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 [M. Royo and M. 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 ${\mathrm{SrTiO}}_3$, obtaining excellent agreement with the available literature data.

• Received 21 December 2021
• Accepted 20 January 2022

DOI:https://doi.org/10.1103/PhysRevB.105.064101