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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