Anisotropy in two-dimensional arrays of collinear in-plane rotated identical particles with arbitrary charge or polarization distribution

Abstract

As the size and separation between nanometric objects arranged on a two-dimensional lattice become progressively smaller, the influence of interparticle coupling increases to the point that it may dominate the system's collective behavior. In this paper, a simple method to calculate isotropic and anisotropic interaction energies of charged or polarized particles in two-dimensional arrays is developed, where anisotropy refers to changes in energy upon in-plane rotation. The calculations are performed in the framework of a multipole expansion in spherical coordinates. The role of the array symmetry with respect to the order of the expansion is deduced from the symmetry properties of the interaction. The interaction energy is calculated exactly to infinite distance by means of lattice sums; thus, no cut-off radius to nearest neighbors is introduced. Several lattice symmetries, rectangular, quadratic, and hexagonal, up to multifold rotationally symmetric quasicrystals are investigated, and the influence of local disorder is discussed.