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We reveal that due to the presence of disorder oscillations of the orderparameter amplitude called the Higgs mode can be effectively excited by theexternal electromagnetic radiation in usual BCS superconductors. This mechanismworks for superconductors with both isotropic s-wave and anisotropic, such asd-wave, pairings. The non-linear response in the presence of impurities iscaptured by the quasiclassical formalism. We demonstrate that analyticalsolutions of the Eilenberger equation with impurity collision integral andexternal field drive coincide with the exact summation of ladder impuritydiagrams. Using the developed formalism we show that resonant third-harmonicsignal observed in recent experiments is naturally explained by the excitationof Higgs mode mediated by impurity scattering.

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