Theoretical approach to resonant inelastic x-ray scattering in iron-based superconductors at the energy scale of the superconducting gap

We develop a phenomenological theory to predict the characteristic features of the momentum-dependent scattering amplitude in resonant inelastic x-ray scattering (RIXS) at the energy scale of the superconducting gap in iron-based superconductors. Taking into account all relevant orbital states as well as their specific content along the Fermi surface we evaluate the charge and spin dynamical structure factors for the compounds LaOFeAs and LiFeAs, based on tight-binding models which are fully consistent with recent angle-resolved photoemission spectroscopy (ARPES) data. We find a characteristic intensity redistribution between charge and spin dynamical structure factors which discriminates between sign-reversing and sign-preserving quasiparticle excitations. Consequently, our results show that RIXS spectra can distinguish between $s_\pm$ and $s_{++}$ wave gap functions in the singlet pairing case. In addition, we find that an analogous intensity redistribution at small momenta can reveal the presence of a chiral $p$-wave triplet pairing.