Excitonic structure in CsPbBr$_3$ nanocubes, nanorods and nanoplatelets: the effect of dimensionality

We present a theoretical study comparing the excitonic ground state properties of CsPbBr$_3$ nanocrystals with different dimensionality: nanorods (1D), nanoplatelets (2D) and nanocubes (3D). All three systems are described on equal footing, by means of a general variational effective mass model, which captures the influence of quantum confinement, dielectric confinement, electron-hole correlations and polaronic effects (within a Haken model). The strongly confined directions squeeze the exciton (X) wavefunction and enhance Coulomb attractions along the weakly confined directions. This stimulates superradiance, thus making radiative recombination rates speed up from cubes to platelets and to rods, in line with recent experiments. The anisotropic local field factor is a secondary, yet non-negligible, mechanism further enhancing radiative rates. X binding energies are also determined primarily by the directions of strong confinenement, which is also consistent with experiments. Weakly confined directions become however influential for small aspect ratios. Dielectric confinement plays a major role in determining the binding energies, and less so in the interparticle-distances. For all dimensionalities, the biexciton (XX) geometry is that of a distorted tetrahedron, rather than squared or linear distributions that would result in Coulomb-governed 2D and 1D structures.