Two-fold rotational symmetric Bogoliubov Fermi surface in tetragonal Fe(Se,S*

The intriguing iron based superconductor FeSe exhibits rich phenomena at low temperatures upon chemical pressure, including time reversal symmetry breaking, nematic criticality and topological phases. For sufficiently large S-substitution, the system recovers C4 symmetry in its normal state, and at the same time acquires a nonzero density of states at zero energy at zero temperature in its superconducting state, consistent with the existence of a so-called Bogoliubov Fermi surface (BFS). Recent angle-resolved photoemission (ARPES) experiments has found more direct evidence for BFSs in such materials, but despite the tetragonal normal state, the BFSs seems to be curiously only two-fold symmetric. In this work we search for a microscopic model that can support the coexistence of singlet pairing with other orders, including interband nonunitary triplet pairing with magnetization, and discuss several candidates that indeed stabilize ground states with BFSs. We show that with proper choice of the coupling strength of the various orders in our model, spontaneous breaking of  C4 rotational symmetry is realized at low temperatures. This feature resembles the findings of recent ARPES experiments.