Colloidal lead halide perovskite nanocrystals (LHP NCs_, APbX3, where A=Cs⁺, FA⁺, FA=formamidinium; X=Cl, Br, I) have become a research spotlight owing to their spectrally narrow (~100 meV) fluorescence, tunable over the entire visible spectral region of 400-800 nm, as well as facile colloidal synthesis. These NCs are attractive single-photon emitters and building blocks for creating controlled, aggregated states exhibiting collective luminescence phenomena. Attaining such states through the spontaneous self-assembly into long-range ordered superlattices (SLs) is a particularly attractive avenue. The atomically flat, sharp cubic shape of LHP NCs is also of interest because the vast majority of prior work had invoked NCs of spherical shape. Long-range ordered SLs with the simple cubic packing of cubic perovskite NCs exhibit sharp red-shifted lines in their emission spectra and superfluorescence (a fast collective emission resulting from coherent multi-NCs excited states).

When CsPbBr₃ NCs are combined with spherical dielectric NCs, perovskite-type ABO₃ binary NC SLs form, wherein CsPbBr₃ nanocubes occupy B- and/or O-sites, while spherical dielectric Fe₃O₄ or NaGdF₄ NCs reside on A-sites. When truncated-cuboid PbS NCs are added to these systems, ternary ABO₃-phase form (PbS NCs occupy B-sites). Such ABO₃ SLs, as well as other newly obtained SL structures (binary NaCl, AlB₂- and ABO₆ types, columnar assemblies with disks, etc.), exhibit a high degree of orientational ordering of CsPbBr₃ nanocubes. These mesostructures also exhibit superfluorescence, characterized, at high excitation density, by emission pulses with ultrafast (22 ps) radiative decay and Burnham-Chiao ringing behavior with a strongly accelerated build-up time. Co-assembly of steric-stabilized CsPbBr₃ nanocubes with disk-shaped LaF₃ NCs yields six columnar structures with AB, AB₂, AB₄, and AB₆ stoichiometry, not observed before with NC systems comprising spheres and disks. Combining CsPbBr₃ nanocubes with large and thick NaGdF₄ nanodisks results in the orthorhombic SL resembling CaC₂ structure with pairs of CsPbBr₃ NCs on one lattice site. Additionally, we have also implemented two substrate-free methods of SL formation. The first method involves oil-in-oil templated assembly that leads to the formation of binary supraparticles, while the second method utilizes self-assembly at the liquid-air interface.