Current-density implementation for calculating flexoelectric coefficients

TL;DR

This paper presents a first-principles density-functional perturbation theory method to calculate flexoelectric coefficients, including new expressions for current density in nonlocal pseudopotentials, enabling more accurate and direct computation of tensor components.

Contribution

The authors develop a novel DFT-based approach to compute all components of the flexoelectric tensor directly from a unit cell, improving upon previous supercell methods.

Findings

Validated methodology on noble gas atoms

Calculated flexoelectric constants for cubic oxides

Addressed technical issues in current density definition

Abstract

The flexoelectric effect refers to polarization induced in an insulator when a strain gradient is applied. We have developed a first-principles methodology based on density-functional perturbation theory to calculate the elements of the bulk, clamped-ion flexoelectric tensor. In order to determine the transverse and shear components directly from a unit cell calculation, we calculate the current density induced by the adiabatic atomic displacements of a long-wavelength acoustic phonon. Previous implementations based on the charge-density response required supercells to capture these components. Our density-functional-theory implementation requires the development of an expression for the current density that is valid for the case of nonlocal pseudopotentials, and long-wavelength phonon perturbations. We benchmark our methodology on simple systems of isolated noble gas atoms, and apply it to calculate the clamped-ion flexoelectric constants for a variety of technologically important cubic oxides. We also discuss some technical issues that are associated with the definition of current density in a nonlocal pseudopotential context, and their relevance to the calculation of macroscopic response properties of crystals.