Ultranodal pair states in iron-based superconductors.

We show that multiband superconductors with dominant spin singlet, intraband pairing of spin-1/2 electrons can undergo a transition to a state with Bogolibuov Fermi surfaces -- surfaces of zero energy excitations that are topologically protected in the superconducting state -- if spin-orbit coupling, interband pairing and time reversal symmetry breaking are also present. These latter effects may be quite small, but still drive the transition to the topological state if the nodal structure of the intraband pairing is appropriate. Such a state should display a nonzero zero-bias density of states and corresponding residual Sommerfeld coefficient as for a disordered nodal superconductor, but occurring even in the pure case. We present a model appropriate for iron-based superconductors where the topological transition associated with the creation of a Bogoliubov Fermi surface can be studied. The model gives results that strongly resemble experiments on FeSe$_{1-x}$S$_x$ across the nematic transition, where this ``ultranodalu0027u0027 behavior may already have been observed.