Anharmonicity driven unusual particle-to-wave-like phonon crossover leads to ultralow thermal conductivity in Tl ₂ AgI ₃

Realization of unusual particle-to-wave-like crossover in phonon transport and understanding its fundamental structural origin can guide the design of materials with ultralow thermal conductivity. Here, we report such a crossover from particle-like phonon propagation to wave-like coherence with increasing temperature in the zero-dimensional (0D) metal halide, Tl₂AgI₃. Composed of discrete (Tl₆I)⁵⁺ and (Ag₃I₈)^5- subunits, the structure exhibits intrinsic lattice instability governed by Pauling's third rule where face-sharing of polyhedra drives Coulombic cationic repulsion causing local distortion of Ag atoms, as confirmed by synchrotron X-ray pair distribution function (X-PDF) analysis and ab initio molecular dynamics (AIMD) simulations. Anharmonic low-energy rattling of Tl is evidenced within the (Tl₆I)⁵⁺ framework. These structural disorders generate low-frequency localized and anharmonic optical phonons that hybridize with acoustic branches, strongly suppressing lattice thermal conductivity ([Formula: see text]). Consequently, [Formula: see text] drops to ~0.18 W/m.K at 125 K and remains nearly temperature independent, signaling a breakdown of the phonon-gas model, attributed to phonon localization and wave-like coherence, modeled using the linearized Wigner transport equation (LWTE). The phonon localization in the 0D crystal structure results in a crossover from populations conductivity ([Formula: see text]) associated with particle-like phonon propagation to coherence conductivity ([Formula: see text]) through wave-like tunneling, at 175 K. Our study reveals 0D structural confinement along with anharmonic local structural dynamics can enable particle-to-wave-like phonon crossover, establishing a pathway to mixed phononic regimes and suppressed thermal transport.