Fig. 1. (Color online) (a) The optimized structure of CHPs with 325-type, they own the isostructural model with space group of Pnma, isolated [Cu₂X₅]^3– anion unit is composed of two types of Cu⁺ sites, a trigonal site and a tetragonal site. (b) Calculated phase stability regions versus μ_Cu and μ_X (referring to the chemical potential of Cu and X from that of their elementary substance) from left to right for the X site of I, Br, and Cl element and up to down for Cs and Rb element on A site, respectively. The cyan polygon region represents thermodynamic stability growth region, which is encircled by possible competing phases using colored line (red, blue, violet, and pink). A, Cu, and X atoms are in purple, coral and brown, respectively.

Fig. 2. (Color online) (a) The structure model of CHPs with 123-type, they all own octahedral structure with the space group of Cmcm (No. 63), composed of edge-sharing [CuX₄] tetrahedron 1D chain. (b) Calculated thermodynamic stability regions of ACu₂X₃ (A = Rb and Cs; X = Cl, Br, and I) CHPs versus μ_Cu and μ_X (deviation of actual chemical potential of Cu and X from that of their elementary substance). The above from left to right is the CHP for the X site of I, Br, and Cl element, and up to down is for Cs and Rb element on A site, respectively. The cyan polygon region represents thermodynamic stable interval, which is surrounded by competing phases using colored line (red, blue, orange, violet, and pink). A, Cu, and X atoms are in purple, coral and brown, respectively.

Fig. 3. (Color online) (a) The structure model of CHPs with 213-type, they possess isostructural model with Pnma symmetry, which is composed of 1D [Cu–X] tetrahedron chain with isolated alkali metal cation (Rb⁺ , Cs⁺ ). (b) Calculated phase stability regions in cyan polygon of A₂CuX₃ (A = Cs and Rb; X = I, Br, and Cl) CHPs versus μ_Cu and μ_X (deviation of actual chemical potential of Cu and X from that of their elementary substance). The cyan polygon region indicates thermodynamic phase stability growth interval, which is encompassed by competing phases with colored line (red, blue, and pink). A, Cu, and X atoms are in purple, coral and brown, respectively.

Fig. 4. (Color online) (a) The structure model of 459-type CHPs with space group of Pc, they own isolated [Cu₅X₉]^4– anion with three types of Cu⁺ ions, a tetrahedral site, a trigonal site and a 2-fold coordination site. (b) Calculated thermodynamic stability regions of 459-type CHPs against μ_Cu and μ_X (deviation of actual chemical potential of Cu and X from that of their elementary substance). The cyan polygon region reveals thermodynamic stable growth interval and each colored line corresponds to one most probable competing phase. A, Cu, and X atoms are in purple, coral and brown, respectively.

Fig. 5. (Color online) (a) The structure model of 214-type CHPs, most of them possess octahedral space group Pnma with isolated [Cu–X] tetrahedron. But for Rb₂CuCl₄, it owns Cmca symmetry with 2D [Cu₂Cl₄]^2– layers, induced by [Cu-Cl] octahedron Jahn-Teller distortion. (b) Calculated thermodynamic stability regions of A₂CuX₄ (A = Rb and Cs; X = Cl, Br, and I) halide perovskites versus μ_Cu and μ_X (deviation of actual chemical potential of Cu and X from that of their elementary substance). The horizontal and vertical axis is from I to Cl element and from Cs to Rb element, respectively. The cyan polygon region shows thermodynamic stability growth interval, which is encircled by most probable competing phases with colored lines (red, blue, violet, and pink). A, Cu, and X atoms are in purple, coral and brown, respectively.

Fig. 6. (Color online) (a) The structure model of 113-type CHPs, even though they possess different structures, they all have the same [CuX₆] octahedron unit via face- and corner-sharing. (b) Calculated thermodynamic stability regions of ACuX₃ (A = Rb and Cs; X = Cl, Br, and I) versus μ_Cu and μ_X (deviation of actual chemical potential of Cu and X from that of their elementary substance). The horizontal and vertical axis is from I to Cl element and from Cs to Rb element, respectively. The cyan polygon region represents thermodynamic stable growth interval, which is surrounded by most probable competing phases using colored line (red, blue, orange, violet, and pink). A, Cu, and X atoms are in purple, coral and brown, respectively.

Fig. 7. (Color online) (a) The structure model of 327-type CHPs, they all own tetragonal space group Ccca with isolated [Cu₂X₇]^3– anion composing of elongated [Cu–X] octahedron unit. (b) Calculated thermodynamic stability regions of 327-type CHPs versus μ_Cu and μ_X (deviation of actual chemical potential of Cu and X from that of their elementary substance). The cyan polygon region represents phase stability growth condition, which is encircled by competing phases using colored line (red, blue, violet, and pink). A, Cu, and X atoms are in purple, coral and brown, respectively.

Table 1. The Space group of existing CHPs with various types encompassing 325-, 123-, 213-, 459-, 214-, 113-, and 327-type from inorganic crystal structure database (ICSD). ‘√’ and blank grid symbol indicates the existing and non-existing phase in experiment, respectively.

Table 2. Calculated decomposition energies together with ODP in the CHPs A_lCu_mX_n (A = Rb and Cs; X = Cl, Br, and I; l, m, and n are integers).

Table 3. The relative energy per formula unit (eV/f.u.) of 214-type CHPs including Cs₂CuI₄, Rb₂CuI₄, and Rb₂CuBr₄ in the different space group encompassing Pnma and Cmca, which are all non-existing phase in the ICSD.

Table 4. The relative energy per formula unit (eV/f.u.) of 113-type CHP including CsCuI₃, RbCuI₃, and RbCuBr₃ in the different space group containing C2221, P6₁22, Pbcn, which are non-existing phase in the ICSD.

Table 5. Summary for the stability region and decomposition energy of ODP in the different type CHPs A_lB_mX_n (A = Rb and Cs; B = Cu; X = Cl, Br, and I; l, m, and n are integers; named as lmn-type). For each type CHP, number 1 and 2 represent decomposition energy and stability region, respectively. ‘√’ and ‘×’ symbols indicate ‘stable’ and ‘non-stable’ phase, respectively. Yellow square shows that this type is existing phase from inorganic Crystal Structure Database (ICSD).