We theoretically analyze two-dimensional coherent spectroscopy (2DCS) signals for disordered superconductors in two limits: one is the narrow-band limit with sinusoidal pulse waves and the other is the broad-band limit with delta-function pulses. While the 2DCS signal in the narrow-band limit is related to the third-order nonlinear susceptibilities ${\chi }^{\left(3\right)}(3\mathrm{\Omega };\mathrm{\Omega },\mathrm{\Omega },\mathrm{\Omega })$ (third harmonic generation) and ${\chi }^{\left(3\right)}(\mathrm{\Omega };\mathrm{\Omega },\mathrm{\Omega },-\mathrm{\Omega })$ (ac Kerr effect), we find that in the broad-band limit the signal along the diagonal and horizontal lines in the two-dimensional frequency space is related to another nonlinear susceptibility ${\chi }^{\left(3\right)}(\mathrm{\Omega };\mathrm{\Omega },0,0)$ (dc Kerr effect). We numerically evaluate those susceptibilities for a lattice model of superconductors based on the BCS mean-field theory and self-consistent Born approximation for impurities. The 2DCS signals in the narrow-band and broad-band limits show threshold and resonance behaviors at the superconducting-gap frequency, respectively, whose physical origin is discussed in light of quasiparticle and Higgs-mode excitations.

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• Quasiparticles & collective excitations
• Superconductivity
• Superconductors
• Terahertz spectroscopy