Abstract
We theoretically investigate the resonance of third harmonic generation (THG) that has been observed at frequency being half of the superconducting gap in a multiband disordered superconductor NbN. The central question is whether the dominant contribution to the THG resonance comes from the Higgs mode (the collective amplitude mode of the superconducting order parameter) or quasiparticle excitations. To resolve this issue, we analyze a realistic three-band model with effective intraband and interband phonon-mediated interactions estimated from first-principles together with nonmagnetic impurity scatterings. Using the estimated pairing interactions with multiband impurity scattering rates being varied from clean to dirty regimes, we calculate the THG susceptibility for NbN in a channel-resolved manner by means of the BCS and self-consistent Born approximations. In the dirty regime, which is close to the experimental situation, the leading contribution is given by the paramagnetic channel of the Higgs mode having almost no polarization-angle dependence, while the second leading contribution comes from the paramagnetic channel of quasiparticles generally showing significant polarization-angle dependence. The result is consistent with the recent experimental observation of no polarization-angle dependence of THG, giving firm evidence that the Higgs mode dominantly contributes to the THG resonance in NbN superconductors.
Highlights
The standard microscopic theory of superconductivity, i.e., the BCS theory, predicts the presence of the collective amplitude mode of the superconducting order parameter [1,2,3,4,5,6], which is recently referred to as the Higgs mode due to the close analogy with the Higgs boson in particle physics
The results show that the third harmonic generation (THG) resonance is dominated by the paramagnetic channel in the dirty regime in NbN, in which the Higgs-mode contribution generally becomes larger than the quasiparticle contribution
We study the resonance of third harmonic generation and its polarization-angle dependence in disordered NbN superconductors based on the effective three-band model constructed from first-principles calculations on the electron and phonon band structures of NbN
Summary
The standard microscopic theory of superconductivity, i.e., the BCS theory, predicts the presence of the collective amplitude mode of the superconducting order parameter [1,2,3,4,5,6], which is recently referred to as the Higgs mode due to the close analogy with the Higgs boson in particle physics (for recent reviews, see Refs. [7,8]). Based on the nonequlibrium dynamical mean-field theory [22], it has been shown that the Higgs mode can contribute to THG with an order of magnitude comparable to quasiparticles [23] Another possibility is to depart from the clean limit and consider the effect of disorders or impurity scattering. We study the polarization-angle dependence of THG in NbN superconductors with disorders (Fig. 1) For this purpose, we use an effective three-band model including the phonon-mediated multiband pairing interactions for NbN. With the estimated ratio between the intraband and interband pairing interactions, the quasiparticles always show clear polarization-angle dependence of THG, while the Higgs mode does not in general, except in the vicinity of the parameter region where the interband impurity scattering rate vanishes.
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