Robust accidental nodes and zeroes and critical quasiparticle scaling in iron-based multiband superconductors

We study multigap superconductivity, with strong angular variations of one of the gaps, as appropriate for certain iron-based high-temperature superconductors. We solve the gap equations of this model and find that the nodes or zeroes in the gap function present at Tc - although purely accidental -- typically survive down to T=0. Based on this result, we investigate the line of quantum transitions at which gap zeroes first appear. The peculiar "zero-point" critical scaling emanating from this line dominates quasiparticle thermodynamics and transport properties over much of the phase diagram, and supplants more familiar forms of scaling associated with accidental nodes.