Extended Data Fig. 9: Luminescence spectroscopy of ABO₃-type binary superlattices made from 8.6-nm CsPbBr₃ and 16.5-nm NaGdF₄ nanocrystals on a carbon-coated Cu grid.

a, Photoluminescence (PL) spectrum, which, similarly to Fig. 5, is composed of two bands (coupled and uncoupled nanocrystals). b, Photoluminescence intensity for the uncoupled (blue circles) and coupled (red circles) nanocrystal bands, on a logarithmic scale. Fits to the data (red solid lines) reveal sublinear behaviour, with fitted power-law exponents m ≈ 0.4–0.5. These exponents differ from those when using Si₃N₄ as a substrate, indicative of non-radiative processes at higher fluences and much enhanced superlattice–substrate interaction in the case of a conductive carbon film. c, Streak camera images obtained with an excitation fluence of 175 μJ cm⁻². In contrast to the results reported in the main text for ABO₃-type superlattices on Si₃N₄-membranes, no evidence of drastic shortening or time oscillations was found. Furthermore, a pronounced dynamic redshift characterizes the initial decay, which could be related to thermal effects (rapid cooling after heating through the excitation pulse). This is in stark contrast with typical superfluorescence spectral dynamics¹³ (Fig. 5), which exhibits a dynamic blueshift versus time¹³. d, Spectrally integrated time-resolved emission intensity traces for two excitation fluences (8 μJ cm⁻², black; 175 μJ cm⁻², red). Although a slight shortening of the decay is clearly observed, this is probably due to a non-radiative process, presumably energy transfer to the substrate, given the sublinear fluence dependence observed in b and the reduction of the fluorescence lifetime of uncoupled nanocrystals from 350 ps to about 100 ps even at low fluences. Carbon-coated grids might introduce absorbing states, which strongly influence the exciton dynamics and the onset of superfluorescence emission. This pronounced substrate effect is unsurprising given that superlattices are morphologically two-dimensional, being at most 10 unit cells in thickness.