Robust accidental nodes and zeros 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 zeros in the gap function present at T-c-although purely accidental-typically survive down to T = 0. Based on this result, we investigate the line of quantum transitions at which gap zeros first appear. The peculiar zero-point quantum 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 the accidental nodes.