Approaching the Limit of Intrinsic Crystalline Thermal Insulation

Crystalline materials with ultralow thermal conductivity ($\kappa$) are potential thermal barrier coatings or thermoelectrics, yet the discovery of ultralow-$\kappa$ materials remains inefficient due to the limitations of trial-and-error approaches. Herein, we propose a state-of-the-art high-throughput workflow that integrates universal machine learning interatomic potentials with high-fidelity phonon transport theories to accelerate the exploration of thermal insulators. Applying this approach, we identify dozens of crystalline materials with intrinsic room-temperature $\kappa$ values below 0.2 $\rm W m^{-1} K^{-1}$. Among them, we report and experimentally validate CsTlI$_4$, a record-breaking material with an ultralow $\kappa$ of 0.14 $\rm W m^{-1} K^{-1}$ at 300 K. Structural and bond analyses reveal that a hierarchical bonding framework, consisting of multi-coordinated Cs-I and antibonding Tl-I interactions, leads to weak chemical bonding and a soft lattice. These features reduce phonon group velocities, enhance phonon scattering, and induce strong vibrational mismatch between sublattices, collectively suppressing both particle-like phonon propagation and wave-like tunneling. Beyond this specific system, we establish physically interpretable descriptors based on interatomic force constants that correlate strongly with ultralow $\kappa$ and capture the role of bonding hierarchy and coordination environments in governing thermal transport. This work demonstrates a robust data-driven strategy for accelerating the discovery of thermal insulators and provides microscopic insight into how hierarchical bonding and strong anharmonicity cooperate to impede heat-carrying vibrations.