Electronic Raman response of a superconductor across a time reversal symmetry breaking phase transition

Polarization-resolved electronic Raman spectroscopy is an important experimental tool to investigate collective excitations in superconductors. In this paper, we present a general theory that allows us to study the evolution of all Raman active collective modes in multiple symmetry channels across a time reversal symmetry (TRS) breaking superconducting transition. This comprehensive approach reveals that multiple modes belonging to different symmetry channels show a tendency to soften, even when the interactions in the subleading channel are held constant. This indicates an increased competition induced by the proximity to the TRS breaking transition. The entry into the TRS broken phase is marked by the introduction of an additional mode into the gap in multiple symmetry channels. This additional modes have a phase character complementary to the ones that are already present. Even though all the modes in the TRS broken phase acquire an amplitude character, we explicitly demonstrate that the coupling to the Raman probe is exclusively through the phase sector. We demonstrate that the Raman spectrum collected in lower symmetry channels shows a selective sensitivity to the sign of the ground-state order parameters and the sign of the interband interactions. Finally, we demonstrate the applicability of an interaction induced selection rule that clearly explains the spectral weights of various modes in various irreducible representations, including the possible of dark Leggett and Bardasis-Schrieffer modes.