Towards a bulk theory of flexoelectricity

TL;DR

This paper establishes a bulk-based theoretical framework for flexoelectricity in elemental cubic crystals, demonstrating that surface effects are negligible and that responses to phonons and strain gradients are equivalent.

Contribution

It provides a rigorous proof that flexoelectricity in these crystals is purely a bulk property, independent of surface contributions, and links phonon and strain gradient responses.

Findings

Surface contributions to flexoelectricity are negligible in the thermodynamic limit.

Flexoelectric responses to phonons and strain gradients are equivalent.

Flexoelectric tensor can be expressed solely as a bulk property.

Abstract

Flexoelectricity is the linear response of polarization to a strain gradient. Here we address the simplest class of dielectrics, namely elemental cubic crystals, and we prove that therein there is no extrinsic (i.e. surface) contribution to flexoelectricity in the thermodynamic limit. The flexoelectric tensor is expressed as a bulk response of the solid, manifestly independent of surface configurations. Furthermore, we prove that the flexoelectric responses induced by a long-wavelength phonon and by a uniform strain gradient are identical.