Efficient Cross-layer Thermal Transport with Atypical Glassy-like Phenomena 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 rates 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 anharmonic scattering induced by Cu- and Cs-dominated phonon modes plays a non-negligible role in suppressing particle-like propagation. 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 effective thermal transport across layers, sharply contrasting with traditional layered materials. As a result, the non-monotonic temperature dependence of coherences' thermal conductivity results from the combined effects of anharmonic scattering rates and anharmonic phonon renormalization. Our work not only reveals the significant contributions from the off-diagonal terms of heat flux operators in crystalline CsCu$_4$Se$_3$, but also explains the non-monotonic relationship between wave-like thermal conductivity and anharmonic scattering, providing insights into the microscopic mechanisms driving anomalous heat transport.