Two-dimensional ferroelectric crystal with temperature-invariant ultralow thermal conductivity

We report the discovery of temperature-invariant ultralow thermal conductivity ($\kappa$) in monolayer $\beta'$-In$_2$Se$_3$, a two-dimensional ferroelectric crystal with in-plane polarization. Using a combination of generalized Wigner transport equation theory and machine-learning-assisted molecular dynamics simulations, we reveal that the balance between particle-like phonon propagating and wave-like tunneling transport mechanisms results in a propagating-tunneling-invariant (PTI) ultralow thermal conductivity of approximately 0.6 W/mK (comparable to that of glass) over a broad temperature range ($150<T<800$~K). This behavior stems from intrinsic strong lattice anharmonicity driven by ferroelectric dipolar fluctuations, eliminating the need for extrinsic structural modifications. In contrast, the $\alpha$-In$_2$Se$_3$~monolayer, which shares the same stoichiometry, exhibits a conventional temperature-dependent thermal conductivity, $\kappa (T) \propto T^{-1}$, typical of simple crystals. Furthermore, we demonstrate that the anharmonicity in $\beta'$-In$_2$Se$_3$~can be precisely modulated by an external electric field, enabling on-demand control of thermal transport properties, including modifying the temperature scaling behavior of heat conductivity and achieving a large thermal switching ratio of $\approx$2.5. These findings provide fundamental insights into the interplay between field-tunable lattice anharmonicity, phonon dynamics, and thermal transport mechanisms.