  Polarization-resolved electronic Raman spectroscopy is an important
experimental tool to investigate collective excitations in superconductors. In
this work, 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. These new 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 irreps,
including the possible of $``$dark$"$ Leggett and Bardasis-Schrieffer modes.

Mesoscale and Nanoscale Physics;Superconductivity