Abstract
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.
Highlights
In recent years with the emergence of terahertz (THz) spectroscopy, studies on matter were possible in regimes which were inaccessible before [1,2,3]
One interesting field within the THz studies are excitations of collective modes like the Higgs mode in superconductors [4,5,6,7,8,9]. In equilibrium this mode arises due to the spontaneous U(1) symmetry breaking in the superconducting state which is characterized by a Mexican hat-shaped free energy potential (Fig. 1)
How an arbitrary gap symmetry affects the third-harmonic generation (THG) intensity and that composite gap-symmetries can lead to additional resonances
Summary
In recent years with the emergence of terahertz (THz) spectroscopy, studies on matter were possible in regimes which were inaccessible before [1,2,3]. Experiments on several different cuprates were performed, where a possible new mode at an energy below the symmetric 2 Higgs mode was observed in the THG spectrum [52] This experiment and further ongoing efforts in performing these kinds of experiments on unconventional superconductors require an understanding of the underlying physics. Other papers pointed out that for superconductors in the dirty-limit the paramagnetic coupling to light plays a crucial role which leads to a dominant Higgs contribution in the THG signal [56,57,58,59,60] This shows that a careful analysis of an experiment has to be performed in order to interpret the data correctly.
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