  Lead halide perovskite nanocrystals are promising materials for classical and
quantum light emission. To understand these outstanding properties, a thorough
analysis of the band-edge exciton emission is needed which is not reachable in
ensemble and room temperature studies because of broadening effects. Here, we
report on a cryogenic-temperature study of the photoluminescence of single
CsPbBr$_3$ NCs in the intermediate quantum confinement regime. We reveal the
size-dependence of the spectral features observed: the bright-triplet exciton
energy splittings, the trion and biexciton binding energies as well as the
optical phonon replica spectrum. In addition, we show that bright triplet
energy splittings are consistent with a pure exchange model and that the
variety of polarisation properties and spectra recorded can be rationalised
simply by considering the orientation of the emitting dipoles and the
populations of the emitting states.
