Origin of two-hole triplet splitting in circular quantum dots

► The triplet projections of X+ in quantum dots are split at zero field. ► This is understood from the symmetries of the hole Luttinger spinor. ► The optical spectrum of X+ is analyzed for different aspect ratios. ► The spin purity of X+ triplets decreases with the aspect ratio. ► We explain the different photoluminescence spectra observed for X2− and X2+.