Fig. 3: Spin-splitting in chiral MHPs.

a A representative unit cell of a relaxed MHP (organic cations are omitted) and (b) the corresponding Brillouin zone in the reciprocal space used for band structure calculations. c Schematic representation of spin-polarized subbands separated in k-space along one dimension of a Rashba or Dresselhaus semiconductor. The ↑ and ↓ arrows denote, respectively, +1/2 and −1/2 like spin character. \({E}^{-}\) and \({E}^{+}\) denote the two spin subbands, and \(\Delta {E}^{\pm }\) denotes the energy difference between them at a characteristic momentum offset, \({{{{{{\bf{k}}}}}}}_{0}\). d–i DFT-PBE+SOC band structures of chiral [S-4-NO₂-MBA]₂PbBr₄⋅H₂O (d), [R-4-Cl-MBA]₂PbBr₄ (e), [S-2-Me-BuA]₂PbBr₄ (f), [S-4-NH₃-MBA]PbI₄ (g), [R-4-Cl-MBA]₂PbI₄ (h), and [S-MHA]₂PbI₄ (i) along select k-paths. Relaxed atomic geometries were used for band structure calculations. Pb-, Br-, I- and organic-derived electronic states are highlighted in purple, green, yellow, and black colors, respectively. Note that the focus of these plots is the degree of SOC near the inorganic-derived conduction band edges, not the alignment of energy levels or the exact fundamental gap.