Monte Carlo Study of Crystalline Order and Defects on Weakly Curved Surfaces

We numerically study the ground states of particles interacting via a repulsive Yukawa potential on two rigid substrates shaped as isolated and periodically arranged bumps characterized by a spatially varying Gaussian curvature. Below a critical aspect ratio that describes the substrate deformation, the lattice is frustrated, but defect free. A further increase of the aspect ratio triggers defect unbinding transitions that lower the total potential energy by introducing dislocations either in isolation or within grain boundaries. In the presence of very strong deformations, isolated disclinations are nucleated. We show that the character and spatial distribution of defects observed in the ground state reflect the symmetries and periodicity of the two model surfaces investigated in this study.