Phase signatures in third-harmonic response of Higgs and coexisting modes in superconductors

Abstract

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.

arXiv comment22 pages, 10 figures

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• Observation of terahertz second harmonic generation from Dirac surface states in the topological insulator Bi${}_2$Se${}_3$
• Quench-drive spectroscopy and high-harmonic generation in BCS superconductors
• Surface resistance and amplitude mode under uniform and static external field in conventional superconductors
• Exact Continuum Representation of Long-range Interacting Systems and Emerging Exotic Phases in Unconventional Superconductors