Microscopic origin of ultranodal superconducting states in spin-1/2 systems

Several unconventional superconductors show indications of zero-energy excitations in the superconducting state consistent with the existence of a so-called Bogoliubov Fermi surface (BFS). In particular, FeSe doped with S seems to acquire a nonzero density of states at zero energy at low temperatures when doped into the tetragonal phase, consistent with a previously proposed phenomenological theory assuming an anisotropic spin singlet pairing gap coexisting with a nonunitary interband triplet component. Here we search for a microscopic model that can support the coexistence of singlet pairing with other orders, including interband nonunitary triplet pairing, and discuss several candidates that indeed stabilize ground states with Bogoliubov Fermi surfaces. We show that with proper choice of the coupling strength of the various orders in our model, spontaneous breaking of $C_4$ rotational symmetry is realized at low temperatures, in accordance with recent angle-resolved photoemission experiments in Fe(Se,S) in the tetragonal phase.