Anharmonicity Driven by Vacancy Ordering Unlocks High-performance Thermoelectric Conversion in Defective Chalcopyrites II-III$_2$-VI$_4$

Defective chalcopyrites have recently emerged as promising thermoelectric materials because their ordered intrinsic vacancies can profoundly reshape both lattice dynamics and electronic structure. Here, we present a comprehensive theoretical investigation of the lattice thermal and carrier transport properties of II-III$_2$-VI$_4$ defective chalcopyrites by combining first-principles calculations with machine-learning interatomic potentials. We show that vacancy ordering enhances lattice distortion, leading to strong anharmonicity and metavalent bonding. The interplay of soft low-frequency phonons, strongly negative Gr\"uneisen parameters, and a substantially enlarged four-phonon scattering phase space results in four-phonon-scattering-dominated heat transport, yielding ultralow lattice thermal conductivity. Meanwhile, systematic anion substitution at the VI-site provides an effective route to tune the electronic structure: reduced anion electronegativity weakens metal-anion hybridization, shifts anion $p$ states upward, narrows the band gap, and thereby improves electrical transport. Benefiting from this synergy between vacancy-induced phonon suppression and anion-regulated electronic optimization, CdGa$_2$Te$_4$ exhibits an ultralow lattice thermal conductivity of 0.19 W$\cdot$m$^{-1}$K$^{-1}$ and a high room-temperature $ZT$ of 0.957. This work not only predicts defective chalcopyrites as a promising platform for high-performance thermoelectrics but also provides a practical design strategy by integrating vacancy ordering, higher-order phonon scattering, and anion-dependent band engineering.