Classification of Symmetry Derived Pairing at M Point in FeSe

Using the constraints imposed by the crystalline symmetry of FeSe and the experimentally observed phenomenology, we analyze the possible pairing symmetry of the superconducting order parameter focusing on intercalated and monolayer FeSe compounds. Such analysis leads to three possible pairing symmetry states -- s-wave, d-wave, and helical p-wave. Despite the differences in the pairing symmetry, each of these states is fully gapped with gap minimum centered above the normal state Fermi surface, in agreement with photoemission data of Y. Zhang et al. The analysis provides additional insights into the possible pairing mechanism for each of these states, highlighting the detrimental role of the renormalized repulsive intra-orbital Hubbard $U$ and inter-orbital $U'$ , and the beneficial role of the pair hopping $J'$ and the Hunds $J$ terms, as well as the spin-orbit coupling in the effective low-energy Hamiltonian.