Topological phases in nanoparticle monolayers: Why crystalline, hexatic, and isotropic-fluid phases coexist at the same temperature?

Topological phases are stable configurations of matter in 2-dimensions (2D) formed via spontaneous symmetry breaking. These play a crucial role in determining the system properties. Though a number of fundamental studies on topological phase transitions and topological defect dynamics have been conducted with model colloidal systems (typically microns in size), the same is lacking on nanoparticle monolayers (NPMLs, typically made of ligand-coated sub-ten nanometer particles). Here, we show that in an evaporation-driven self-assembly process, the three topological phases, namely crystalline, hexatic, and isotropic-fluid phases, can coexist within the same NPML. We associate this coexistence with the local variation in particle size, which can be described by a unique frequency parameter (p25), quantifying the fraction of NPs that has size deviation greater than or equal to 25% of the mean size (where the deviation,ζ is defined as ζ = ((|Size-mean|)/mean)). The p25-values for the three phases are distinctly different: crystalline arrangement occurs when p25 < ∼0.02, while a hexatic phase exists for 0.02 ≤ p25 ≤ 0.1. For p25 ≥ 0.1, the isotropic-fluid phase occurs. Following KTHNY-theory, we further numerically extrapolate the occurrence of each phase to the accumulated excess planar strain in the NPML due to the presence of various topological defects in the structures.