  In the family of iron-based superconductors, LaFeAsO-type materials possess
the simplest electronic structure due to their pronounced two-dimensionality.
And yet they host superconductivity with the highest transition temperature
Tc=55K. Early theoretical predictions of their electronic structure revealed
multiple large circular portions of the Fermi surface with a very good
geometrical overlap (nesting), believed to enhance the pairing interaction and
thus superconductivity. The prevalence of such large circular features in the
Fermi surface has since been associated with many other iron-based compounds
and has grown to be generally accepted in the field. In this work we show that
a prototypical compound of the 1111-type, SmFe0.92Co0.08AsO, is at odds with
this description and possesses a distinctly different Fermi surface, which
consists of two singular constructs formed by the edges of several bands,
pulled to the Fermi level from the depths of the theoretically predicted band
structure by strong electronic interactions. Such singularities dramatically
affect the low-energy electronic properties of the material, including
superconductivity. We further argue that occurrence of these singularities
correlates with the maximum superconducting transition temperature attainable
in each material class over the entire family of iron-based superconductors.
