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Recent thermal conductivity measurements on $\mathrm{Sr_2 Ru O_4}$ [E.Hassinger et al., Phys. Rev. X 7, 011032 (2017)] were interpreted as favoring apairing gap function with vertical line nodes while conflicting with chiral$p$-wave pairing. Motivated by this work we study the effects of deepsuperconducting gap minima on impurity induced quasiparticle thermal transportin chiral $p$-wave models of $\mathrm{Sr_2 Ru O_4}$. Combining aself-consistent T-matrix analysis and self-consistent Bogoliubov-de-Gennescalculations, we show that the dependence of the residual thermal conductivityon the normal state impurity scattering rate can be quite similar to the$d$-wave pairing state that was shown to fit the thermal conductivitymeasurements, provided the normal state impurity scattering rate is largecompared with the deep gap minima. Consequently, thermal conductivitymeasurements on $\mathrm{Sr_2RuO_4}$ can be reconciled with a chiral $p$-wavepairing state with deep gap minima. However, the data impose seriousconstraints on such models and these constraints are examined in the context ofseveral different chiral $p$-wave models.

Effects of deep superconducting gap minima and disorder on residual thermal transport in $\mathrm{Sr_2 Ru O_4}$