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We study multigap superconductivity, with strong angular variations of one ofthe gaps, as appropriate for certain iron-based high-temperaturesuperconductors. We solve the gap equations of this model and find that thenodes 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 lineof quantum transitions at which gap zeroes first appear. The peculiar"zero-point" critical scaling emanating from this line dominates quasiparticlethermodynamics and transport properties over much of the phase diagram, andsupplants more familiar forms of scaling associated with accidental nodes.

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