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 Sr_2RuO_4. Our theory is useful to correctly analyze the thermal conductivity in any near-nodal superconductor.