We investigate the lattice thermal-transport properties of intercalation compounds $X\mathrm{Nb}{Y}_2$ ($X=\mathrm{Li}$, $\mathrm{Na}$; $Y$ = $\mathrm{S}$, $\mathrm{Se}$) using the unified theory of thermal transport. The calculations reveal that soft optical phonons exhibit strong hybridization with acoustic branches, leading to a non-negligible contribution to the lattice thermal conductivity. Our results suggest that the stereochemically active lone-pair electrons on the chalcogen atoms enhance the anharmonic phonon-phonon interactions, leading to a reduction in the thermal conductivity. The weak coupling of interlayer vibrational modes, particularly along the out-of-plane direction, results in negligible wavelike tunneling phonon transport at room temperature. However, its strong temperature dependence highlights a growing contribution of coherent phonon transport at elevated temperatures. Simultaneously, the intercalation of alkali-metal atoms enhances interlayer interactions, leading to more collective atomic vibrations and promoting particlelike phonon transport. While this transition facilitates more efficient thermal conduction across layers, it partially counteracts the intended suppression of lattice thermal conductivity, thereby compromising thermoelectric optimization in the out-of-plane direction. On the electronic side, a multivalley band structure near the Fermi level enhances the power factor via improved carrier scattering phase space, while the introduction of alkali-metal layers reduces electrical-conductivity anisotropy. These combined effects yield a maximum thermoelectric figure of merit $Z_T\approx 2.9$ at 700 K.

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• Anharmonic lattice dynamics
• Lattice thermal conductivity
• Phonons
• Valley degrees of freedom
• Thermoelectrics
• Transition metal dichalcogenides
• Boltzmann theory
• Density functional calculations