Lattice-mediated bulk flexoelectricity from first principles

TL;DR

This paper introduces a first-principles method to compute lattice-mediated bulk flexoelectricity, simplifying previous approaches and validated on cubic crystals and SrTiO3 with results matching existing data.

Contribution

The paper develops a new analytical and computational approach to calculate lattice-mediated flexoelectricity from first principles, avoiding complex numerical derivatives.

Findings

Validated the method on cubic crystals and SrTiO3.

Achieved excellent agreement with literature data.

Generalized sum rules relating flexoelectricity and elasticity.

Abstract

We present the derivation and code implementation of a first-principles methodology to calculate the lattice-mediated contributions to the bulk flexoelectric tensor. The approach is based on our recent analytical long-wavelength extension of density-functional perturbation theory [Royo and Stengel, Phys. Rev. X 9, 021050 (2019)], and avoids the cumbersome numerical derivatives with respect to the wave vector that were adopted in previous implementations. To substantiate our results, we revisit and numerically validate the sum rules that relate flexoelectricity and uniform elasticity by generalizing them to regimes where finite forces and stresses are present. We also revisit the definition of the elastic tensor under stress, especially in regards to the existing linear-response implementation. We demonstrate the performance of our method by applying it to representative cubic crystals and to the tetragonal low-temperature polymorph of SrTiO$_3$, obtaining excellent agreement with the available literature data.