Nonlinear electromagnetic response and Higgs mode excitation in BCS superconductors with impurities

Abstract

We reveal that due to the presence of disorder oscillations of the order parameter amplitude called the Higgs mode can be effectively excited by the external electromagnetic radiation in usual BCS superconductors. This mechanism works for superconductors with both isotropic s-wave and anisotropic, such as d-wave, pairings. The non-linear response in the presence of impurities is captured by the quasiclassical formalism. We demonstrate that analytical solutions of the Eilenberger equation with impurity collision integral and external field drive coincide with the exact summation of ladder impurity diagrams. Using the developed formalism we show that resonant third-harmonic signal observed in recent experiments is naturally explained by the excitation of Higgs mode mediated by impurity scattering.

arXiv commentnew references added, typos corrected

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• Theory of driven Higgs oscillations and third-harmonic generation in unconventional superconductors
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• Influence of scattering on optical response of superconductivity
• Contribution of Collective Excitations to Third Harmonic Generation in Multiband Superconductors: the case of MgB${}_2$
• Phase signatures in third-harmonic response of Higgs and coexisting modes in superconductors
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• Classification of Lifshitz invariant in multiband superconductors: an application to Leggett modes in the linear response regime in Kagome lattice models
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• Two-dimensional coherent spectroscopy of disordered superconductors in the narrow-band and broad-band limits
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• Third-harmonic generation in superconductors: Role of quantum geometry in the competition between Higgs mode and quasiparticles
• Terahertz nonlinear response in cuprate superconductors and the Higgs field in doped Mott insulators
• Tangent equations of motion for nonlinear response functions
• Two-dimensional THz spectroscopy in electronic systems: a many-body diagrammatic approach