

TL;DR

This paper demonstrates how the Raman response in multiband superconductors reveals the nature of pairing interactions, highlighting the Leggett mode as a key signature distinguishing intra- and interband pairing, with implications for iron-based superconductors.

Contribution

It provides a gauge-invariant theoretical framework showing the Leggett mode's dominance in Raman response and links experimental observations to interband pairing mechanisms.

Findings

Leggett mode dominates Raman response in multiband superconductors.

Intra-band pairing shows a distinct phase fluctuation peak, as in MgB2.

Interband pairing shifts the Leggett resonance to twice the gap, matching iron-based superconductor data.

Abstract

The Raman response in a superconductor is a powerful probe to investigate the symmetry of the superconducting gap. Here we show that in a multiband superconductor it also offers the unique opportunity to establish if the driving pairing interaction has an intraband or interband character. In the model with one hole and one electron band the full gauge-invariant Raman response, obtained by accounting for the fluctuations of both the density and superconducting phase degrees of freedom, is always dominated by the Leggett mode, regardless its nature. However, while in the case of intra-band dominated pairing the Josephson-like phase fluctuations of the two condensates identify a well-defined peak, as observed in MgB$_2$, for dominant interband pairing the Leggett resonance is pushed at twice the largest gap, resembling apparently a pair-breaking peak. The latter case is in very good agreement with experimental data in iron-based superconductors, suggesting that an interband pairing mechanism should be at play in these systems. These results have also interesting implications for the non-linear optical response probed by means of intense THz fields.