Macroscopic Polarization from Nonlinear Gradient Couplings.

We show that a lattice mode of arbitrary symmetry induces a well-defined macroscopic polarization at first order in the momentum and second order in the amplitude. We identify a symmetric flexoelectric-like contribution, which is sensitive to both the electrical and mechanical boundary conditions, and an antisymmetric Dzialoshinskii-Moriya-like term, which is unaffected by either. We develop the first-principles methodology to compute the relevant coupling tensors in an arbitrary crystal, which we illustrate with the example of the antiferrodistortive order parameter in SrTiO_{3}.

In-Plane Flexoelectricity in Two-Dimensional D_{3d} Crystals.

We predict a large in-plane polarization response to bending in a broad class of trigonal two-dimensional crystals. We define and compute the relevant flexoelectric coefficients from first principles as linear-response properties of the undistorted layer by using the primitive crystal cell. The ensuing response (evaluated for SnS_{2}, silicene, phosphorene, and RhI_{3} monolayers and for a hexagonal BN bilayer) is up to 1 order of magnitude larger than the out-of-plane components in the same material. We illustrate the topological implications of our findings by calculating the polarization textures that are associated with a variety of rippled and bent structures. We also determine the longitudinal electric fields induced by a flexural phonon at leading order in amplitude and momentum.

Natural Optical Activity from Density-Functional Perturbation Theory.

We present an accurate and computationally efficient first-principles methodology to calculate natural optical activity. Our approach is based on the long-wave density-functional perturbation theory and includes self-consistent field terms naturally in the formalism, which are found to be of crucial importance. The final result is expressed exclusively in terms of response functions to uniform field perturbations and avoids troublesome summations over empty states. Our strategy is validated by computing the natural optical activity tensor in representative chiral crystals (trigonal Se, α-HgS, and α-SiO_{2}) and molecules (C_{4}H_{4}O_{2}), finding excellent agreement with experiment and previous theoretical calculations.

Accurate Prediction of Hall Mobilities in Two-Dimensional Materials through Gauge-Covariant Quadrupolar Contributions.

Despite considerable efforts, accurate computations of electron-phonon and carrier transport properties of low-dimensional materials from first principles have remained elusive. By building on recent advances in the description of long-range electrostatics, we develop a general approach to the calculation of electron-phonon couplings in two-dimensional materials. We show that the nonanalytic behavior of the electron-phonon matrix elements depends on the Wannier gauge, but that a missing Berry connection restores invariance to quadrupolar order. We showcase these contributions in a MoS_{2} monolayer, calculating intrinsic drift and Hall mobilities with precise Wannier interpolations. We also find that the contributions of dynamical quadrupoles to the scattering potential are essential, and that their neglect leads to errors of 23% and 76% in the room-temperature electron and hole Hall mobilities, respectively.

Frequency Splitting of Chiral Phonons from Broken Time-Reversal Symmetry in CrI_{3}.

Conventional approaches for lattice dynamics based on static interatomic forces do not fully account for the effects of time-reversal-symmetry breaking in magnetic systems. Recent approaches to rectify this involve incorporating the first-order change in forces with atomic velocities under the assumption of adiabatic separation of electronic and nuclear degrees of freedom. In this Letter, we develop a first-principles method to calculate this velocity-force coupling in extended solids and show via the example of ferromagnetic CrI_{3} that, due to the slow dynamics of the spins in the system, the assumption of adiabatic separation can result in large errors for splittings of zone-center chiral modes. We demonstrate that an accurate description of the lattice dynamics requires treating magnons and phonons on the same footing.

Curved Magnetism in CrI_{3}.

Curved magnets attract considerable interest for their unusually rich phase diagram, often encompassing exotic (e.g., topological or chiral) spin states. Micromagnetic simulations are playing a central role in the theoretical understanding of such phenomena; their predictive power, however, rests on the availability of reliable model parameters to describe a given material or nanostructure. Here we demonstrate how noncollinear-spin polarized density-functional theory can be used to determine the flexomagnetic coupling coefficients in real systems. By focusing on monolayer CrI_{3}, we find a crossover as a function of curvature between a magnetization normal to the surface to a cycloidal state, which we rationalize in terms of effective anisotropy and Dzyaloshinskii-Moriya contributions to the magnetic energy. Our results reveal an unexpectedly large impact of spin-orbit interactions on the curvature-induced anisotropy, which we discuss in the context of existing phenomenological models.

Convert Widespread Paraelectric Perovskite to Ferroelectrics.

While nature provides a plethora of perovskite materials, only a few exhibit large ferroelectricity and possibly multiferroicity. The majority of perovskite materials have the nonpolar CaTiO_{3}(CTO) structure, limiting the scope of their applications. Based on the effective Hamiltonian model as well as first-principles calculations, we propose a general thin-film design method to stabilize the functional BiFeO_{3}(BFO)-type structure, which is a common metastable structure in widespread CTO-type perovskite oxides. It is found that the improper antiferroelectricity in CTO-type perovskite and ferroelectricity in BFO-type perovskite have distinct dependences on mechanical and electric boundary conditions, both of which involve oxygen octahedral rotation and tilt. The above difference can be used to stabilize the highly polar BFO-type structure in many CTO-type perovskite materials.

Nonadiabatic Born Effective Charges in Metals and the Drude Weight.

In insulators, Born effective charges describe the electrical polarization induced by the displacement of individual atomic sublattices. Such a physical property is at first sight irrelevant for metals and doped semiconductors, where the macroscopic polarization is ill defined. Here we show that, in clean conductors, going beyond the adiabatic approximation results in nonadiabatic Born effective charges that are well defined in the low-frequency limit. In addition, we find that the sublattice sum of the nonadiabatic Born effective charges does not vanish as it does in the insulating case, but instead is proportional to the Drude weight. We demonstrate these formal results with density functional perturbation theory calculations of Al and electron-doped SnS_{2} and SrTiO_{3}.

Direct and Converse Flexoelectricity in Two-Dimensional Materials.

Building on recent developments in electronic-structure methods, we define and calculate the flexoelectric response of two-dimensional (2D) materials fully from first principles. In particular, we show that the open-circuit voltage response to a flexural deformation is a fundamental linear-response property of the crystal that can be calculated within the primitive unit cell of the flat configuration. Applications to graphene, silicene, phosphorene, boron nitride, and transition-metal dichalcogenide monolayers reveal that two distinct contributions exist, respectively of purely electronic and lattice-mediated nature. Within the former, we identify a key metric term, consisting in the quadrupolar moment of the unperturbed charge density. We propose a simple continuum model to connect our findings with the available experimental measurements of the converse flexoelectric effect.

Switching a Polar Metal via Strain Gradients.

Although rare, spontaneous breakdown of inversion symmetry sometimes occurs in a material which is metallic: these are commonly known as polar metals or ferroelectric metals. Their polarization, however, is difficult to switch via an electric field, which limits the experimental control over band topology. Here we investigate, via first-principles theory, flexoelectricity as a possible way around this obstacle with the well-known polar metal LiOsO_{3}. The flexocoupling coefficients are computed for this metal with high accuracy with an approach based on real-space sums of the interatomic force constants. A Landau-Ginzburg-Devonshire-type first-principles Hamiltonian is built and a critical bending radius to switch the material is estimated, whose order of magnitude is comparable to that of BaTiO_{3}.

Using High Multipolar Orders to Reconstruct the Sound Velocity in Piezoelectrics from Lattice Dynamics.

Information over the phonon band structure is crucial to predicting many thermodynamic properties of materials, such as thermal transport coefficients. Highly accurate phonon dispersion curves can be, in principle, calculated in the framework of density-functional perturbation theory. However, well-established techniques can run into trouble (or even catastrophically fail) in the case of piezoelectric materials, where the acoustic branches hardly reproduce the physically correct sound velocity. Here we identify the culprit in the higher-order multipolar interactions between atoms and demonstrate an effective procedure that fixes the aforementioned issue. Our strategy drastically improves the predictive power of perturbative lattice-dynamical calculations in piezoelectric crystals and is directly implementable for high-throughput generation of materials databases.

Electron-Phonon beyond Fröhlich: Dynamical Quadrupoles in Polar and Covalent Solids.

We include the treatment of quadrupolar fields beyond the Fröhlich interaction in the first-principles electron-phonon vertex in semiconductors. Such quadrupolar fields induce long-range interactions that have to be taken into account for accurate physical results. We apply our formalism to Si (nonpolar), GaAs, and GaP (polar) and demonstrate that electron mobilities show large errors if dynamical quadrupoles are not properly treated.

Visualization of moiré superlattices.

Moiré superlattices in van der Waals heterostructures have given rise to a number of emergent electronic phenomena due to the interplay between atomic structure and electron correlations. Indeed, electrons in these structures have been recently found to exhibit a number of emergent properties that the individual layers themselves do not exhibit. This includes superconductivity1,2, magnetism3, topological edge states4,5, exciton trapping6 and correlated insulator phases7. However, the lack of a straightforward technique to characterize the local structure of moiré superlattices has thus far impeded progress in the field. In this work we describe a simple, room-temperature, ambient method to visualize real-space moiré superlattices with sub-5-nm spatial resolution in a variety of twisted van der Waals heterostructures including, but not limited to, conducting graphene, insulating boron nitride and semiconducting transition metal dichalcogenides. Our method uses piezoresponse force microscopy, an atomic force microscope modality that locally measures electromechanical surface deformation. We find that all moiré superlattices, regardless of whether the constituent layers have inversion symmetry, exhibit a mechanical response to out-of-plane electric fields. This response is closely tied to flexoelectricity wherein electric polarization and electromechanical response is induced through strain gradients present within moiré superlattices. Therefore, moiré superlattices of two-dimensional materials manifest themselves as an interlinked network of polarized domain walls in a non-polar background matrix.

ABINIT: Overview and focus on selected capabilities.

abinit is probably the first electronic-structure package to have been released under an open-source license about 20 years ago. It implements density functional theory, density-functional perturbation theory (DFPT), many-body perturbation theory (GW approximation and Bethe-Salpeter equation), and more specific or advanced formalisms, such as dynamical mean-field theory (DMFT) and the "temperature-dependent effective potential" approach for anharmonic effects. Relying on planewaves for the representation of wavefunctions, density, and other space-dependent quantities, with pseudopotentials or projector-augmented waves (PAWs), it is well suited for the study of periodic materials, although nanostructures and molecules can be treated with the supercell technique. The present article starts with a brief description of the project, a summary of the theories upon which abinit relies, and a list of the associated capabilities. It then focuses on selected capabilities that might not be present in the majority of electronic structure packages either among planewave codes or, in general, treatment of strongly correlated materials using DMFT; materials under finite electric fields; properties at nuclei (electric field gradient, Mössbauer shifts, and orbital magnetization); positron annihilation; Raman intensities and electro-optic effect; and DFPT calculations of response to strain perturbation (elastic constants and piezoelectricity), spatial dispersion (flexoelectricity), electronic mobility, temperature dependence of the gap, and spin-magnetic-field perturbation. The abinit DFPT implementation is very general, including systems with van der Waals interaction or with noncollinear magnetism. Community projects are also described: generation of pseudopotential and PAW datasets, high-throughput calculations (databases of phonon band structure, second-harmonic generation, and GW computations of bandgaps), and the library libpaw. abinit has strong links with many other software projects that are briefly mentioned.

Photoflexoelectric effect in halide perovskites.

Harvesting environmental energy to generate electricity is a key scientific and technological endeavour of our time. Photovoltaic conversion and electromechanical transduction are two common energy-harvesting mechanisms based on, respectively, semiconducting junctions and piezoelectric insulators. However, the different material families on which these transduction phenomena are based complicate their integration into single devices. Here we demonstrate that halide perovskites, a family of highly efficient photovoltaic materials1-3, display a photoflexoelectric effect whereby, under a combination of illumination and oscillation driven by a piezoelectric actuator, they generate orders of magnitude higher flexoelectricity than in the dark. We also show that photoflexoelectricity is not exclusive to halides but a general property of semiconductors that potentially enables simultaneous electromechanical and photovoltaic transduction and harvesting in unison from multiple energy inputs.

Observation of Uncompensated Bound Charges at Improper Ferroelectric Domain Walls.

Low-temperature electrostatic force microscopy (EFM) is used to probe unconventional domain walls in the improper ferroelectric semiconductor Er0.99Ca0.01MnO3 down to cryogenic temperatures. The low-temperature EFM maps reveal pronounced electric far fields generated by partially uncompensated domain-wall bound charges. Positively and negatively charged walls display qualitatively different fields as a function of temperature, which we explain based on different screening mechanisms and the corresponding relaxation time of the mobile carriers. Our results demonstrate domain walls in improper ferroelectrics as a unique example of natural interfaces that are stable against the emergence of electrically uncompensated bound charges. The outstanding robustness of improper ferroelectric domain walls in conjunction with their electronic versatility brings us an important step closer to the development of durable and ultrasmall electronic components for next-generation nanotechnology.

Low-Temperature Dielectric Anisotropy Driven by an Antiferroelectric Mode in SrTiO_{3}.

Strontium titanate (SrTiO_{3}) is the quintessential material for oxide electronics. One of its hallmark features is the transition, driven by antiferrodistortive (AFD) lattice modes, from a cubic to a ferroelastic low-temperature phase. Here we investigate the evolution of the ferroelastic twin walls upon application of an electric field. Remarkably, we find that the dielectric anisotropy of tetragonal SrTiO_{3}, rather than the intrinsic domain wall polarity, is the main driving force for the motion of the twins. Based on a combined first-principles and Landau-theory analysis, we show that such anisotropy is dominated by a trilinear coupling between the polarization, the AFD lattice tilts, and a previously overlooked antiferroelectric (AFE) mode. We identify the latter AFE phonon with the so-called "R mode" at ∼440 cm^{-1}, which was previously detected in IR experiments, but whose microscopic nature was unknown.

Erratum: Macroscopic Polarization from Antiferrodistortive Cycloids in Ferroelastic SrTiO_{3} [Phys. Rev. Lett. 119, 137601 (2017)].

This corrects the article DOI: 10.1103/PhysRevLett.119.137601.

Macroscopic Polarization from Antiferrodistortive Cycloids in Ferroelastic SrTiO_{3}.

Based on a first-principles based multiscale approach, we study the polarity P of ferroelastic twin walls in SrTiO_{3}. In addition to flexoelectricity, which was pointed out before, we identify two new mechanisms that crucially contribute to P: a direct "rotopolar" coupling to the gradients of the antiferrodistortive oxygen tilts, and a trilinear coupling that is mediated by the antiferroelectric displacement of the Ti atoms. Remarkably, the rotopolar coupling presents a strong analogy to the mechanism that generates a spontaneous polarization in cycloidal magnets. We show how this similarity allows for a breakdown of macroscopic inversion symmetry (and therefore a macroscopic polarization) in a periodic sequence of parallel twins. These results open new avenues towards engineering pyroelectricity or piezoelectricity in nominally nonpolar ferroic materials.

Large Flexoelectric Anisotropy in Paraelectric Barium Titanate.

The bending-induced polarization of barium titanate single crystals has been measured with an aim to elucidate the origin of the large difference between theoretically predicted and experimentally measured flexoelectricity in this material. The results indicate that part of the difference is due to polar regions (short-range order) that exist above T(C) and up to T*≈200-225 °C. Above T*, however, the flexovoltage coefficient still shows an unexpectedly large anisotropy for a cubic material, with (001)-oriented crystals displaying 10 times more flexoelectricity than (111)-oriented crystals. Theoretical analysis shows that this anisotropy cannot be a bulk property, and we therefore interpret it as indirect evidence for the theoretically predicted but experimentally elusive contribution of surface piezoelectricity to macroscopic bending-induced polarization.