High-order Anharmonic Scattering and Wide-Temperature-Range Glassy Thermal Transport in Crystalline CsCu$_4$Se$_3$

Understanding lattice dynamics and thermal transport in crystalline compounds with intrinsically low lattice thermal conductivity ($\kappa_L$) is crucial in condensed matter physics. In this work, we investigate the lattice thermal conductivity of crystalline CsCu$_4$Se$_3$ by coupling first-principles anharmonic lattice dynamics with a unified theory of thermal transport. We consider the effects of both cubic and quartic anharmonicity on phonon scattering and energy shifts, as well as the diagonal and off-diagonal terms of heat flux operators. Our results reveal that the vibrational properties of CsCu$_4$Se$_3$ are characterized by strong anharmonicity and wave-like phonon tunneling. In particular, the strong three- and four-phonon scattering induced by Cu atoms significantly suppresses particle-like propagation while enhancing wave-like tunneling. Moreover, the coherence-driven conductivity dominates the total thermal conductivity along the $z$-axis, leading to an anomalous, wide-temperature-range (100-700 K) glassy-like thermal transport. Importantly, the significant coherence contribution, resulting from the coupling of distinct vibrational eigenstates, facilitates efficient thermal transport across layers, sharply contrasting with traditional layered materials. Finally, we established a criterion linking anharmonic scattering to the frequency differences between eigenstates, which effectively explains the non-monotonic temperature dependence of coherence thermal conductivity. Our work not only reveals the impact of higher-order anharmonic self-energies in crystalline CsCu$_4$Se$_3$, but also examines the dynamic evolution of wave-like thermal conductivity, providing insights into the microscopic mechanisms driving anomalous heat transport.