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Register a new userTheory of driven Higgs oscillations and third-harmonic generation in unconventional superconductors
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Higgs spectroscopy is a new field in which Higgs modes in nonequilibrium superconductors are analyzed to gain information about the ground state. One experimental setup in which the Higgs mode in s-wave superconductors was observed is periodic driving with THz light, which shows resonances in the third-harmonic generation (THG) signal if twice the driving frequency matches the energy of the Higgs mode. We derive expressions of the driven gap oscillations for arbitrary gap symmetry and calculate the THG response. We demonstrate that the possible Higgs modes for superconductors with non-trivial gap symmetry can lead to additional resonances if twice the driving frequency matches the energy of these Higgs modes and we disentangle the influence of charge density fluctuations (CDF) to the THG signal within our clean-limit analysis. With this we show that THG experiments on unconventional superconductors allow for a detection of their Higgs modes. This paves the way for future studies on realistic systems including additional features to understand the collective excitation spectra of unconventional superconductors.
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Third-harmonic generation (THG) experiments on superconductors can be used to investigate collective excitations like the amplitude mode of the order parameter known as Higgs mode. These modes are visible due to resonances in the THG signal if the driving frequency matches the energy of the mode. In real materials multiple modes can exist giving rise to additional THG contributions, such that it is difficult to unambiguously interpret the results. In this paper, we additionally analyze the phase of the THG signal, which contains microscopic details beyond classical resonances as well as signatures of couplings between modes which are difficult to observe in the amplitude alone. We investigate how the Higgs mode, impurities or Coulomb interaction affects the phase response and consider exemplary two systems with additional modes. We argue that extracting this phase information could be valuable in future experiments.
In contrast to conventional s-wave superconductivity, unconventional (e.g. p or d-wave) superconductivity is strongly suppressed even by relatively weak disorder. Upon approaching the superconductor-metal transition, the order parameter amplitude becomes increasingly inhomogeneous leading to effective granularity and a phase ordering transition described by the Mattis model of spin glasses. One consequence of this is that at low enough temperatures, between the clean unconventional superconducting and the diffusive metallic phases, there is necessarily an intermediate superconducting phase which exhibits s-wave symmetry on macroscopic scales.
We propose an inductive method to measure critical current density $J_c$ in bulk superconductors. In this method, an ac magnetic field is generated by a drive current $I_0$ flowing in a small coil mounted just above the flat surface of superconductors, and the third-harmonic voltage $V_3$ induced in the coil is detected. We present theoretical calculation based on the critical state model for the ac response of bulk superconductors, and we show that the third-harmonic voltage detected in the inductive measurements is expressed as $V_3= G_3omega I_0^2/J_c$, where $omega/2pi$ is the frequency of the drive current, and $G_3$ is a factor determined by the configuration of the coil. We measured the $I_0$-$V_3$ curves of a melt-textured $rm YBa_2Cu_3O_{7-delta}$ bulk sample, and evaluated the $J_c$ by using the theoretical results.
Recent advances in time-domain terahertz (THz) spectroscopy have unveiled that resonantly-enhanced strong THz third-harmonic generation (THG) mediated by the collective Higgs amplitude mode occurs in s-wave superconductors, where charge-density fluctuations (CDF) have also been shown to contribute to the nonlinear third-order susceptibility. It has been theoretically proposed that the nonlinear responses of Higgs and CDF exhibit essentially different polarization dependences. Here we experimentally discriminate the two contributions by polarization-resolved intense THz transmission spectroscopy for a single-crystal NbN film. The result shows that the resonant THG in the transmitted light always appears in the polarization parallel to that of the incident light with no appreciable crystal axis dependence. When we compare this with the theoretical calculation here with the BCS approximation and the dynamical mean-field theory for a model of NbN constructed from first principles, the experimental result strongly indicates that the Higgs mode rather than the CDF dominates the THG resonance in NbN. A possible mechanism for this is discussed such as the retardation effect in the phonon-mediated pairing interaction beyond BCS.
We report on time-resolved linear and nonlinear terahertz spectroscopy of the two-band superconductor MgB$_2$ with the superconducting transition temperature $T_c approx$ 36 K. Third-harmonic generation (THG) is observed below $T_c$ by driving the system with intense narrowband THz pulses. For the pump-pulse frequencies $f=$ 0.3, 0.4, and 0.5 THz, temperature-dependent evolution of the THG signals exhibits a resonance maximum at the temperature where $2f=2Delta_pi(T)$, for the dirty-limit superconducting gap $2Delta_pi=$ 1.03 THz at 4 K. In contrast, for $f=$ 0.6 and 0.7 THz with $2f>2Delta_pi$, the THG intensity increases monotonically with decreasing temperature. Moreover, for $2f<2Delta_pi$ the THG is found nearly isotropic with respect to the pump-pulse polarization. These results suggest the predominant contribution of the driven Higgs amplitude mode of the dirty-limit gap, pointing to the importance of scattering for observation of the Higgs mode in superconductors.
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