Ordered crystalline compounds exhibiting ultralow and glasslike thermal conductivity are both fundamentally and technologically important, where phonon quasiparticles dominate their heat transport. Understanding the microscopic mechanisms that govern such unusual transport behavior is necessary to unravel the complex interplay of crystal structure, phonons, and collective excitations of these quasiparticles. Here, we use state-of-the-art first-principles calculations based on quantum density functional theory to investigate the origin of experimentally measured unusually low and glassy thermal conductivity in semiconducting TlAgTe that possesses disconnected chains of Tl atoms within its three-dimensional crystalline framework made up of distorted ${\mathrm{AgTe}}_4$ tetrahedra. Utilizing a unifying framework of anharmonic lattice dynamics theory that combine phonon self-energy induced frequency renormalization, particlelike Peierls (${\kappa }_l^P$), and wavelike coherent (${\kappa }_l^C$) thermal transport contributions, including three- and four-phonon scattering channels, we successfully explain the experimental results both in terms of magnitude and temperature dependence. Our analysis reveals that TlAgTe exhibits several localized phonon modes arising from concerted rattlinglike vibrations of Tl and Ag atoms, which show strong temperature dependence and enhanced four-phonon scattering rates that are dominated by Umklapp processes, suppressing ${\kappa }_l^P$ to ultralow values. The ensuing strong anharmonicity induced by local structural distortions, lone-pair electrons, and rattlinglike vibrations of the cations lead to a transition from particlelike behavior to wavelike tunneling (i.e., coherent) characteristics of the phonon modes above 40 ${\text{cm}}^{-1}$, contributing significantly to ${\kappa }_l^C$, which increases with temperature. Our analysis uncovers an important structure-property relationship, which may be used in designing materials with tunable thermal conductivity.

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• Anharmonic lattice dynamics
• Lattice thermal conductivity
• Phonons
• Ordered compounds
• Semiconductors
• Boltzmann theory
• First-principles calculations