56 pages, 12 figures, 7 tables. To be published in "Flexoelectricity in Solids: From Theory to Applications", A.K. Tagantsev and P. Yudin, eds. (World Scientific, Singapore)
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.
We develop a general and unified first-principles theory of piezoelectric and flexoelectric tensor, formulated in such a way that the tensor elements can be computed directly in the context of density-functional calculations, including electronic and lattice contributions. We introduce a practical supercell-based methods for calculating the flexoelectric coefficients from first principles, and demonstrate them by computing the coefficients for a variety of cubic insulating materials, including C, Si, MgO, NaCl, CsCl, BaZrO3, BaTiO3, PbTiO3 and SrTiO3.
We demonstrate that the frozen-ion contribution to the flexoelectric coefficient is given solely in terms of the sum of third moments of the charge density distortions induced by atomic displacements, even for ferroelectric or piezoelectric materials. We introduce several practical supercell-based methods for calculating these coefficients from first principles, and demonstrate them by computing the coefficients for C, Si, MgO, NaCl, SrTiO$_3$, BaTiO$_3$, and PbTiO$_3$. Three important subtleties associated with pseudopotentials, the treatment of surfaces, and the calculation of transverse com…
Based on recent developments in the first-principles theory of flexoelectricity, we generalize the concept of absolute deformation potential to arbitrary nonpiezoelectric insulators and deformation fields. To demonstrate our formalism, we calculate the response of the band edges of SrTiO$_3$ to both dynamic (sound waves) and static (bending) mechanical loads, respectively at the bulk level and in a slab geometry. Our results have important implications for the understanding of strain-gradient-related phenomena in crystalline insulators, formally unifying the description of band-structure and e…
We present the derivation and code implementation of a first-principles methodology to calculate the lattice-mediated contributions to the bulk flexoelectric tensor. The approach is based on our recent analytical long-wavelength extension of density-functional perturbation theory [Royo and Stengel, Phys. Rev. X 9, 021050 (2019)], and avoids the cumbersome numerical derivatives with respect to the wave vector that were adopted in previous implementations. To substantiate our results, we revisit and numerically validate the sum rules that relate flexoelectricity and uniform elasticity by general…
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-d…
The polarization response of a material to a strain gradient, known as flexoelectricity, holds great promise for novel electromechanical applications. Despite considerable recent progress, however, the effect remains poorly understood. From both the fundamental and practical viewpoints, it is of crucial importance to know whether the coupling coefficients are primarily governed by the properties of the bulk material or by the details of the sample surface. Here we provide, by means of first-principles calculations, quantitative evidence supporting the latter scenario. In particular, we demonst…
Density-functional perturbation theory (DFPT) is nowadays the method of choice for the accurate computation of linear and non-linear 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 wavevector, ${\bf q}$, at essentially the same computational cost as the lattice-periodic case. Here we show that ${\bf q}$ can be formally treated as a perturbation parameter, and used in conjunction with established results of perturbation theory (e.g. the "2n+1" theor…
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, BN and transition-metal dichalcogenide monolayers reveal that two distinct contributions exist, respectively of purely electronic and lattice-medi…
We derive the complete flexoelectric tensor, including electronic and lattice-mediated effects, of an arbitrary insulator in terms of the microscopic linear response of the crystal to atomic displacements. The basic ingredient, which can be readily calculated from first principles in the framework of density-functional perturbation theory, is the quantum-mechanical probability current response to a long-wavelength acoustic phonon. Its second-order Taylor expansion in the wavevector q around the Gamma (q=0) point in the Brillouin zone naturally yields the flexoelectric tensor. At order one in q…
We present an ab initio simulation of $90^{\circ}$ ferroelastic twins that were recently observed in methyl ammonium lead iodide. There are two inequivalent types of $90^{\circ}$ walls that we calculate to act as either electron or hole sinks which suggests a possible route to enhancing charge carrier separation in photovoltaic devices. Despite separating non-polar domains, we show these walls to have a substantial in-plane polarisation of $\sim 6 \phantom{|} μ\text{C}\phantom{|}\text{cm}^{-2}$, due in part to flexoelectricity. We suggest this in turn could allow for the photoferroic effect an…
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, cannot be switched via an electric field, which limits the experimental control over band topology. Here we shall 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 a completely new approach based on real-space sums of th…
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 (AFD) 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 si…
Flexoelectricity is the polar response of an insulator to strain gradients such as bending. While the size dependence of this effect makes it weak in bulk systems in comparison to piezoelectricity, it suggests that it plays a bigger role in nanoscale systems such as thin films and nanotubes (NTs). In this paper we demonstrate using first-principles calculations that the walls of carbon nanotubes (CNTs) and transition metal dichalcogenide nanotubes (TMD NTs) are polarized in the radial direction, the strength of the polarization increasing as the size of the NT decreases. For CNTs and TMD NTs w…
First-principles calculations combining density functional theory and many-body perturbation theory can provide microscopic insight into the dynamics of electrons and phonons in materials. We review this theoretical and computational framework, focusing on perturbative treatments of scattering, dynamics and transport of coupled electrons and phonons. We discuss application of these first-principles calculations to electronics, lighting, spectroscopy and renewable energy.
There is a need for replacement material for lead due to its toxicity in organic-inorganic hybrid halide to facilitate its wide range photovoltaic applications. Here, first-principle calculations are used to screen some of the elements from the periodic table.
Ferroelectricity in the Dion-Jacobson CsBiNb$_2$O$_7$ from first principles
我们从第一性原理研究了Dion-Jacobson CsBiNb $_2$ O $_7$中的铁电性。利用群论分析和第一性原理密度泛函计算的总能量和声子，我们进行了系统的研究周围的顺电原型相的能量表面。我们的研究结果表明，$_2$是一个铁电体的极化P $_s$ =40 $μ$ C cm $^{-2}$。我们提出进一步的实验来澄清这一点。
Using first principles density functional calculations, together with exact diagonalization of Fe-Mo Hamiltonian constructed in a first principles Wannier function basis, we studied the electronic structure of La doped double perovskite compound Sr$_2$FeMoO$_6$. Our calculation show stabilization of kinetic energy driven antiferromagnetic phase for La rich compounds, in agreement with the results obtained on the basis of previous model calculations.
Discoveries of topological states and topological materials reshape our understanding of physics and materials over the last 15 years. First-principles calculations have been playing a significant role in bridging the theory of topology and experiments by predicting realistic topological materials. In this article, we overview the first-principles methodology on topological quantum materials. First, we unify different concepts of topological states in the same band inversion scenario. Then, we discuss the topology using first-principles band structures and newly-established topological materia…
We report detailed experimental investigation of the transport and magnetic properties of orthorhombic NiSi along with first principles studies of this phase and related nickel silicides. Neutron scattering shows no evidence for magnetism, in agreement with first principles calculations. Comparison of first principles results and experimental results from our measurements and literature show a weak electron phonon coupling. We discuss transport and other properties of NiSi and find behavior characteristic of a weak correlated metal far from magnetism. Trends among the nickel silicides as a fun…
We present results of an extensive set of first-principles density functional theory calculations of point defect formation, binding and clustering energies in austenitic Fe with dilute concentrations of Cr and Ni solutes.
We present a new first-principle theory for the calculation of the macroscopic second-order susceptibility chi^(2), based on the Time-Dependent Density-Functional Theory approach. Our method allows to include straightforwardly the many-body effects. We apply the theory to the computation of the Second-Harmonic Generation spectroscopy, showing a very good agreement with experiment for cubic semiconductor GaAs.
An extensive set of first-principles density functional theory calculations have been performed to study the behaviour of He, C and N solutes in austenite, dilute Fe-Cr-Ni austenitic alloys and Ni in order to investigate their influence on the microstructural evolution of austenitic steel alloys under irradiation.
The electronic and magnetic properties of transition-metal doped $β$-Ge3N4 have been studied using first-principles calculations. The results show that the substitutional transition-metal impurities tend to cluster. The V and Cr doped Ge3N4 compounds are ferromagnetic semiconductors, while the compounds with Mn and Fe doping show a half-metallic ferromagnetic character.
We show carriers dynamics on bulk Silicon in the sub pico-second time scale. The results are obtained from a first-principles implementation of the the Kadanoff-Baym equations within the generalized Baym-Kadanoff ansatz and the complete collision approximation. The resulting scattering term is similar to the scattering described within the semi-classical Boltzmann equation.
Using first principles calculations, we present a magnetostructural effect in the BiFeO3-BiMnO3 nanocheckerboard that is not found in either bulk parent compound or in BiFeO3-BiMnO3 superlattices. We also demonstrate that the atomic-scale checkerboard has a multiferroic ground state with the desired properties of each constitutent material: polar and ferrimagnetic due to BiFeO3 and BiMnO3 respectively.
Interest in first-principles calculations within the multiferroic community has been rapidly on the rise over the last decade. Initially considered as a powerful support to explain experimentally observed behaviours, the trend has evolved and, nowadays, density functional theory calculations has become also an essential predicting tool for identifying original rules to achieve multiferroism and design new magneto-electric compounds. This chapter aims to highlight the key advances in the field of multiferroics for which first-principles methods have contributed significantly. The essential theo…
Based on first principles calculations, we predict and characterize the flexibility of two aluminium-based Metal-Organic Frameworks (MOFs), CAU-13 and NOTT-300. Both materials have a wine rack topology similar to that of MIL-53(Al), the archetypal breathing MOF, yet their flexibility has not been demonstrated so far.
A systematic first principles evaluation of the insertion behavior of multi-valent cations in orthorhombic V$_2$O$_5$ is performed. Layer spacing, voltage, phase stability, and ion mobility are computed for Li$^+$, Mg$^{2+}$, Zn$^{2+}$, Ca$^{2+}$, and Al$^{3+}$ intercalation in the $α$ and $δ$ polymorphs.
Phonon plays essential roles in dynamical behaviors and thermal properties, which are central topics in fundamental issues of materials science. The importance of first principles phonon calculations cannot be overly emphasized. Phonopy is an open source code for such calculations launched by the present authors, which has been world-widely used. Here we demonstrate phonon properties with fundamental equations and show examples how the phonon calculations are applied in materials science.
Efficient method for magnetic structure exploration based on first-principles calculations: application to MnO and hexagonal ferrites SrFe$_{12}$O$_{19}$
The structural, elastic, magnetic properties, as well as electronic structure and chemical bonding picture of new oxide 3d1-perovskite BaVO3, recently synthesized, were systematically investigated involving the first-principles FLAPW-GGA calculations. The obtained results are discussed in comparison with available experimental data, as well as with those obtained before for isostructural and isoelectronic SrVO3 perovskite.
Melting of MgO was studied using a multicanonical ensemble method combined with a first-principles calculation. This approach has been successively performed by using a rather simple functional form for a model inter-atomic potential that is determined from first-principles and a novel approximation treating auxiliary degrees of freedom, such as electron thermal excitations, within a multicanonical ensemble method. Although a rather simple model potential was used, this approach could distinguish differences due to the exchange-correlation potential used in the first-principles calculations. T…
In search of a reliable methodology for the prediction of light absorption and emission of Ce$^{3+}$-doped luminescent materials, 13 representative materials are studied with first-principles and semiempirical approaches. In the first-principles approach, that combines constrained density-functional theory and $Δ$SCF, the atomic positions are obtained for both ground and excited states of the Ce$^{3+}$ ion. The structural information is fed into Dorenbos' semiempirical model. Absorption and emission energies are calculated with both methods and compared with experiment. The first-principles ap…
Diffusion Monte Carlo is one of the most accurate scalable many-body methods for solid state systems. However, to date, spin-orbit interactions have not been incorporated into these calcualtions at a first-principles level; only having been applied to small systems. In this technique, we use explicitly correlated first-principles quantum Monte Carlo calculations to derive an effective spin-orbit model Hamiltonian. The simplified model Hamiltonian is then solved to obtain the energetics of the system. To demonstrate this method, benchmark studies are performed in main-group atoms and monolayer …
We performed first principles calculations for epitaxially strained orthorhombic CaTiO$_3$. The computational results reveal the existence of a metastable ferroelectric phase at compressive strain with unexpected in-plane polarization. Symmetry analysis indicates that two distortion modes at the X point combine to induce the polarization, leading to characterization as a hybrid improper ferroelectric. Our work demonstrates a mechanism for improper ferroelectricity in simple perovskites without the need for symmetry lowering by layering or cation ordering.
In order to clarify phase relation of Zn2SiO4 system, first-principles DFT calculations of 11 phases were conducted. We confirmed that phases III and IV are retrograde phases. Instead, Na2CrO4- and Ag2CrO4-structured phases are most likely candidate structures for high-pressure phases of III and IV, respectively. A transition of phase II to spinel found during optimization was discussed in relation to similar transition known for nitrides.
We investigate the temperature and pressure dependences of the electrical resistivity for bcc and hcp Fe using the low-order variational approximation and theoretical transport spectral functions calculated from first principles linear response linear-muffin-tin-orbital method in the generalized-gradient approximation. The calculated values are in close agreement with available experimental data, and show strong increase with temperature and decrease with pressure. We also discuss the behavior of the electrical resistivity for the bcc -> hcp phase transition.
