Theoretical Prediction of Mixed-Valence Layered Halide Perovskites Cs₄M(IV)M(II)₂X₁₂(M = Ge, Sn; X = Cl, Br)

Charge-ordered compounds (i.e., Cu+/Cu2+, Au+/Au3+, In+/In3+, Tl+/Tl3+, Sb3+/Sb5+, and Bi3+/Bi5+) have been widely explored because of their unique physical properties. Here, a new class of 111-oriented mixed-valence layered halide perovskites Cs4M(IV)M(II)2X12 (M = Ge, Sn; X = Cl, Br) with C2/m, R-3m, and I41/amd space groups was predicted by first-principles calculations. Based on the decomposition enthalpy, the phonon spectrum, and the mechanical stability criteria, we found that Cs4GeGe2Cl12 (C2/m and R-3m), Cs4GeGe2Br12 (R-3m), and Cs4GeGe2Br6Cl6 (R-3m) exhibit thermodynamic, dynamical, and mechanical stability. The electronic structure calculations show that the predicted band gap of stable Cs4Ge(IV)Ge(II)2X12 varies from 1.16 to 2.25 eV. And an isolated intermediate conduction band contributed by the Ge(IV) 4s states below the Ge(II)/Ge(IV) 4p states is observed in these compounds, which is similar to previously reported Cs4CuSb2Cl12 but different from Cs4CdM(III)2Cl12 (M = Sb, Bi). In addition, the calculated static dielectric constant and optical absorption coefficient of Cs4GeGe2Br12 are close to those of typical double perovskites (e.g., Cs2AgBiBr6). We believe that our work enriches the family of mixed-valence halide perovskites and provides a new platform for potential optoelectronic semiconductor design.