Simulation of Coulomb Crystallization of Molecules on Graphene

The KTHNY theory predicts continuous phase transitions of classical particles on 2D surfaces that are mediated by the evolution of defects. Previous experiments have utilized micron-sized colloidal particles to observe these transitions, but controlling these particles with high precision has been challenging. Through a molecularly decorated, gate-tunable graphene device, we can achieve more precise control over particle interactions and density, offering a more insightful approach to testing the predictions of the KTHNY theory. To determine the range of critical particle density for phase transitions, we conducted simulations of charged particles diffusing on a graphene surface using the Kinetic Monte Carlo method. We analyzed both the translational and rotational order parameters, as well as the structure factors of these particles in relation to particle density and interaction. Our simulations and analysis primarily agree with the hypotheses of the KTHNY theory, while also indicating directions for future experimental work.