Optical and Raman selection rules for the pairing symmetry in chiral superconductors

Unconventional superconductivity has non-s-wave pairing order parameters, whose pairing symmetries are often difficult to determine experimentally. We propose a new method to probe the pairing symmetry with optical spectroscopy. Different pairing symmetries correspond to distinct electron symmetry fractionalization, leading to different quantum numbers of optical excitations. This gives rise to selection rules for the particle-hole continuum in optical/Terahertz absorption spectroscopy, and Raman scattering spectroscopy. We apply this approach to chiral superconductors with strong spin-orbit couplings, and to singlet superconductors with weak spin-orbit couplings, where the parity of the pairing order parameters can be determined unambiguously from spectroscopy measurements. We demonstrate the signature of these selection rules in optical spectra using specific examples.