Unified ab initio formulation of flexoelectricity and strain-gradient elasticity

TL;DR

This paper reveals a fundamental connection between flexoelectricity and strain-gradient elasticity, emphasizing the importance of their simultaneous treatment for accurate physical modeling and introducing a first-principles framework to compute relevant properties.

Contribution

It establishes a unified ab initio formulation linking flexoelectricity and strain-gradient elasticity, highlighting gauge invariance and providing a practical computational approach.

Findings

Identified gauge invariance in strain-gradient and flexoelectric energies.

Constructed a thermodynamic functional incorporating strain-gradient effects.

Applied the formalism to SrTiO3 revealing strong nonlocal elasticity contributions.

Abstract

The theories of flexoelectricity and that of nonlocal elasticity are closely related, and are often considered together when modeling strain-gradient effects in solids. Here I show, based on a first-principles lattice-dynamical analysis, that their relationship is much more intimate than previously thought, and their consistent simultaneous treatment is crucial for obtaining correct physical answers. In particular, I identify a gauge invariance in the theory, whereby the energies associated to strain-gradient elasticity and flexoelectrically induced electric fields are individually reference-dependent, and only when summed up they yield a well-defined result. To illustrate this, I construct a minimal thermodynamic functional incorporating strain-gradient effects, and establish a formal link between the continuum description and ab initio phonon dispersion curves to calculate the relevant tensor quantities. As a practical demonstration, I apply such a formalism to bulk SrTiO$_3$, where I find an unusually strong contribution of nonlocal elasticity, mediated by the interaction between the ferroelectric soft mode and the transverse acoustic branches. These results have important implications towards the construction of well-defined thermodynamic theories where flexoelectricity and ferroelectricity coexist. More generally, they open exciting new avenues for the implementation of hierarchical multiscale concepts in the first-principles simulation of crystalline insulators.