Structural Diversity in Multicomponent Nanocrystal Superlattices Comprising Lead Halide Perovskite Nanocubes

Nanocrystal (NC) self-assembly is a versatile platform for materials engineering at the mesoscale. The NC shape anisotropy leads to structures not observed with spherical NCs. This work presents a broad structural diversity in multicomponent, long-range ordered superlattices (SLs) comprising highly luminescent cubic CsPbBr3 NCs (and FAPbBr3 NCs) coassembled with the spherical, truncated cuboid, and disk-shaped NC building blocks. CsPbBr3 nanocubes combined with Fe3O4 or NaGdF4 spheres and truncated cuboid PbS NCs form binary SLs of six structure types with high packing density; namely, AB2, quasi-ternary ABO3, and ABO6 types as well as previously known NaCl, AlB2, and CuAu types. In these structures, nanocubes preserve orientational coherence. Combining nanocubes with large and thick NaGdF4 nanodisks results in the orthorhombic SL resembling CaC2 structure with pairs of CsPbBr3 NCs on one lattice site. Also, we implement two substrate-free methods of SL formation. Oil-in-oil templated assembly results in the formation of binary supraparticles. Self-assembly at the liquid–air interface from the drying solution cast over the glyceryl triacetate as subphase yields extended thin films of SLs. Collective electronic states arise at low temperatures from the dense, periodic packing of NCs, observed as sharp red-shifted bands at 6 K in the photoluminescence and absorption spectra and persisting up to 200 K.

A ssembly of monodisperse nanocrystals (NCs) into long-range ordered superlattices (SLs) makes an ideal platform for creating materials with controlled and programmed functionalities that result not only from the combination and enhancement of size-dependent properties of constituent building blocks but also from synergistic effects and emergent interactions between neighboring NCs. 1,2 Early examples include conductivity enhancement in binary SLs of Ag 2 Te with PbTe NCs, 3 exchange coupling effects in assemblies of magnetic NCs, 4 and near-field plasmonicplasmonic resonance in the SL comprising gold NCs. 5 Various strategies have been developed for the fabrication of single and multicomponent SL structures with desired dimensionality and geometry, including colloid destabilization by nonsolvent diffusion, 6 drying-induced assembly over tilted substrate, 7,8 or at a liquid−air interface 9−11 and microemulsion-templated assembly. 12,13 Self-organization of NCs may be further governed by the external electric and magnetic fields. 14,15 The assembly of steric-stabilized colloidal NCs coated with hydrocarbon ligand chains relies on relatively weak (van der Waals, dipole−dipole, magnetic, Coulombic) interactions between NCs 1,16 with the considerable role of entropic contributions. 7 For example, the gain in free volume entropy upon self-assembly of monodisperse spherical NCs favors the formation of the densest possible structures with face-centered cubic ( fcc) or hexagonal close packing. 1,17 For binary mixtures of spherical NCs, over 20 structures analogous to known atomic lattices were reported. Typically, the observed structure is the one having higher packing density (η) for a given NC size ratio, γ = d B /d A , where d B is the diameter of a smaller B-component and d A is the diameter of a larger A-component, both computed taking into account the dimensions of the core and ligand shell. 2,18−20 In the simple optimal packing model (OPM), 21 the effective diameter of steric-stabilized NCs is calculated assuming that the ligand shell is space-filling along the axis connecting neighboring NCs. Commonly observed are  4 and NaGdF 4 NCs, 10.7−11.7 nm truncated cuboid PbS NCs, thick NaGdF 4 disks (31.5 nm in diameter and 18.5 nm thick), and 6.5− 28.4 nm disk-shaped LaF 3 NCs. Structures in solid and dashed frames were obtained with 8.6 and 5.3 nm CsPbBr 3 NCs, respectively. HAADF-STEM image illustrates a sharp shape of a CsPbBr 3 nanocube. The graph is a space-filling analysis within a hard-particle model for NaCl-, AlB 2 -, and AB 2 -and within OTM for ABO 3 -and ABO 6 -type SLs comprising larger spherical and smaller cubic NCs; the dashed line corresponds to the density of fcc packing of spherical NCs. those binary SL structures, whose hard-particle packing densities are close to or exceed the packing density of fcc packing of spheres (η = 0.74).
Advancements in NC synthesis methodologies with exquisite NC size-and shape-engineering motivate the exploration of different SL structures. 22−24 The phase behavior of assemblies from shape-anisotropic NCs can be explained by the presence of directional entropic forces, which lead to dense local packing. 25 Already with single-component SLs of nonspherical NCs, minor differences in NC shape were reported to change the resulting structure; for instance, in the case of cubes vs truncated cubes such as Pt, PbS, or iron oxide. 26−29 A plethora of different binary SLs had been observed combining spherical NCs with several nonspherical NCs such as triangular nanoplates (columnar and threedimensional structures), 18 nanowires and rhombic nanoplates (wherein chains of nanowires or stacked face-to-face plates template the assembly of spheres into ordered one-dimensional arrays), 30−32 nanorods (forming three-dimensional superstructures with the positional and orientational ordering of building blocks), 33,34 and branched octapod NCs. 35 Very little work has been reported for mixtures of exclusively nonspherical, anisotropic NCs. These are binary lamellar SL of shape-complementary nanoplates, 33 several columnar SLs from the mixtures of nanodisks and nanorods, 36,37 and, very recently, thin-film SLs from PbTe cubes coassembled with triangular nanoplates. 38 Lead halide perovskite NCsthe latest generation of semiconductor quantum dots introduced in 2015 39 have attracted much attention for their enhanced properties as narrow-band, bright light emitters 40−42 and are intensely investigated for both classical light generation (light-emitting diodes, down-conversion in LCDs) 43,44 and as single-photon sources. 45,46 Being synthetically available as sharp, monodisperse cubes with edge-length tunable in 5−20 nm, 47−49 perovskite NCs are attractive highly uniform, shape-engineered building blocks for SLs. Since 2017, CsPbBr 3 NCs had been reported to form superstructures with simple-cubic packing (scp). 50−57 At cryogenic temperatures, single-component CsPbBr 3 NC SLs were found to exhibit superfluorescence. There, in contrast to spontaneous emission where the individual NCs emit photons randomly and independently, a coherent coupling among several NCs in superfluorescent domains leads to collective emission, resulting in ultrafast (few tens of picoseconds) bursts of photons. 53 These findings stimulated exploration of multicomponent SLs with perovskite NCs, as a means of attaining programmable positional and orientational order of these coherent light emitters. 58,59 Fundamentally important is that these were the original trials to coassemble cubic NCs with other shapes, and the outcome was vastly different from the results of the all-sphere NC selfassembly. Specifically, when CsPbBr 3 nanocubes are coassembled with spherical dielectric NaGdF 4 NCs, the binary perovskite b-ABO 3 -type SL forms, with cubes occupying B and O sites. Perovskite-type SL had not been reported, and not observed in our reference experiments, for all-sphere mixtures, which can be rationalized by much higher computed packing densities of this lattice when using cubes on B/O-sites. We then utilized the nonequivalence of B and O sites to incorporate the third component, truncated cubic PbS NCs, on a slightly larger B-site, yielding a ternary ABO 3 -type SL. 58 In the subsequent work, CsPbBr 3 cubes were combined with thin LaF 3 disks (1.6 nm in thickness, 6.5−28.4 nm in diameter), yielding six columnar structures, wherein columns of disks and cubes form a two-dimensional periodic pattern, and four threedimensional structures that feature face-to-face contacts between cubes and disks of comparable size. 59 Here, we present a detailed survey and comprehensive discussion of all multicomponent SL structures ( Figure 1) obtained by combining cubic CsPbBr 3 NCs (and FAPbBr 3 NCs) with diverse spherical and nonspherical NCs into multicomponent SLs. Beyond refs 58 and 59, a broader selection of building blocks was utilized (truncated cuboids and thick disks), additional structure types are presented (AB 2 , b-ABO 6 , CaC 2 ), and their formation was rationalized using space-filling calculations. Generally, cubic shape and facile ligand-deformability at the vertices and edges yield denser packing compared to spheres. In total, six structures were found in small cube-large sphere and small cube-large truncated cube mixtures, of which three are identical to those commonplace in all-sphere assemblies (NaCl, AlB 2 , and CuAu types) and the other three are exclusive to the use of cubes as smaller component (AB 2 , b-ABO 3 , b-ABO 6 ). Unlike columnar structures with thin LaF 3 disks, thick NaGdF 4 nanodisks (18.5 nm thick, 31.5 nm in diameter) yield a CaC 2 -like lattice with clusters of two 8.6 nm cubes. In all presented structures, cubic NCs are orientationally locked. While the screening of SL formation in this work and in our earlier reports (refs 58 and 59) were conducted by drying the colloids directly on the microscopy substrates, we also present the adaptation of the on-liquid formation of SLs as free-floating membranes for perovskite NCs, wherein a suited subphase solvent such as glyceryl triacetate is proposed. This polar solvent does not disperse apolar NC colloids drop-casted atop nor chemically damages the perovskite NCs. We also present the utility of the microemulsion-based method for the formation of multicomponent SLs comprising perovskite NCs. These SLs give rise to collective electronic states across perovskite NCs at low temperatures, as is evidenced by their photoluminescence (PL) and absorption spectra containing sharp red-shifted bands persisting up to 200 K.

RESULTS AND DISCUSSION
Due to rather ionic bonding and specifics of surface termination with a high propensity of lead atoms to maintain octahedral coordination, perovskite NCs tend to expose nonreconstructed, CsBr-terminated facets [(100) in pseudocubic notation], essentially without truncation. 60 Sharp nanocubes CsPbBr 3 with the edge lengths of 5.3 and 8.6 nm were synthesized by the hot-injection method (see respective luminescence and absorption spectra in Figure S1). 61,62 The NCs were coated by didodecyldimethylammonium bromide (DDAB), which is the shortest ligand still rendering these NCs colloidally stable. As manifested by the distinct diffraction arcs in the wide-angle selected-area electron diffraction (ED) pattern from the assembled monolayer (see Figure S2), nanocubes align face-to-face with the [001] zone axis parallel to the electron beam. CsPbBr 3 nanocubes crystallize in orthorhombic Pnma structure with six facets terminated by four {101} and two {010} planes. 60 31 Six arcs originating from {100} lattice planes imply slight hexagonal faceting of nanospheres. The decreased sodium-to-gadolinium ratio in the precursor solution and increased reaction time lead to NaGdF 4 nanodisks (31.5 nm in diameter and 18.5 nm in thickness). The size distribution of NCs used in experiments was in the range from 2.9 to 7.7% [standard size deviation based on 200 particles, see transmission electron microscopy (TEM) characterization in Figure  S2]. In most experiments, SLs were grown as polycrystalline films on a range of substrates (carbon-coated copper-grids and Si 3 N 4 membranes on Si grids) by drying the NC mixtures in toluene.
Coassembly of CsPbBr 3 Cubes with Spheres. First, we will discuss the systems of cubic 8.6 and 5.3 nm CsPbBr 3 NCs with spherical Fe 3 O 4 and NaGdF 4 NCs. 8.6 nm CsPbBr 3 nanocubes with spherical NCs can form NaCl-, AlB 2 -(along with AB 2 -), and b-ABO 3 -type SLs, depending on particle number ratio. Figure 2a shows NaCl-type SL obtained as a dominant product at a low CsPbBr 3 -to-NaGdF 4 particle number ratio (ca. 1.2:1 and γ = 0.439). Wide-angle ED measured from a single SL domain reveals the orientation of CsPbBr 3 cubes with ⟨100⟩ directions coinciding with ⟨100⟩ SL , that is, each cube interacts with six spheres through flat facets; subscript "SL" denotes Miller indices of an SL. At high cubeto-sphere particle ratios (ca. 4.2:1), a b-ABO 3 -type SL is the sole product (Figure 3a The formation of NaCl and b-ABO 3 SLs with cubic NCs can be rationalized by their high packing densities, exceeding those of fcc packing of spheres ( Figure 1). 58 The coordination environment of B-and O-positioned cubes in b-ABO 3 -type structure is different, for example, at γ ≥ 0.414, O-cubes interact through vertices, while B-cubes are rattlers. Targeted incorporation of larger (compared to perovskite cubes) truncated cuboidal PbS NCs (11.7 nm) on B-sites leads to a three-component t-ABO 3 -type SL with higher packing density than that of b-ABO 3 lattice comprising the same sizes of spheres (21.5 and 25.1 nm) and perovskite cubes (8.6 nm), Figure 3o−r. Wide-angle ED confirms the same orientation of O-site perovskite cubes as in the binary lattice, and PbS truncated cubes preserving the orientation of B-site perovskite cube. The PbS incorporation into the structure is apparent from high contrast in high-angle annular dark-field scanning TEM (HAADF-STEM) images (Figure 3p,r). The completeness of the substitution of CsPbBr 3 cubes on B site by PbS NCs is evident from the absence of (110) reflection ("1" in Figure 3q) expected from the center perovskite cube, while the (220) reflection originating from PbS ("2" in Figure 3q) is intensely diffracting in the analogous direction. These structures are also described in our previous work, ref 58.
At the intermediate particle number ratios (ca. 2.2:1, cubesto-spheres), the dominant product is an AlB 2 -type SL.  Figure S3) and AlB 2 -type SLs, in which, similar to larger cubes, a high degree of orientational order is observed. AlB 2 -type binary SLs are obtained with iron oxide NCs (11.2− 15.6 nm, γ = 0.443, 0.405, 0.368, 0.336, Figure 5 and Figure  S4). Structural peculiarities of the AlB 2 binary SL are detailed here for the case of 12.5 nm Fe 3 O 4 NCs ( Figure 5). The grazing-incidence small-angle X-ray scattering (GISAXS) pattern shows strong, periodic reflections ( Figure 5c) owing to long-range order and complex, base-centered orthorhombic symmetry (C222), resulting from the stacking of hexagonal CsPbBr 3 and Fe 3 O 4 layers, with an in-plane A−B−A−B packing direction, as also confirmed by energy-dispersive X-ray spectroscopy (EDX-STEM, on Figure 5g). See Supplementary Note 1 and Figure S5 for further details on GISAXS SL  and averaging of large homogeneous areas of TEM images (insets in Figure 5i,l). Small-angle ED and wide-angle ED patterns (for [120] SL -orientation) confirm the preferential orientation of nanocubes analogously to AlB 2 -lattices with larger CsPbBr 3 NCs, albeit with much weaker intensities of perovskite reflections due to reduced scattering factor of small NCs. The broader arcs indicate a higher orientational freedom of smaller nanocubes within the SL. The (111) and (110) lattice planes of CsPbBr 3 are normal to [001] SL and [010] SL , respectively, as in the binary SLs with larger cubes. However, there are three sets of {110} CsPbBr 3 lattice planes with a common [111] zone axis that is parallel to [001] SL . Therefore, 60°rotation around [001] SL does not change the position of diffraction spots. Consequently, there are two possible relative orientations of nanocubes: half of the cubes being 60°rotated about [001] SL ("O1") or all having the same orientation ("O2", Figure 6a). We would also note that ambiguity in this rotational orientation around [001] SL , as well as the possibility of the partial rattling of cubes along the same direction (not resolvable with TEM images), complicates the packing density analysis (Figure 6b). Our analysis shows that a combined effect of the "O2"-orientation and cube displacement along [001] SL direction can lead to the hard-particle packing densities of 0.7−0.8 in the γ range of 0.35−0.70 (see detailed discussion and calculations in the Supplementary Note 2).
Next to AlB 2 -type binary SLs and for both sizes of nanocubes combined with Fe 3 O 4 spheres, another AB 2 structure belonging to the tetragonal crystal system, namely the P4 2 /mmc space group, concomitantly forms ( Figure 7 and Figures S8−S10). This structure can be viewed as derived from the AlB 2 structure with a small modification: Shifting of each fourth (100) lattice plane along [011] vector, the corresponding lattice plane and the direction of shifting are marked in Figure 7d. This AB 2 -type packing is characterized by spherical NCs forming trigonal prisms, highlighted in Figure 7d, alternating in two perpendicular directions normal to the out-of-plane [001] SL , with cubic NCs occupying each void orienting in the same way as in the trigonal prismatic void of AlB 2 -type lattice, hence retaining the AB 2 stoichiometry. Such ordering is in agreement with the contrast differences in TEM, HAADF-STEM images, EDX elemental mapping, and wideangle ED patterns of [001] SL projection ( Figure 7 and Figures S9 and S10). Its wide-angle ED displays reflections originating from (110) and (111) CsPbBr 3 lattice planes (four arcs of each kind) running normal to [100] SL and [010] SL , which implies two relative orientations of nanocubes with a 90°angle between [111] directions because reflections from (110) and (111) planes of one nanocube cannot appear in the same direction. The higher yield of AlB 2 -type SLs indicates its lower formation energy barrier compared to AB 2 SLs, while the calculated packing densities of both structures coincide up to γ ≤ 0.435 (see for details Supplementary Note 3 and Figure 1 and Figure S8).
At γ = 0.315 (5.3 nm CsPbBr 3 and 16.9 nm Fe 3 O 4 NCs) and high cube-to-sphere particle number ratio (ca. 12:1), binary b-ABO 6 -type SL forms ( Figure 8). It possesses a Pm3̅ m space group with cubic NCs occupying one B-site (1b Wyckoff position) and six O-sites (6f Wyckoff position). This structure can also be viewed as ABO 3   We also observed the formation of b-ABO 3 -type SL at a high cube-tosphere particle number ratio in the solution (Figure 9m,n). Interestingly, as evident from distinct arcs in wide-angle ED, a high degree of orientational ordering of A-site NCs was observed in all these structures, especially in AlB 2 -and AB 2types featuring hexagonal motifs, further pointing to the hexagonal faceting of NaGdF 4 NCs. Specifically, in NaCl-type SL, the (100) lattice planes tend to align normally to the inplane ⟨110⟩ SL . At γ < 0.414, NaCl-type SL is defined by the fcc sublattice of A-particles with cubes rattling in the voids and neighboring NaGdF 4 NCs prefer to interact through the surfaces faceted by (100) and (001) planes. Interestingly, at γ > 0.414 (see Figure 2a,b for γ = 0.439), when A-particles contact O-cubes, the preferred orientation of NaGdF 4 NCs is different, they orient faceted surfaces toward cube facets, as manifested by a higher intensity of (100) and (002) wide-angle ED reflections along ⟨100⟩ SL . In AlB 2 -type SL, NaGdF 4 NCs within one hexagonal layer contact each other predominantly  Coassembly of CsPbBr 3 Cubes with Truncated Cuboids. We then studied the assembly behavior of the system comprising CsPbBr 3 cubes and truncated cuboid PbS NCs. Intriguingly, truncated cubes can behave similarly to spheres and occupy A-sites in binary ABO 3 -and NaCl-type SLs, albeit losing orientational freedom. The b-ABO 3 -type SLs form from the mixtures of 8.6 nm CsPbBr 3 nanocubes with 10.7−11.7 nm truncated cubic PbS NCs ( Figure 10). The corresponding size ratios (γ = 0.72−0.78) are much higher compared to the systems with spherical NCs as an Acomponent wherein b-ABO 3 -type SL forms up to γ = 0.54. EDX-STEM maps confirm that PbS NCs occupy only A-sites. Eight (100) and (110) maxima which appear in the directions normal to ⟨100⟩ SL and ⟨110⟩ SL together with eight (111) maxima with a splitting angle of 19.5°in wide-angle ED pattern indicate the presence of B-and O-positioned CsPbBr 3 cubes with the same orientations as in the b-ABO 3 -type SLs comprising spheres on A-sites. Moreover, as can be seen from TEM image and wide-angle ED analysis, namely the higher intensity of the reflections "2" and "3" which originate mainly from strongly diffracting PbS NCs compared to the intensity of the reflections "1" and "4" which are produced only by CsPbBr 3 NCs, the orientation of PbS NCs is not random and matches the orientation of O-site CsPbBr 3 nanocubes residing on the unit cell faces parallel to the substrate. Such PbS orientation implies contacts between PbS vertices and faces of the other O-site cubes residing on perpendicular to the substrate facets of ABO 3 lattice (see insets in Figure 10a,d), making the truncated shape of larger cubes beneficial for the formation of b-ABO 3 structure. For example, such a structure could not be obtained from the binary mixtures of sharp cubic CsPbBr 3 NCs of two sizes.
At lower CsPbBr 3 loading, the dominant product is NaCltype SL which is characterized by the alignment of ⟨100⟩ directions of both CsPbBr 3 and PbS NCs coinciding with ⟨100⟩ SL , as is evident from ED. Figure 11a−c shows TEM and HAADF-STEM images of binary domains with gradually increasing thickness, in agreement with the vanishing difference in intensities of neighboring SL site projections of NaCltype SL. A much higher wide-angle ED intensity of (200) and (220) peaks compared to that of (100) and (110) results from stronger scattering on PbS lattice planes, which contribute only to the former set of reflections and do not to the latter due to higher Fm3̅ m symmetry of the PbS lattice; furthermore, (200) Figure 6. Possible relative orientations of CsPbBr 3 nanocubes within AlB 2 -type SL and packing fractions predicted by OPM packing analysis according to the hard-particle model. In both orientations, the body-diagonal of the cubes is parallel to the c-axis of the hexagonal SL unit cell, that is, [001] SL . In orientation "O1", the cubes are mutually rotated by 60°, whereas in orientation "O2", they are identically aligned. A significant increase in the packing fraction can be achieved if the B-cubes in orientation "O2" are not locked in the 2d Wyckoff positions, that is, are allowed to slide along the [001] SL ("O2 S3"). Wide-angle ED patterns from [120] SL -(see, for instance, Figures 4e and 5b) and [001] SL -oriented domains (Figure 5j) point to the alignment of all cubes with one body diagonal parallel to [001] SL and (110) CsPbBr 3 planes are orthogonal to [010] SL . Hence these two orientations can be proposed. Experimentally, however, there exists no evidence to differentiate between these two structures, and hence both were considered for the analysis of lattice parameters and packing densities. Excluded is also a substantial orientational disorder in any dimension. and (220) reflections from PbS and CsPbBr 3 add up due to similar lattice constants (Figure 11g and Figure S11). The 8.6 nm CsPbBr 3 cubes with 10.7 nm PbS truncated cubes also form a CuAu-type SL (Figure 12a−f). Typically observed is the [101] SL orientation (Figure 12a). The site occupancies are confirmed by recording HAADF-STEM images of [101] SL -oriented domains at 0°and 45°tilting angles and comparing them with the modeled CuAu projections (Figure 12d,e). Complex wide-angle ED pattern (Figure 12b), contrary to b-ABO 3 -and NaCl-type SLs, reveals several different orientations of PbS cuboids that reside on equivalent lattice sites. Similar orientational behavior of PbS NCs is observed in AlB 2 -type SL assembled from 5.3 nm CsPbBr 3 NCs (Figure 12g−i). The [010] SL and [001] SL orientations that are common to AlB 2 -type SLs from all-sphere systems were observed (Figure 12g) consequently, the conclusion whether cube orientation is the same as in the AlB 2 -type SL with spherical NCs on the A-site.
Coassembly of CsPbBr 3 Cubes with Thick Nanodisks. Combining 8.6 nm perovskite nanocubes with larger NaGdF 4 disks (31.5 nm in diameter and 18.5 nm in thickness) resulted in the formation of an SL structure featuring the periodic clustering of two CsPbBr 3 NCs, which we interpret as a CaC 2like SL (Figure 13), albeit with an orthogonal unit cell metric due to anisotropic shape of the NaGdF 4 NCs. SEM images of the surface of SL domains (Figure 13d,e) show the occupancy of one lattice site by pairs of cubes with face-to-face alignment. Within one layer, cubes are surrounded by four vertically oriented disks, two of which approach cubes by flat faces and the other two by their rims. Nanodisks from the next layer assemble on top of cubes from the previous layer, emulating the CaC 2 -like packing. Such ordering is in agreement with the contrast observed in TEM of the monolayer domain ( Figure  S12) and TEM and HAADF-STEM image of multilayer (Figure 13a,b) and was unambiguously confirmed by electron tomography reconstruction of ordered SL domains (see Supplementary Video 2). Four narrow arcs from (100) and (110) CsPbBr 3 lattice planes in the wide-angle ED reveal the orientation of perovskite cubes, pointing their faces along three lattice vectors (Figure 13c). However, the more pronounced (100) peak along the shortest lattice vector may indicate some tilt of the cubes around this direction.
Self-assembly of Perovskite NCs on Liquid Subphase. Thus, far, the presented SLs were obtained by casting the small volume of the mixture of NCs (ca. 28−35 μL in toluene) over the substrates located in the tilted vial. This simple approach allows for facile screening of the SL formation yet has its drawbacks too. For instance, the range of suitable substrates is rather limited to hydrophobic surfaces. The obtained films usually are characterized by cracks between SL domains that reduce surface coverage. Moreover, adhesion of the SL domain to the substrate, while it still contains solvent, may result in additional crack formation within the domain. 20 Dryingmediated assembly on the surface of an immiscible liquid, usually a polar solvent such as ethylene glycols and acetonitrile, used as support was introduced to overcome these issues, allows for obtaining centimeter-scale SL membranes transferable to the arbitrary substrate, enabling integration of thinfilm SLs into devices. 9 This method is, however, difficult to extend to perovskite NCs as even a small but finite solubility in the subphase polar solvent compromises their structural integrity.
After the extensive screening of possible alternatives, we find that glyceryl triacetate is both immiscible with nonpolar solvents such as toluene and hydrocarbons and also does not disperse or chemically harm perovskite NCs and can be utilized as a support in the liquid−air interfacial assembly (see Figure 15a). We also note that fluorinated solvents, such as FC-40, satisfy the aforementioned requirements, but the nonpolar solvents have a low tendency to spread into a needed thin liquid layer on this fluorinated subphase due to limited wettability. Noteworthy, perfluorodecalin featuring partial miscibility with hexane was successfully used as a substrate for obtaining three-dimensional nearly isotropic perovskite SLs. 54 The self-assembly on glyceryl triacetate occurs within several minutes to several hours depending upon solvent evaporation rate (hexane, octane, decane, or dodecane). Figure 15b−d shows an extended monolayer of CsPbBr 3 NCs assembled on the surface of glyceryl triacetate from the solution of NCs in octane. Mixtures of NCs yield ordered binary mono-and multilayers with different structures depending on the concentration, particle number, and size ratios (Figure 15e−g).

Self-Assembly of Binary Supraparticles Comprising
Perovskite NCs. Microemulsion-templated self-assembly is another method enabling the control over the superstructure dimensionality and allows for the formation of three-dimensional supraparticles upon the assembly in spherical confinement of the "oil" droplet (colloid) stabilized in an immiscible solvent with the aid of a surfactant. 66,67 Potentially, such ordered multicomponent supraparticles can serve as building blocks for mesoscale materials with hierarchical order, wherein the properties could be defined by constituent NCs, their packing within the supraparticles, and finally by the ordering of supraparticles themselves. Furthermore, dispersed individual supraparticles can be, in principle, manipulated and deposited on-demand into desired locations within photonic and other structures. Colloidal spheres of mono-and binary SLs were reported to form from the emulsions of nonpolar solvents in water. 12 70 Here, we extend the method to binary SLs with perovskite NCs (Figure 16).  Supraparticles with b-ABO 3 -type structures can be obtained from the emulsions of 8.6 nm CsPbBr 3 and 18.6 nm NaGdF 4 NCs (Figure 16b). Smaller domains appear to be single crystalline, albeit, as revealed by electron tomography reconstruction 71 (see Supplementary Video 3), they may possess structural defects such as nanocube vacancies. The growth inside larger droplets leads to 500−1500 nm supraparticles and is characterized by several nucleation sites resulting in polycrystalline SLs 72 (see SEM images in Figure  16b). Perovskite cubes with thick NaGdF 4 disks form supraparticles with the ordering analogous to the CaC 2 -like structure (Figure 16c) presented earlier ( Figure 13).
Collective Optical Properties of b-ABO 3 and AlB 2type SLs. An exceptional emissivity of lead halide perovskite NCs motivates the exploration of their properties at both single-particle and ensemble levels. Here, we focus on the optical properties where, already on the single-NC level, perovskite NCs are standing out because of their exceptionally fast radiative rates and high oscillator strength 73 and long exciton coherence. 45,74 Scalable self-assembly from colloids makes for an attractive path to the controlled aggregate states of these bright emitters. The relationship between the periodic mesostructure and emerging collective luminescent characteristics can then be delineated and rationalized. Collective PL properties had been observed in our earlier work on monocomponent CsPbBr 3 NC SLs 53 and binary ABO 3 -type SLs (CsPbBr 3 cubes + NaGdF 4 spheres), 58 studied at cryogenic temperatures. Already with cw-excitation, coupling between perovskite NCs is apparent from the sharp PL band,  red-shifted with respect to the excitonic PL of uncoupled NCs. Furthermore, for the same samples, pulsed excitation with higher fluencies gives rise to superradiant emission, specifically superfluorescence. Superfluorescence emerges when coherence is established over a number of excited emitters via a common radiation field, forming a giant dipole. This then manifests itself as short (subnanosecond) and intense (proportional to the squared number of coupled emitters) bursts of light.
Herein, we survey the behavior of the red-shifted PL band, as well as concomitant absorption band, from the coupled NCs in relation to the lattice structure and NC size and composition. Such energetically shifted emission and absorption bands are well-known for molecular aggregates, where the    coherent coupling in J-/H-aggregates can lead to super/ subradiant emission. 75 Hence, we interpret the emergence of this additional emission band next to the excitonic PL band as emission that originates from coupled NC that is induced by the NC assembly into ordered SLs. The energy splitting between these bands may be viewed as a signature of the coupling strength. In Figure 17a, we show the emission spectra of two b-ABO 3 SLs with 8.6 nm CsPbBr 3 nanocubes and iron oxide NCs of different sizes. As the A-sphere (Fe 3 O 4 ) size increases from 14.5 to 19.5 nm, so does also the lattice parameter and hence the B−O sites distance (from 10.2 to 11.8 nm), as seen experimentally by TEM and GISAXS. The PL peak energy splitting between uncoupled NCs and the coupled NCs decreases from 54 ± 7 meV to 37 ± 5 meV (Figure 17a). In b-ABO 3 -type SLs, NCs are in very close proximity (the distance between inorganic cores of perovskite NCs is below 1.4 nm), potentially allowing a wave function tunneling. Contrary to the long-range dipole−dipole coupling, which exhibits a characteristic 1/D 6 scaling of the coupling strength as a function of the distance D between the dipoles, Dexter-like wave function tunneling is expected to exhibit exponential behavior. The exact determination of the underlying physical mechanism responsible for the NC coupling remains to be further explored; in particular, whether B−O or O−O sites couple by the short-range wave function overlap or whether there exists longer-range B−B (a unit cell apart) dipolar coupling or similar.
In molecular aggregates, the coupling between the constituent molecules and, therefore, the aggregate emission band can exhibit peculiar temperature trends. 75 In order to shed light on the role of such phonon-related processes within the NC aggregates, temperature-dependent measurements were carried out on AlB 2 SLs formed by 5.3 nm CsPbBr 3 NCs and 12.5 nm iron oxide NCs. We chose this SL structure given the large energetic splitting (ca. 140 meV) observed for this SL type. Although the geometry of the perovskite NC sublattice and crystallographic alignment of NCs is vastly different than in b-ABO 3 SLs, thus precluding a trustful comparison, the enhanced red-shift could be assigned to the shorter NC−NC distance (ca. 9.5 nm) and higher quantum confinement obtained with 5.3 nm CsPbBr 3 NCs. Figure 18a shows typical PL spectra at low (6 K) and elevated (100 K) temperatures, whereas complete temperature evolution is shown in Figure 18b. While the emission band of the uncoupled NCs (near 2.50 eV) shifts only slightly to blue, the emission from the coupled NCs shifts more, reducing the energetic splitting and decreasing in relative intensity while broadening. Spectral substructure of the coupled PL band is occasionally seen (inset of Figure 18a), which we attribute to several distinct aggregate domains being present within the excitation beam spot of ca. 2 μm 2 . We note that while a large fraction of studied SLs display the red-shifted emission from coupled NCs, its appearance still varies from sample to sample, probably due to the very short-range nature of the coupling, being it either wave function tunneling or partial necking of the NCs.
The ratio between the coupled (aggregate) and the uncoupled (nonaggregate) NC emission is plotted in Figure  18c, along with an Arrhenius fit, returning activation energy of about 14 meV, close to the LO-phonon energy in CsPbBr 3 NCs (17 meV). 76,77 This suggests that a phonon-driven mechanism similar to that in molecular aggregates reduces the effective number of coupled emitters N with temperature rise. This notion is supported by rather linear correlation obtained when plotting the splitting ΔE between the coupled and the uncoupled emission bands vs the square root of the peak area of the coupled emission (using the temperature-dependent data), which represents the number of coupled emitters (ΔE ∝ √N, Figure 18d). This dependency and the emission of coupled NCs being far from the expected bulk emission (ca. 2.3 eV, 535−540 nm) as well as a very strong quenching of the red aggregate band already at intermediate temperatures would hardly be reconcilable with an alternative assumption that the red-shifted emission peak could originate from the bulk material forming during the aggregation process. 78 The latter would imply an order of magnitude reduction of bulk emission quantum yield just within this temperature range.
Further evidence for red-shifted PL band originating from coupled NCs is found in the absorption spectra, presented here for b-ABO 3 -type SLs (8.8 nm CsPbBr 3 + NaGdF 4 NCs, Figure  19). These SLs exhibit two emission bands with a relative energetic splitting (ΔE) scaling with the NC-to-NC distances: on average, 45 and 37 meV for 15.1 and 18.2 nm NaGdF 4 NCs, respectively (Figure 19, top and middle panels). The redshifted band is also resolved in absorption, similar to our earlier studies on single-component SLs. 53 Similar to the PL behavior, the relative energetic splitting scales with the lattice parameter of the SL. The temperature behavior is analogous too; an additional absorption band vanishes when reaching 200 K (Figure 19), being strong evidence that rules out the hypothesis attributing the red-shifted PL band to bulk inclusions. 78 In particular, while a drop of the PL intensity from the bulk inclusions upon heating could be rationalized by the rapidly decaying PL quantum yield, the absorbance must persist.

CONCLUSIONS
In summary, we have presented a full survey of multicomponent SLs comprising sharp, sub-10 nm cubic perovskite NCs, obtained thus far in our experiments by combining them with spherical, truncated cubic, and disk-shaped NCs. Three SL structure types are of the kind commonly reported for binary mixtures of spherical NCs (NaCl, AlB 2 , and CuAu types). Three other binary structures (perovskite ABO 3 , AB 2 , ABO 6 ) are related to the cubic shape of perovskite NC building blocks. AB 2 can be viewed as derived from AlB 2 by slipping each fourth (100) SL in an [011] SL direction. ABO 6 can be conceived as the ABO 3 lattice, wherein each O-site is occupied by two 5.3 nm CsPbBr 3 cubes. When an anisotropic NC counter building block is utilized, namely, thick NaGdF 4 nanodisks (18.5 nm thick, 31.5 nm in diameter), a CaC 2 -like lattice forms, wherein the 8.6 nm cubes occupy the "C 2 -site", and the anisotropy of disks reduces tetragonal symmetry of the unit cell into orthogonal. In all studied SLs, cubic NCs are orientationally locked. We also report a substrate-less growth of thin-film SLs by drying colloids atop of an immiscible liquid (glyceryl triacetate) or of SL supraparticles with the aid of emulsion. Low-temperature PL and absorption spectra attest emergence of collective states in these highly dense aggregates of highly luminescent NCs.
Synthesis of CsPbBr 3 NCs. The 8.6 nm NCs were synthesized following the method reported in ref 62. In a 25 mL three-neck flask, PbBr 2 (55 mg, ABCR, 98%) was degassed three times, suspended in 5 mL of ODE, and degassed three times again at room temperature. The suspension was quickly heated to 180°C, when the temperature reached 120°C, 0.5 mL of OA and oleylamine (0.5 mL, OLA, Strem, 97%, distilled) were injected. At 180°C, preheated to about 100°C cesium oleate solution in ODE (0.6 mL) was injected. The reaction mixture was cooled immediately to room temperature with an ice bath. The crude solution was centrifuged at 12,100 rpm (equivalent to 20,130 relative centrifugal force) for 5 min, the supernatant was discarded, and the precipitate was dispersed in hexane (0.3 mL, Sigma-Aldrich, anhydrous, 95%). The solution was centrifuged again at 10,000 rpm for 3 min, and the precipitate was discarded. Then, OLA/OA ligands were exchanged by DDAB treatment. 0.3 mL hexane, toluene (0.6 mL, Sigma-Aldrich, anhydrous, 99.8%), and DDAB (0.14 mL, 0.05 M in toluene, Sigma-Aldrich, 98%) were added to the supernatant and stirred for 1 h, followed by destabilization with ethyl acetate (1.8 mL, Sigma-Aldrich, 99.9%), centrifuging at 12,100 rpm for 3 min and redispersing in 0.6 mL of toluene. Synthesis of 5.3 nm CsPbBr 3 NCs was adopted from ref 61 followed by DDAB treatment. The concentration of CsPbBr 3 NCs was calculated from the optical absorption at 335 nm using the reported molar extinction coefficient. 79 The concentration of other NCs was determined gravimetrically, accounting for capping ligands with the grafting densities stated in Supplementary Note 2.
Synthesis of NaGdF 4 NCs by Thermal Decomposition of Gadolinium Trifluoroacetate. 31 Gadolinium trifluoroacetate (147 mg, 0.267 mmol), NaF (16.1−22.4 mg, 0.383−0.533 mmol, lower loading resulted in larger NCs size, Merk, 99.99%), 4 mL of OA, and 4 mL of ODE were degassed in a three-neck flask at 125°C for 70 min. Then the solution was heated to 312°C at 15°C/min under nitrogen and kept at this temperature for 75 min. The reaction mixture was cooled to room temperature, and 36 mL of ethanol (Merck, 99.8%) was added to destabilize the colloidal solution. The NCs were precipitated by centrifugation at 4000 rpm for 3 min and washed three additional times with hexane (along with 25 μL OA) and ethanol (1 to 1.5 by volume). After purification, NCs were stored in 2 mL of hexane. Gadolinium trifluoroacetate was synthesized by reaction of Gd 2 O 3 (2.159 g, 6 mmol, Sigma-Aldrich, 99.9%) with trifluoroacetic acid (7.4 mL, 95 mmol, Sigma-Aldrich, 99%) and 12.4 mL of water under reflux (93°C) for 1 h. The white product was isolated by evaporation of the unreacted acid and water under vacuum at 60°C and dried overnight under vacuum.
For the synthesis of NaGdF 4 disks, gadolinium trifluoroacetate (221 mg, 0.4 mmol), NaF (29.5 mg, 0.7 mmol), 6 mL of OA, and 6 mL of ODE were degassed in a three-neck flask at 125°C for 90 min. Then the solution was heated to 312°C at 15°C/min under nitrogen and kept at this temperature for 83 min. The reaction mixture was cooled to room temperature, then 2 mL of hexane and 36 mL of ethanol were added to destabilize the colloidal solution. The NCs were precipitated by centrifugation at 5000 rpm for 2 min and washed additionally twice with hexane (along with 40 μL of OA) and ethanol (1:2.5 by volume). After purification, NCs were stored in 2 mL of toluene.
Synthesis of Truncated Cubic PbS NCs. 80 63 For the synthesis of iron oleate complex, FeCl 3 (1.658 g, 10 mmol, Alfa-Aesar, 98%) and sodium oleate (9.125 g, 30 mmol, TCI, 97%) were dissolved in a mixture of 35 mL of hexane, 20 mL of ethanol, and 15 mL of distilled water. After stirring under nitrogen at 65°C for 5 h, the upper organic layer was separated and washed five times with warm water, followed by centrifugation and isolation in a separatory funnel. The waxy solid product was isolated using a rotary evaporator and dissolved in ODE to form 0.4 mol/kg solution. In a typical synthesis of 15.6 nm Fe 3 O 4 NCs, iron oleate complex in ODE (5 mL), OA (0.8 mL, 2.53 mmol), and 5 mL of ODE were loaded into a three-neck flask and vacuum dried at 110°C for 90 min. The reaction mixture was then heated under nitrogen from 200 to 312°C with a constant heating rate of 2°C/min and maintained at this temperature for 30 min after the initiation took place. The solution was cooled to room temperature and washed with 3 mL of hexane and 12 mL of acetone, followed by centrifugation at 8000 rpm for 3 min. The precipitate was dissolved in 3 mL of hexane with 25 μL of OA. After two additional rounds of purification with hexane and acetone (2:1 by volume), the NCs were dispersed in 3 mL hexane. The size of NCs was controlled by varying the concentration of OA (higher for larger NCs) and reaction temperature (higher for larger NCs).
Synthesis of 12.5 nm LaF 3 Nanodisks by Thermal Decomposition of Lanthanum Trifluoroacetate. 37 Lanthanum trifluoroacetate (192 mg), LiF (31.2 mg, Sigma-Aldrich, 99.99%), 6 mL of OA, and 6 mL of ODE were degassed in a 25 mL three-neck flask at 125°C for 2 h. Then the solution was heated to 300°C at 15°C /min under nitrogen and kept at this temperature for 70 min. The reaction mixture was cooled to room temperature, and 3 mL of hexane along with ethanol (30 mL) was added to destabilize the colloidal solution. The NCs were precipitated by centrifugation at 4000 rpm for 2 min and washed two additional times with hexane (along with 10−30 μL of OA) and ethanol (1:1 by volume). After purification, NCs were dispersed in 3 mL of hexane, and residual LiF, which is not soluble in nonpolar solvents, was separated by centrifugation at 4000 rpm for 2 min. Lanthanum trifluoroacetate was synthesized by reaction of La 2 O 3 (3.24 g, Sigma-Aldrich, 99.999%) with trifluoroacetic acid (16 mL) and 16 mL of water under reflux (93°C) for 1 h. The white product was isolated by evaporation of the unreacted acid and water under vacuum at 60°C and dried overnight under vacuum.
For the assembly of single-component CsPbBr 3 NCs film at the liquid−air interface, a 1 × 1 cm 2 Teflon well was filled with 0.5 mL of glyceryl triacetate (Sigma-Aldrich, 99%), CsPbBr 3 NCs in octane (0.4 μM, 20 μL) were dropped onto the surface, and then the well was covered by glass slide and octane slowly evaporated. After drying was completed, the film was transferred to a carbon-coated TEM grid, and the substrate was further dried under vacuum to get rid of the residual subphase. For the assembly of NaCl-type film, the mixture of 8.6 nm CsPbBr 3 NCs (4.3 μM, 2.5 μL, in toluene), 19.5 nm Fe 3 O 4 NCs (39 mg/mL, 2.5 μL, in toluene), and 10 μL of decane was dropped onto the surface of glyceryl triacetate in Teflon well following the aforementioned procedure. For the assembly of the AlB 2 -type film, the mixture of 8.6 nm CsPbBr 3 NCs (4.3 μM, 9 μL, in toluene), 19.5 nm Fe 3 O 4 NCs (39 mg/mL, 6 μL, in toluene), and 100 μL of decane was dropped onto the surface of glyceryl triacetate (1.5 mL) in Petri dish (3 cm in diameter), covered by glass slide following the aforementioned procedure.
Electron Microscopy Characterization. TEM and HAADF-STEM images as well as ED and small-angle ED patterns were collected with the use of JEOL JEM2200FS microscope operating at 200 kV accelerating voltage. EDX-STEM maps and HAADF-STEM images at different tilt angles were recorded using an FEI Titan Themis microscope operated at 300 kV equipped with a SuperEDX detector, with the aid of a motorized dual-axis tomography holder. Captured TEM and electron diffraction images were compared with the ones simulated in Crystal Maker 10.4.5 and Single Crystal 3.1.5 software, purchased from CrystalMaker Software Ltd. Electron tomography was carried out in HAADF-STEM mode at 300 kV using a small beam semiconvergence angle of 2.5 mrad, to increase the depth of field. Images were recorded over a tilt angle range ± (57− 72)°and interval 2−3°. Reconstruction was done using IMOD with a Back Projection algorithm and SIRT-like radial filter. 81 The tomograms were recorded on SLs self-assembled on carbon-coated TEM grids as continuous films or via a microemulsion technique. SEM images were obtained on a FEI Helios 660 operated at 3−7 kV using immersion mode.
Atomic Force Microscopy. ScanAsyst-AiIR probes were used to analyze the topography of the SLs on the Bruker Icon 3 atomic force microscope.
GISAXS Characterization. GISAXS measurements were performed at the Austrian SAXS beamline of the electron storage ring ELETTRA using a photon energy of 8 keV. 82 The beamline setup was adjusted to a sample to detector distance of 1961.43 mm to result in an accessible horizontal scattering vector q-range of −1.2 nm −1 < q H < 1.8 nm −1 and vertical scattering vector q-range of −0.1 nm −1 < q V < 2.9 nm −1 . The X-ray beam was collimated to a spot size at the sample of approximately 200 μm × 200 μm. The images were recorded using the Pilatus 1 M detector (Dectris, Switzerland) with an exposure time of 10 s per image. Reference patterns to calibrate the q-scale were collected of silver-behenate (d-spacings of 5.838 nm). Samples were mounted on a 2-axis goniometer stage with 0.001°angular precision, allowing us to ensure an incidence angle of 0.04°for the measurements (determined by alignment of the specular reflection on the detector). The presented data were corrected for fluctuations of the primary intensity. Data treatment was done using the NIKA2D 83 (geometry correction and calibration) as well as GIXSGUI 84 (lattice indexing) software packages.
Optical Spectroscopy. For the PL measurements, the sample was mounted on an XYZ nanopositioning stage inside an evacuated liquidhelium coldfinger cryostat and cooled to 6 K. Nanocrystals were excited with a fiber-coupled excitation laser at a photon energy of 3.06 eV with pulses of 50 ps duration. A long working-distance, 100×, microscope objective with a numerical aperture of 0.7 was used for both excitation and detection, leading to a Gaussian excitation spot with a 1/e 2 diameter of 1.4 μm. The emission was then dispersed in a 750 mm monochromator by a 3000 lines per mm grating and detected with a back-illuminated, cooled EMCCD camera.
For absorption and PL experiments reported in Figure 19, a custom-made setup, enabling both experiments to probe the same sample area, was used. The samples were placed on the coldfinger of a Janis CCS-150 closed-cycle optical refrigerator, allowing temperature variation within the 10−300 K range. Steady-state PL was excited by a 405 nm diode laser, focused onto a ∼2 μm diameter spot, via a Mitutoyo long working distance objective with 50× magnification and 0.55 numerical aperture. The emission was detected via the same objective, using a long-pass filter to block the excitation laser, while spectrally analyzed by a 0.75 m Acton750i Princeton spectrometer equipped with a 1024 × 256 pixels PIXIS charge-coupled device (CCD) camera. For absorption measurements, a tungsten-halogen white light source was coupled into a 600 μm core multimode fiber, and the output beam was focused onto the sample via the same microscope objective described above. The transmitted beam was coaxially collected and analyzed via the same combination of spectrometer and CCD described above.
Optical Properties of CsPbBr 3 NCs in Toluene. Optical absorption spectra were measured with Jasco V770 spectrometer in transmission mode. PL spectra were measured in a 90°configuration using Horiba Fluoromax-4P+ equipped with a photomultiplier tube and a monochromatized 150 W xenon lamp as an excitation source.