Systematic treatment of displacements, strains, and electric fields in density-functional perturbation theory

TLDR

Density‑functional perturbation theory enables calculation of elastic, dielectric, Born‑charge, and piezoelectric tensors in insulating crystals, but their definitions become coupled and boundary‑condition dependent in polar materials. The authors present a unified, systematic method for computing all such response tensors. They demonstrate the approach on hexagonal ZnO and rhombohedral BaTiO₃ at zero temperature.

Abstract

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 defined as second derivatives of an appropriately defined energy functional with respect to atomic-displacement, electric-field, 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 definitions. For example, it is generally necessary to distinguish between elastic tensors defined under different electrostatic boundary conditions, and between dielectric tensors defined under different elastic boundary conditions. Here, we describe an approach for computing all of these various response tensors in a unified and systematic fashion. Applications are presented for two materials, hexagonal ZnO and rhombohedral $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_{3}$, at zero temperature.