κ = κ E + κ L ). However, S, ρ, and κ E are strongly coupled with each other, leading a net enhancement in zT to be difficult.Recently, band engineering approaches, such as band convergence [1,2] or nestification, [3] have been found to decouple these parameters at some degree for an enhancement in power factor by increasing band degeneracy (N v ). These have been demonstrated in various materials, such as PbTe, [1,4,5] SnTe, [6,7] GeTe, [8] Mg 2 Si, [9] half-Heusler, [10,11] Te, [3] and significant enhancements in zT have been achieved. Alternatively, reducing lattice thermal conductivity, the only one independent parameter determining the thermoelectric performance, has also found to be effective for enhancing zT. Successful approaches include nanostructuring, [12] rattling impurities, [13] lattice anharmonicity, [14,15] dislocations, [16] and point defects (substitutions, [17] vacancy, [18] and interstitials [7,19] ).In addition to advancing known thermoelectrics by the strategies mentioned above, numerous efforts have also been focused on exploration of new thermoelectric materials. These materials are typified by β-Zn 4 Sb 3 , [20] Cu 2 Se, [21] and Cu 2 S, [22] SnSe, [14] CsAg 5 Te 3 . [23] The commonness shared among these promising thermoelectrics is their inherently low lattice thermal conductivity, which can result from various mechanisms such as low sound velocity, [24] complex crystal structure, [20,25] liquid-like ions, [20,21,26,27] and lattice anharmonicity. [14] These works clearly indicate the importance of an intrinsically low lattice thermal conductivity for exploring new thermoelectrics.Lattice thermal conductivity (κ L ) is determined by phonon dispersion and the scattering of phonons. [28] As an inherent scattering for all crystalline solids, Umklapp processes usually dominate in the working temperature range of thermoelectrics. It is known that the strength of such a scattering, characterized by the Grüneisen parameter, does not vary by a factor of 3 for known materials. [29,30] This would lead a difference on κ L due to inherent Umklapp to be limited within an order of magnitude. However, known crystalline materials show intrinsic lattice thermal conductivities spanning within orders of magnitude. [31,32] This implies that the biggest availability for manipulating the lattice thermal conductivity relies on the phonon dispersion.Materials with simple crystal structures, such as pure elements, usually show extremely high inherent lattice thermal conductivity (≈3000 W m −1 K −1 at 300 K for diamond). [32] This is due to: (1) the Recent discoveries of novel thermoelectric materials largely rely on an intrinsic low lattice thermal conductivity. This results from various mechanisms including low sound velocity, complex crystal structure, liquid-like ions, and lattice anharmonicity. Here semiconducting Ag 9 AlSe 6 with many weakly bonded and highly disordered cations is shown to be a promising novel thermoelectric material, due to its ultralow lattice thermal conductivity (κ L ) of ≈0.3 W m ...