Collective mode spectroscopy in time-reversal symmetry breaking superconductors

Time-reversal symmetry breaking (TRSB) superconductors show a rich collective mode spectrum. In general, collective excitations in superconductors can provide crucial information on the symmetry of the broken phase, in particular, serving as a fingerprint for determining the groundstate gap symmetry. In this work, we consider several even parity two-dimensional TRSB superconductors characterized by an order parameter of the form $\Delta = \Delta_1 + i\Delta_2$. We provide a classification scheme of the collective excitations in the above systems as a function of the ratio between the components $\Delta_1/\Delta_2$. In order to excite the modes in the systems we have adopted two different probes: a quench of the condensate symmetry and a finite momentum transfer induced by an external electric field. Both methods allow us to excite and characterize the different modes in the spectra. To further interpret the results of the numerical calculations we provide a Ginzburg-Landau analysis and we construct a dynamical theory, deriving the linearized equations of motion in the pseudospin formalism. Our results could help distinguish between different order parameters symmetries of a TRSB superconducting condensate and estimate the magnitude of its different components.