Systematic Treatment of Displacements, Strains and Electric Fields in Density-Functional Perturbation Theory

The methods of density-functional perturbation theory may be used to calculate various physical response properties of insulating crystals including elastic, dielectric, Born charge, and piezoelectric tensors. These and other important tensors may be dened as second derivatives of an appropriately dened energy functional with respect to atomic-displacement, electric- eld, or strain perturbations, or as mixed derivatives with respect to two of these perturbations. The resulting tensor quantities tend to be coupled in complex ways in polar crystals, giving rise to a variety of variant denitions. For example, it is generally necessary to distinguish between elastic tensors dened under different electrostatic boundary conditions, and between dielectric tensors dened under different elastic boundary conditions. Here, we describe an approach for computing all of these various response tensors in a unied and systematic fashion. Applications are presented for two materials, hexagonal ZnO and rhombohedral BaTiO3, at zero temperature.