Metavalent Bonding-Induced Phonon Hardening and Giant Anharmonicity in BeO

The search for materials with intrinsically low thermal conductivity ($\kappa_L$) is critical for energy applications, yet conventional descriptors often fail to capture the complex interplay between bonding and lattice dynamics. Here, first-principles calculations are used to contrast the thermal transport in covalent zincblende (zb) and metavalent rocksalt (rs) BeO. We find that the metavalent bonding in rs-BeO enhances lattice anharmonicity, activating multi-phonon scattering channels and suppressing phonon transport. This results in an ultralow $\kappa_L$ of 24 W m$^{-1}$ K$^{-1}$ at 300 K, starkly contrasting with the zb phase (357 W m$^{-1}$ K$^{-1}$). Accurately modeling such strongly anharmonic systems requires explicit inclusion of temperature-dependent phonon renormalization and four-phonon scattering. These contributions, negligible in zb-BeO, are essential for high-precision calculations of the severely suppressed $\kappa_L$ in rs-BeO. Finally, we identify three key indicators to guide the discovery of metavalently bonded, incipient-metallic materials: (i) an NaCl-type crystal structure, (ii) large Gr\"uneisen parameters ($\textgreater$2), and (iii) a breakdown of the Lyddane-Sachs-Teller relation. These findings provide microscopic insight into thermal transport suppression by metavalent bonding and offer a predictive framework for identifying promising thermoelectrics and phase-change materials.