Strong anharmonicity driven wave-like thermal transport and high thermoelectric performance in TlCu₅Se₃

Thermal transport in crystalline solids generally occurs via particle-like phonon propagation. Here, we demonstrate the dominant unusual wave-like phonon transport and high thermoelectric figure-of-merit (zT) of ∼1.42 at 673 K in crystalline TlCu₅Se₃ due to the strong anharmonicity exerted by confined Cu dynamic disorder and Tl rattling. TlCu₅Se₃ shows an intrinsic ultralow lattice thermal conductivity of (κ_L) 0.3-0.2 W m^-1 K^-1 across the temperature range of 294-673 K. Density functional theory calculations and ab-initio molecular dynamics simulations reveal that strong lattice anharmonicity arises due to confined dynamic disorder of the Cu sublattice. The complex knot-like structure with strong anharmonicity reduces phonon lifetime below the Wigner limit, leading to substantial inter-band phonon coupling and a dominant wave-like coherence. By further tuning cationic vacancies to optimize electrical transport, we achieve an enhanced zT of ∼1.7 at 673 K in TlCu_5-xSe₃ (x = 0.03-0.07), demonstrating that confined ion dynamics not only maintains ultralow κ_L but also enhances thermoelectric performance without compromising the stability.