Scaling of nascent nodes in extended s-wave superconductors

We analyze the low-energy properties of superconductors near the onset of accidental nodes, i.e. zeroes of the gap function not enforced by symmetry. The existence of such nodes has been motivated by recent experiments suggesting a transition between nodeless and nodal superconductivity in iron-based compounds. We find that the low-temperature behavior of the penetration depth, the specific heat, and the NMR spin-lattice relaxation rate are determined by the scaling properties of a quantum critical point associated with the nascent nodes. Although the power-law exponents are insensitive to weak short-range electronic interactions, they can be significantly altered by the curvature of the Fermi surface or by the three-dimensional character of the gap. Consequently, the behavior of macroscopic quantities near the onset of nodes can be used as a criterion to determine the nodal structure of the gap function.