Fig. 3: RD spin-splitting in chiral NPB.
a Schematic representation of a two-fold spin-degenerate electronic band in a conventional semiconductor. b, c Spin-polarized sub-bands (red: down spin; blue: up spin) separated in k-space due to the SOC and inversion asymmetry along one dimension of an RD semiconductor. \(E^ +\) and \(E^ -\) denote the inner and outer spin-polarized branches created by the RD spin-splitting. ∆E denotes the energy difference between the two branches at the characteristic momentum (k0), and \(E_{{\mathrm{RD}}}\) is the characteristic RD energy. d A representative unit cell of the relaxed S-NPB structure in real space and e, its Brillouin zone showing the k-path in reciprocal space used for band plotting in f–h. For the theoretical structures, cell axes were chosen to be consistent for racemic, R- and S-NPB such that the stacking direction is always along the a-direction, and the inorganic layers are parallel to the b–c plane. f–h, The computed DFT+HSE06 electronic band structures of f racemic-NPB, g S-NPB, and h R-NPB shown along selected k-paths. The atomic contributions to the electronic continuum bands are identified for Pb (magenta), Br (green), and organic-derived (black) states. The two-fold spin-degenerate lowest conduction band in f racemic-NPB splits into upper and lower branches in both g S-NPB and h R-NPB mainly along the Γ–Z direction of reciprocal space due to inversion asymmetry in the [PbBr4]2− perovskite layers of S-NPB and R-NPB. Full band structures of R-, S-, and racemic-NPB for all the k-paths are presented in Supplementary Fig. 13.
