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

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.

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Cited by in corpus (6)

• Revealing novel aspects of light-matter coupling in terahertz two-dimensional coherent spectroscopy: the case of the amplitude mode in superconductors
• High-order nonlinear terahertz probing of the two-band superconductor MgB${}_2$: Third- and fifth-order harmonic generation
• Amplitude mode in a multi-gap superconductor MgB${}_2$ investigated by terahertz two-dimensional coherent spectroscopy
• Optically active Higgs and Leggett modes in multiband pair-density-wave superconductors with Lifshitz invariant
• Superconductivity with repulsion: a variational approach
• Raman response in superconducting multiorbital systems with application to nickelates