First-principles theory of flexoelectricity

TL;DR

This paper reviews first-principles methods for understanding flexoelectricity in crystals, deriving key tensors from acoustic phonon responses, and analyzing surface effects with a case study on SrTiO3.

Contribution

It extends the theoretical formalism to second order in wavevector for flexoelectricity and provides a detailed analysis of surface effects and a practical calculation for SrTiO3.

Findings

Flexoelectric tensor derived from second-order response in wavevector.

Surface termination significantly influences bending-induced voltages.

First-principles calculations reveal strong surface dependence in SrTiO3.

Abstract

In this Chapter we provide an overview of the current first-principles perspective on flexoelectric effects in crystalline solids. We base our theoretical formalism on the long-wave expansion of the electrical response of a crystal to an acoustic phonon perturbation. In particular, we recover the known expression for the piezoelectric tensor from the response at first order in wavevector ${\bf q}$, and then obtain the flexoelectric tensor by extending the formalism to second order in $\bf q$. We put special emphasis on the issue of surface effects, which we first analyze heuristically, and then treat more carefully by presenting a general theory of the microscopic response to an arbitrary inhomogeneous strain. We demonstrate our approach by presenting a full calculation of the flexoelectric response of a SrTiO$_3$ film, where we point out an unusually strong dependence of the bending-induced open-circuit voltage on the choice of surface termination. Finally, we briefly discuss some remaining open issues concerning the methodology and some promising areas for future research.