Thermal conductivity in near-nodal superconductors

The universal behavior of thermal conductivity at low temperatures is usually taken as the signature of gap nodes in superconductors. Here we show that in near-nodal superconductors the thermal conductivity obeys a two-parameter scaling law, and can develop super-universal behavior if the temperature is about half the gap minimum. However, when the temperature is fixed at about one quarter of the gap minimum, the thermal conductivity can develop a dip versus the scattering rate, which is in excellent agreement with the behavior of the experimental thermal conductivity in Sr2RuO4. Our theory is useful to correctly analyze the thermal conductivity in any near-nodal superconductor.