Disentangling Mass-Energy Coupling to Reveal the Intrinsic Lattice Thermal Conductivity of Superionic Cu_2-xS

Strong mass-energy coupling and associated Soret/Dufour effects impede an accurate determination of the lattice thermal conductivity (κ_L) in superionic Cu-S systems. To extract the phononic κ_L under zero net ionic current, we employ a convective-invariant Schur complement framework combined with cepstral analysis. We find that in Cu_1.8S, the percolating vacancy network with confined segment dynamics guides and suppresses random hopping but promotes correlated directional diffusion, leading to lower Cu diffusivity than in Cu₂S despite a higher vacancy concentration. This correlated motion induces strong convective coupling and large nondiffusive energy-flux fluctuations, which cause conventional Green-Kubo estimates to diverge. The Schur complement scheme projects out the ionic flux, thereby isolating the phononic κ_L, whereas cepstral analysis supplies a robust frequency-domain estimator free from integration errors. Furthermore, we demonstrate that, in contrast to Cu₂S, the high-frequency optical phonons in Cu_1.8S are less susceptible to scattering and maintain stable dynamics under ion flow, while the transverse acoustic phonon branches in both compounds remain well-defined without melting in the superionic state. This work validates a reliable computational protocol for phononic thermal transport in superionic conductors and clarifies the distinct phonon and ion correlation effects in the Cu_2-xS system.