Bright-Exciton Splittings in Inorganic Cesium Lead Halide Perovskite Nanocrystals

Since their first synthesis in 2015, the all-inorganic lead halide perovskite nanocrystals Cs_{Pb X 3}(X =Cl ,Br ,I ) have attracted a great deal of attention due to their outstanding electronic and optical properties as well as their performances, which outclass the ones of their II-VI conterparts in many application fields. In addition to these properties, the understanding of the emission features in these systems at the single object scale is crucial, e.g., for nanophotonics and quantum optics devices. Here, the details of the band-edge excitonic emission are theoretically explored. The contribution of the long-range exchange interaction to the bright-exciton splittings is computed in strong and weak confinement regimes using group theory arguments and kṡp approximation. We show that the shape anisotropy with the real crystalline (cubic, tetragonal, or orthorhombic) structures of nanocrystals explain well their emission properties. In the weak confinement regime, splittings are inversely proportional to the cube of the exciton Bohr radius and we observe an increase of the splittings from iodide, to bromide, and then to chloride perovskite compounds. However, in the strong confinement regime, splittings increase inversely proportional to the nanocrystal volume and, for a given nanocrystal size, the splitting values are comparable for the three-halide-perovskite materials. The present theoretical developments lead to quantitative contributions in good agreement with available experimental data mainly in the weak confinement regime.