Layered hybrid organic–inorganic perovskites (HOIPs) with chiral organic ligands exhibit strong natural optical activity (NOA) including circular dichroism (CD) and circularly polarized luminescence around the perovskites’ exciton levels, promising novel spintronic and optoelectronic applications. Macroscopically, NOA in a chiral material is characterized by different refractive indices for left and right circularly polarized light or equivalently, a first-order spatial dispersion effect with dielectric function \(\epsilon (\omega , {\varvec{q}})\) depending on wavevector \({\varvec{q}}\) . The Kubo formula, which connects the dielectric function with microscopic electronic states, can be used to systematically evaluate NOA and identify its microscopic origin. Since a chiral 2D HOIP is a crystalline solid and its exciton states are extended Bloch waves rather than localized levels as in molecular aggregates or solutions, a microscopic description of its NOA must adequately take into account the exciton band structure, which contains a term linear with exciton’s momentum \(K_z\) along the helical axis, \(\alpha _c \tau K_z j_z\) with \(\alpha _c\) , \(\tau\) ( \(=\pm 1\) ), and \(j_z\) ( \(=\pm 1\) ) being the chirality-induced spin–orbit coupling, helicity, and exciton spin polarization. The exciton’s band dispersion in 2D HOIPs along the helical axis is strong due to the long-range dipolar coupling between excitons in adjacent layers, even though the conduction and valence bands are flat. Through the Kubo formula we are able to discern contributions from the exciton band structure and from molecular mixed electrical-magnetic dipole transitions, which can have distinct signatures in NOA spectra and would also result in disparate magnetic CD behaviors. These features can help reveal the origin of NOA in individual chiral HOIPs and tailor them for novel applications.
Graphical abstract
