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Two-Photon Absorption by Impurity Scattering and Amplitude Mode in Conventional Superconductors

We theoretically investigate the two-photon absorption spectrum of conventional s-wave superconductors. The calculation is carried out in the local limit at absolute zero. The direct excitation of quasiparticles is excluded under the condition that the frequency of the external field is lower than twice the magnitude of the superconducting gap. We calculate vertex corrections with the conserving approximation, and show that the amplitude mode is independent of the impurity scattering in the local limit. Because of this property, a diverging absorption edge appears in the dirty limit. We propose this behavior as a probe of the amplitude mode.