Two-dimensional coherent spectroscopy of disordered superconductors in the narrow-band and broad-band limits

Abstract

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 ${\chi }^{(3)}(3\Omega ;\Omega ,\Omega ,\Omega )$ (third harmonic generation) and ${\chi }^{(3)}(\Omega ;\Omega ,\Omega ,-\Omega )$ (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 ${\chi }^{(3)}(\Omega ;\Omega ,0,0)$ (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.

24 pages, 16 figures

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Cited by in corpus (1)

• Third-harmonic generation in superconductors: Role of quantum geometry in the competition between Higgs mode and quasiparticles