Defects in two- and three-dimensional soft lattices: Application to vortices in layered superconductors

It is shown that within continuum theory and linear elasticity the interaction of point defects in two- and three-dimensional lattices with isotropic long-range interaction is ideally screened; i.e., the elastic relaxation of the background lattice exactly compensates the long-range interaction between the defects. A small residual short-range interaction results from the discreteness of the lattice and from the nonlinear elastic displacements. The self-energy of a point defect is also strongly reduced by the lattice relaxation. These general results are applied to the lattices of Abrikosov vortex lines and of point vortices (``pancakes'') in layered superconductors. In the anisotropic lattice of pancakes this screening is not complete. In particular, screening changes the sign of the interlayer interaction, and while without screening the perpendicular magnetic field of a pancake decreases exponentially with increasing distance, the screened field decreases only algebraically due to the long-range elastic displacements of the pancake lattice around a vacancy or interstitial.