Lone-Pair-Induced Lattice Softness Enables Ultralow Thermal Conductivity in Hybrid Organic-Inorganic Perovskite GuaPbI$_3$
Thermal conductivity ($κ$) minimization of inorganic thermoelectrics can only be achieved to a certain extent via nanostructural engineering. Here, we introduce a lone-pair-driven materials design strategy based on chemically induced lattice softness to develop hybrid organic-inorganic perovskites with ultra-low $κ$. A physics-guided symbolic-regression machine-learning framework identifies a lone-pair-dominated compositional regime statistically associated with suppressed lattice $κ$ and selects $\text{GuaPbI}_3$ as a candidate material. Mechanochemical synthesis yields $\text{GuaPbI}_3$ with an ultra-low room-temperature $κ\approx 0.088\text{ W m}^{-1}\text{ K}^{-1}$. Electrical measurements reveal electronically active, bias-dependent bulk conduction pathways despite strong phonon suppression, while impedance spectroscopy confirms predominantly bulk-dominated transport. Density functional theory calculations indicate weakly dispersive valence bands, pronounced valence-conduction asymmetry, and localized electrostatic microenvironments arising from lattice charge redistribution. Calculated transport coefficients suggest strong sensitivity of carrier transport to chemical potential, while Lorenz-number analysis reveals deviations from conventional Wiedemann-Franz behavior near band edges. These observations indicate that lone-pair-rich hybrid frameworks generate intrinsically soft and electronically heterogeneous lattice environments capable of strongly suppressing phonon transport while preserving electronically accessible states. This work establishes chemically induced lattice softness as a viable design principle for identifying ultralow-thermal-conductivity hybrid materials without relying on nanostructuring or extrinsic disorder engineering.