Abstract
Density-functional perturbation theory (DFPT) is nowadays the method of choice for the accurate computation of linear and nonlinear-response properties of materials from first principles. A notable advantage of DFPT over alternative approaches is the possibility of treating incommensurate lattice distortions with an arbitrary wave vector at essentially the same computational cost as the lattice-periodic case. Here we show that can be formally treated as a perturbation parameter and used in conjunction with the established results of perturbation theory (e.g., the “” theorem) to perform a long-wave expansion of an arbitrary response function in powers of the wave-vector components. This procedure provides a powerful general framework to access a wide range of spatial dispersion effects that were formerly difficult to calculate by means of first-principles electronic structure methods. In particular, the physical response to the spatial gradient of any external field can now be calculated at negligible cost by using the response functions to uniform perturbations (electric, magnetic, or strain fields) as the only input. We demonstrate our method by calculating the flexoelectric and dynamical quadrupole tensors of selected crystalline insulators and model systems.
- Received 21 December 2018
DOI:https://doi.org/10.1103/PhysRevX.9.021050
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Erratum
Erratum: First-Principles Theory of Spatial Dispersion: Dynamical Quadrupoles and Flexoelectricity [Phys. Rev. X 9, 021050 (2019)]
Miquel Royo and Massimiliano Stengel
Phys. Rev. X 12, 019903 (2022)
Popular Summary
In materials science and engineering, scientists often assume that crystals respond locally to an externally applied perturbation such as a strain or an electromagnetic field. Microscopically, however, the effects of the perturbation always propagate over a neighborhood around the point of application. At the macroscopic level, this means that the material response depends on gradients of the applied field, which is known as spatial dispersion. While these effects are generally small, they have attracted increasing interest in the past few years. Notable examples are flexoelectricity, the electrical voltage generated by a flexural deformation, and natural optical activity, the rotation of transmitted light polarization by some crystals. Here, we establish a general and efficient quantum-mechanical formalism to address this broad class of problems.
Density-functional perturbation theory (DFPT) is nowadays the state-of-the-art method to accurately calculate from first principles how materials respond to external stimuli. Our new approach consists of incorporating the long-wave method, a mainstay of condensed-matter theory since the early days of quantum mechanics, into the modern tools of DFPT. This allows one to access a broad range of spatial-dispersion properties at a surprisingly small computational cost and with unprecedented accuracy. We demonstrate our method, which we have implemented in a publicly distributed package (abinit), by calculating the flexoelectric tensor and the “dynamical quadrupoles” (i.e., the quadrupolar moment of the charge-density response to an atomic displacement) of several materials. We obtain excellent agreement with earlier studies, whenever available.
Our “long-wave DFPT” significantly extends the scopes and capabilities of perturbative electronic-structure approaches and opens the door to the systematic exploration of a vast range of gradient-related physical properties.
