Metric wave approach to flexoelectricity within density functional perturbation theory

Abstract

Within the framework of density functional perturbation theory (DFPT), we implement and test a novel "metric wave" response-function approach. It consists in the reformulation of an acoustic phonon perturbation in the curvilinear frame that is comoving with the atoms. This means that all the perturbation effects are encoded in the first-order variation of the real-space metric, while the atomic positions remain fixed. This approach can be regarded as the generalization of the uniform strain perturbation of Hamann et al. [D. R. Hamann, X. Wu, K. M. Rabe, and D. Vanderbilt, Phys. Rev. B 71, 035117 (2005)] to the case of inhomogeneous deformations, and greatly facilitates the calculation of advanced electromechanical couplings such as the flexoelectric tensor. We demonstrate the accuracy of our approach with extensive tests on model systems and on bulk crystals of Si and SrTiO3.arXiv:1811.12893v1 [cond-mat.mtrl-sci] 30 Nov 2018

First-Principles Theory of Spatial Dispersion: Dynamical Quadrupoles and Flexoelectricity

“…(101), are satisfied to a high degree of accuracy, and our coefficients are in excellent agreement with those obtained in previous works. [25] The largest deviation is shown by Kr: being it a larger atom, the overlap between neighboring images is likely to be more pronounced than in the other cases, which justifies the discrepancies we observe with respect to the expectations of the isolated atom model. At this stage, it is worth emphasizing that such test is by no means trivial; on the contrary, it represents a very stringent benchmark for our formalism.…”

“…This toy model presents the advantage that its flexoelectric coefficients can be determined analytically, based on the macroscopic electric tensor and the second real-space moment of the unperturbed atomic charge. In particular, the three independent flexoelectric coefficients as calculated from a metric-wave perturbation, must fulfill the conditions [25,35]…”

“…(63) is not a variational function of the A-field response wavefunctions, |iu Aα mk,q . Consequently, when calculating q-derivatives of E E * α λ q , one needs to explicitly derive the functions |iu Aα mk,q as one would do for a "standard" external potential operator (e.g., corresponding to a phonon or a "metric" [25] perturbation, as in the flexoelectric case of Sec. V).…”

“…We shall then write the polarization response to the acoustic phonon at finite q as (following the notation of Ref. 25)…”

“…20, 25, and 35. ) It is useful, at this stage, to recall [25] two crucial properties of the metric wave: (i) both the perturbation and the response vanish at q = 0,…”