Soft Skyrmions, Spontaneous Valence and Selection Rules in Nanoparticle Superlattices

A number of bewildering paradoxes arise in the field of nanoparticle self-assembly: nominal low density superlattices, strong stability of low coordination sites, and a clear but imperfect correlation between lattice stability and the maximum of hard sphere packing, despite the fact that that nanocrystals themselves are, through their ligands, very much compressible. In this study, I show that by regarding nanocrystals as pseudotopological objects ("soft skyrmions"), it is possible to identify and classify the ligand textures that determine their bonding. These textures consist of interacting vortices, where the total vorticity defines a spontaneous valence (coordination). Furthermore, skyrmion interactions are governed by two simple assumptions, which lead to a set of selection rules for superlattice structure. Besides resolving all the above paradoxes, the predictions are completely supported by more than one hundred sixty experiments gathered from the literature, including a wide range of nanocrystal cores and ligands (saturated or unsaturated hydrocarbons, amines, polystyrene, etc.). How those results can be used for addressing more complex structures and guiding future experiments is also addressed.