Contribution of Collective Excitations to Third Harmonic Generation in Multiband Superconductors: the case of MgB$_2$

TL;DR

This paper investigates how collective excitations influence third harmonic generation in multiband superconductors like MgB$_2$, revealing the roles of amplitude and Leggett modes in nonlinear optical responses through theoretical and numerical analysis.

Contribution

It provides a detailed analysis of collective mode contributions to nonlinear THz response in multiband superconductors, clarifying experimental contradictions and highlighting the relevance of specific modes.

Findings

The Higgs mode spectral weight deviates with interband coupling.

Resonance at twice the smaller gap dominates at low frequencies.

Leggett mode influences nonlinear response at higher frequencies.

Abstract

Multiband superconductors can host collective excitations with marked differences with respect to their single-band counterpart. We first study the spectrum of collective amplitude fluctuations in a clean two-bands superconductor, showing that the spectral weight of the Higgs mode rapidly deviates from the naive extension of the single band case as the interband coupling is turned on. These results are then used to critically analyze the non-linear optical response in MgB$_2$, providing an explanation for the apparently contradictory results of recent experiments, pointing towards a selective relevance either of the Leggett mode or of the amplitude fluctuations at twice the lower gap. By using exact numerical simulations and realistic estimate of disorder we compute the relative contribution of the quasiparticle, amplitude and phase fluctuations to the non-linear optical response. We show that at low pumping frequency only the resonance at twice the smaller gap emerges, as due to the BCS response, while the Leggett mode dominates only in a narrow range of higher pumping frequencies matching its low-temperature value. Our findings provide a fresh perspective on the potential of non-linear THz spectroscopy to detect collective modes in other multiband systems, as e.g. iron-based superconductors.