  Bogoliubov Fermi surfaces are contours of zero-energy excitations that are
protected in the superconducting state. Here we show that multiband
superconductors with dominant spin singlet, intraband pairing of spin-1/2
electrons can undergo a transition to a state with Bogoliubov Fermi surfaces if
spin-orbit coupling, interband pairing and time reversal symmetry breaking are
also present. These latter effects may be small, but drive the transition to
the topological state for appropriate nodal structure of the intra-band pair.
Such a state should display 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 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 ultranodal behavior may already have
been observed.
