First-principles calculations of spin-split bands in chiral hybrid organic-inorganic perovskites ($R$/$S$-PEA)PbI$_3$ and ($R$/$S$-NEA)PbI$_3$

Abstract

Chiral hybrid organic-inorganic perovskites provide a promising platform for investigating the physics of chirality-driven spin-split bands because they combine robust molecular chirality with strong spin-orbit coupling from heavy inorganic ions. First-principles calculations including spin-orbit coupling are performed for the one-dimensional chiral perovskites ($R$/$S$-PEA)PbI$_3$ and ($R$/$S$-NEA)PbI$_3$ to compare their spin-split band structures and to identify the factors controlling their differences. In ($R$/$S$-PEA)PbI$_3$, the lowest conduction bands predominantly consist of Pb orbitals, whereas in ($R$/$S$-NEA)PbI$_3$, they are formed by hybridization between Pb orbitals and the lowest unoccupied molecular orbital of NEA. Both compounds exhibit pronounced spin splitting near the valence-band maximum and conduction-band minimum. The effective spin splitting of the edges of the valence bands is stronger in ($R$/$S$-NEA)PbI$_3$, despite similar linear-in-$k$ splitting coefficients near the relevant high-symmetry points. This enhancement originates from larger gaps induced by spin-orbit coupling at high-symmetry points and band (anti)crossings in the multiband structure. For a given molecular handedness, the PEA- and NEA-based compounds exhibit opposite spin textures, consistent with the opposite chiral distortions of the [PbI$_6$]$^{4-}$ octahedra and with the previously observed opposite signs of circular dichroism. Group-theoretical analysis for the nonsymmorphic space group $P2_12_12_1$ further accounts for band sticking, symmetry-enforced degeneracies, and the disappearance of spin polarization at specific Brillouin-zone-boundary points. These results provide a solid foundation for future studies of chirality-dependent electromagnetic responses, including circular dichroism, in chiral hybrid organic-inorganic perovskites.