Interaction-induced thermal conductivity of the unitary Fermi superfluids

In recent experimental investigations of unitary Fermi gases, it has been observed that the thermal conductivity $\ensuremath{\kappa}$ approaches the quantum limit under the phase transition temperature ${T}_{c}$. While relevant theoretical calculations have been conducted for this phenomenon, the interactions among particles within the heat current were neglected, violating conservation laws and revealing a significant disparity between computed results and experimental data. This paper addresses this issue by incorporating particle interactions within the heat current in Feynman diagrams, based on the Ward identity. We derive a modified Kubo-based expression for $\ensuremath{\kappa}$ that accounts for the interaction. We also consider the anomalous thermal conductivity from current transfer via Cooper pairs for the theory completeness. Our computations reveal that near ${T}_{c}$, the fluctuations in the $t$-matrix paradigm are characterized by the pseudogap order and bosonic excitations contribute significantly to $\ensuremath{\kappa}$, leading to a conspicuous peak in addition to the critical universal scaling laws. Our results align well with the experiment near ${T}_{c}$.