Anharmonic phonon dynamics and the origin of ultralow lattice thermal conductivity in CuBiI₄: Implications for thermoelectric applications

Phonon quasiparticles and their anharmonic interactions govern heat transport in insulators. Accurate characterization of phonon frequencies and linewidths, especially beyond the quasiparticle approximation, is essential for understanding anharmonic effects and lattice thermal conductivity. Here, we investigate the anharmonic lattice dynamics and phonon transport in crystalline copper halides CuBiI₄ using the self-consistent phonon (SCPH) theory, combined with the Wigner transport formalism and the quasi-harmonic Green-Kubo method (QHGK). Results show that the three-phonon bubble self-energy substantially renormalizes the phonon dispersion, inducing strong mode-dependent broadening. Depending on strength of the anharmonic scattering, phonons exhibit particlelike, wavelike, or overdamped transport characteristics, with broadened states contributing additional coherent thermal transport channels. We establish a consistent description of the overdamped phonon self-energy and advance the microscopic understanding of the strongly anharmonic phonon thermal transport in CuBiI₄. Overdamped phonon modes significantly hinder the lattice thermal transport by reducing phonon lifetimes. However, the still well-defined phonon dispersions mitigate carrier scattering induced by the local structural disorder. Anisotropic electrical transport properties are obtained by considering polar and non-polar electroacoustic coupling and ionized impurity scattering mechanisms. Upon electron doping, the thermoelectric figure of merit of n-type CuBiI₄ reaches 2.25 at 800 K.