Bi and Te impurity manifolds in Cs₂ZrCl₆: Spin-polarized meta-GGA and band-unfolding insights into dual-color emission

Lead-free vacancy-ordered double perovskites A₂BX₆ have emerged as robust platforms for self-trapped exciton (STE) emission and activator doping. Among them, Cs₂ZrCl₆ is particularly attractive due to its wide bandgap, chemical stability, and electronically zero-dimensional [ZrCl₆] clusters. Here, we use spin-polarized first-principles density functional theory (DFT) to elucidate how Bi³⁺ and Te⁴⁺ dopants modify the electronic structure and optical response of Cs₂ZrCl₆, thereby clarifying the microscopic origin of the experimentally observed blue (Bi), yellow (Te), and dual-color emission in Bi/Te co-doped compositions. Structural relaxations of 2×2×2 supercells within the generalized gradient approximation using the Perdew–Burke–Ernzerhof functional revised for solids (GGA–PBEsol) show that Bi and Te substitution at the Zr site preserves the vacancy-ordered Cs₂ZrCl₆ framework. Subsequent electronic-structure calculations using the modified Becke–Johnson potential with local-density-approximation correlation (MBJ-LDA) yield a bandgap of ~4.5 eV, with band edges dominated by Cl-3p states at the valence-band maximum (VBM) and Zr-4d states at the conduction-band minimum (CBM). Octahedron-projected unfolded band structures and orbital-resolved densities of states reveal narrow impurity manifolds within the gap: a spin-polarized Bi-6p/Cl-3p band carrying a ~1 μ B moment localized on a [BiCl₆] cluster and its coordinating Cl ligands, and a spin-degenerate Te-5p/Cl-3p band associated with non-magnetic [TeCl₆] octahedra. CCD and ELF analyses reveal enhanced Bi–Cl and Te–Cl covalency, confirming these octahedra as deep, localized trap centers. Calculated dielectric functions and derived optical constants display a pronounced sub-gap absorption band at 3.4–3.6 eV, weak for Bi-only, strong for Te-only, and maximal for Bi/Te co-doping. In contrast, the host absorption edge and static optical constants remain nearly unchanged. We propose that these localized impurity manifolds provide electronic precursors for dopant-centered STE formation. Although the present study employs ground-state DFT, the strong localization, enhanced dopant–ligand covalency, and narrow impurity bandwidth are characteristic features commonly associated with STE behavior in related systems. The combined band-unfolding, local-bonding, and optical-response analysis establishes design principles for engineering multiple emissive centers in ns²-doped A₂BX₆ perovskites toward composition-tunable, lead-free phosphors. Spin-polarized DFT reveals that Bi³⁺ and Te⁴⁺ dopants in Cs₂ZrCl₆ create distinct impurity manifolds—Bi magnetic, Te non-magnetic—inside a wide bandgap. These localized [BiCl₆]/[TeCl₆] centers give rise to mid-gap optical absorption and enable blue (Bi), yellow (Te), and dual-color emission in Bi/Te co-doped Cs₂ZrCl₆. • Spin‐polarized DFT (GGA-PBEsol + MBJ-LDA) on pristine and Bi/Te-doped Cs₂ZrCl₆ • Bi³⁺ creates spin-polarized in-gap states; Te⁴⁺ yields spin-degenerate impurity levels • Band unfolding + PDOS identify Bi/Te impurity manifolds without changing host band edges • CDD and ELF reveal strongly localized BiCl₆ / TeCl₆ centers with distinct bonding patterns • Calculated optical spectra link Bi and Te impurity states to blue, yellow, and dual-color emission