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

TL;DR

This paper presents a unified, systematic approach within density-functional perturbation theory to calculate various physical response tensors of insulating crystals, addressing complex couplings and boundary condition distinctions.

Contribution

It introduces a comprehensive method for computing multiple response tensors in a unified framework, handling complex couplings and boundary conditions in polar crystals.

Findings

Applied to ZnO and BaTiO3, demonstrating the method's effectiveness.

Clarified distinctions between different tensor definitions under various boundary conditions.

Enabled accurate calculation of elastic, dielectric, Born charge, and piezoelectric tensors.

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 the total energy 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, wurtzite ZnO and rhombohedral BaTiO3, at zero temperature.