Role of Higgs and Leggett modes for the third harmonic response in noncentrosymmetric superconductors

The amplitude and phase of the third harmonic response in superconductors provide important insights into collective Higgs and Leggett modes, respectively, in the superconducting state. In particular, for twice the incident frequency equal to the binding energy (2w = 2A), one finds a resonance of the amplitude and a corresponding phase jump in the third harmonic response, respectively. We generalize these concepts to superconductors without an inversion symmetry, which can be effectively described by a two-band model with an order parameter consisting of spin-singlet (even parity) and spin-triplet (odd parity) components. In our work we use an effective action approach for the derivation of the nonlinear response and assign the underlying physical processes to their respective Feynman diagrams. We calculate the third harmonic signal exemplary for the noncentrosymmetric compound CePt3Si, showing that it contains contributions from three distinguishable sources, namely the Higgs mode, the Leggett mode, and quasiparticles (broken Cooper-pairs). Only in the clean limit diamagnetic Raman-like processes contribute to the third harmonic signal, whereas the quasiparticle contributions dominate the collective modes for all triplet-singlet ratios of the gap structure. In the dirty limit, we find a significant enhancement of the Higgs mode contributions to the third harmonic response, due to the inclusion of nonvanishing paramagnetic diagrams. Finally, we argue that the phase difference between the third harmonic and the fundamental signal might reveal a jump, where its size is dependent on the light-matter coupling.