Dynamic disordering in discrete states: Disconnected hopping boosts anharmonicity in CuInP₂S₆

Delineation of matter into solid and fluid (liquid and gas) phases is grounded in the contrasting localization and mobility of atomic/molecular aggregates, with the fluid phase distinguished by connected pathways for these entities. Here, we demonstrate that CuInP₂S₆, a layered material, manifests as a unique system differing from both solid and fluid: It is solid but contains disconnected pathways of highly mobile Cu species. Each pathway comprises two main docking sites, facilitating rapid intersite hopping of Cu that disrupts lattice waves of the immobilized sulfur sublattice, thereby inducing strong phonon anharmonicity. The Cu⁺ ions, ordered at low temperatures, become highly activated and dynamically disordered even at room temperature. This suppresses the virial contribution, a dominant heat conduction mechanism in conventional solids, while inducing a moderate liquid-like convective mode of heat transfer. Identifying analogous systems featuring disconnected pathways and dynamical disordering states offers a promising route for increased anharmonicity.