Emergence of Periodic Potential for Point Defects in a 2D Hexagonal Colloidal Lattice

Abstract

We examined the Brownian motion of point defects in a two-dimensional hexagonal colloidal crystal, going beyond the conventional treatment that assumes constant diffusion coefficients. By extracting the spatially varying drift vector and diffusion matrix directly from experimental trajectories, we uncovered richer behavior than predicted by the simple diffusive limit. Within a general stochastic-dynamics framework, these measurements revealed an effective stochastic potential landscape shaped by the crystal's periodic structure. The energy differences between its local minima were consistent, to within an order of magnitude, with previous experimental estimates. Simulations of stochastic trajectories on this reconstructed landscape reproduced the essential features of the observed defect motion. This study illustrates how combining time-series extraction with theoretical analysis can expose effective energy landscapes and provide a powerful route to understanding complex dynamics in colloidal systems.