Elastic Interaction between Surface Defects in Thin Layers

Elastic interactions between defects are investigated in thin layers. Unlike the classical repulsive law $1/r^3$ ( $r=\mathrm{defect}\mathrm{separation}$), we discover that defects in thin layers may either attract or repel each other depending on the direction (though elastic deformation is isotropic) with respect to the local geometric force distribution caused by the defect. Moreover, the force distribution fixes the exponent in the power law $1/r^n$ (e.g., in a square lattice $n=4\mathrm{}$). We discuss the implication of this new behavior in various situations.