Disentangling Mass-Energy Coupling to Reveal the Intrinsic Lattice Thermal Conductivity of Superionic Cu2-xS.

Strong mass-energy coupling and associated Soret/Dufour effects impede an accurate determination of the lattice thermal conductivity (κL) in superionic Cu-S systems. To extract the phononic κL under zero net ionic current, we employ a convective-invariant Schur complement framework combined with cepstral analysis. We find that in Cu1.8S, 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 κL, 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 Cu1.8S 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 Cu2-xS system.