Modern Theory Of Polarization Research Articles

Electric Polarization from a Many-Body Neural Network Ansatz.

Abinitio calculation of dielectric response with high-accuracy electronic structure methods is a long-standing problem, for which mean-field approaches are widely used and electron correlations are mostly treated via approximated functionals. Here we employ a neural network wave function ansatz combined with quantum MonteCarlo method to incorporate correlations into polarization calculations. On a variety of systems, including isolated atoms, one-dimensional chains, two-dimensional slabs, and three-dimensional cubes, the calculated results outperform conventional density functional theory and are consistent with the most accurate calculations and experimental data. Furthermore, we have studied the out-of-plane dielectric constant of bilayer graphene using our method and reestablished its thickness dependence. Overall, this approach provides a powerful tool to accurately describe electron correlation in the modern theory of polarization.

Nonzero spontaneous electric polarization in metals: novel predictive methods and applications

Ferroelectricity in metals has advanced since the initial discovery of nonmagnetic ferroelectric-like metal LiOsO_3, anchored in the Anderson and Blount prediction. However, evaluating the spontaneous electric polarization (SEP) of this metal has been hindered by experimental and theoretical obstacles. The experimental challenge arises from difficulties in switching polarization using an external electric field, while the theoretical limitation lies in existing methods applicable only to nonmetals. Zabalo and Stengel (Phys Rev Lett 126:127601, 2021, https://doi.org/10.1103/PhysRevLett.126.127601) addressed the experimental obstacle by proposing flexoelectricity as an alternative for practical polarization switching in LiOsO_3, which requires a critical bending radius similar to BaTiO_3. In this study, we focus on resolving the theoretical obstacle by modifying the Berry phase and Wannier functions approaches within density functional theory plus modern theory of polarization. By employing these modifications, we calculate the SEP of LiOsO_3, comparable to the polarization of BaTiO_3. We validate our predictions using various ways. This study confirms the coexistence of ferroelectricity and metallicity in this new class of ferroelectric-like metals. Moreover, by addressing the theoretical limitation and providing new insights into polarization properties, our study complements the experimental flexoelectricity proposal and opens avenues for further exploration and manipulation of polarization characteristics. The developed approaches, incorporating modified Berry phase and Wannier function techniques, offer promising opportunities for studying and designing novel materials, including bio- and nano-ferroelectric-like metals. This study contributes to the advancement of ferroelectricity in metals and provides a foundation for future research in this exciting field.

Extended planar defects of oxygen vacancies in ferroelectric hbox {BaTiO}_3 and impact on ferroelectricity

Extended defects of vacancies in ferroelectrics (FE), where vacancies spread over an extended space, are of critical importance in terms of understanding the long-standing problems such as polarization fatigue and aging. However, extended defects in FEs are poorly understood. Here we investigate the extended planar oxygen vacancies in ferroelectric hbox {BaTiO}_3 using density functional theory and the modern theory of polarization. Oxygen vacancies of different charge states, namely {textrm{V}}^{2+}_{{textrm{O}}}, {textrm{V}}^{1+}_{{textrm{O}}}, and {textrm{V}}^{0}_{{textrm{O}}}, are studied. We obtain interesting results such as: (i) The formation energy of planar {textrm{V}}^{2+}_{{textrm{O}}} vacancies can be very small (merely 0.54 eV) even under the oxygen-rich condition, which is considerably smaller than the formation energy (4.0 eV) of planar {textrm{V}}^{0}_{{textrm{O}}} vacancies; (ii) Planar {textrm{V}}^{2+}_{{textrm{O}}} vacancies drastically reduce the ferroelectric polarization in hbox {BaTiO}_3 by more than one order of magnitude, which provides a pivotal (theoretical) evidence that the planar oxygen vacancies could be the origin of polarization fatigue and imprinting. The polarization dead layer caused by planar oxygen vacancies is shown to be around 72 Å. Microscopic origin and insight, based on the local Ti-O relative displacements, are provided to understand these interesting phenomena.

Monolayer group IV monochalcogenides T-MX (M = Sn, Ge; X = S, Se) with fine piezoelectric performance and stability

Monolayer group monochalcogenides (MX; M = Sn, Ge; X = S, Se) in the orthogonal α-phase are excellent piezoelectric materials. In this study, a configuration with bonding features similar to the α-phase is proposed (T-phase) for monolayer MX using the first-principles method. Based on the modern theory of polarization, as implemented in Vienna Ab initio Simulation Package, the T-phase is determined to be an excellent piezoelectric phase for monolayer MX. The in-plane piezoelectric coefficient d11 of T-SnS is 452.3 pm/V, which is larger than that reported for most two-dimensional binary compounds in the α-phase, including α-SnSe (∼250 pm/V). The large piezoelectric coefficients of T-MX mainly stem from its distinctive puckered configuration, which make it extraordinarily flexible along the polarization direction. The study results suggest a possibility for designing high piezoelectric coefficient materials with MX, and the potential application of T-MX in the fields of energy collection and nanoelectromechanical systems needs to be analyzed in future studies.

Polarization jumps by breaking symmetries of two-dimensional Weyl semimetals

The electric polarization as a bulk quantity is described by the modern theory of polarization in insulating systems and cannot be defined in conducting systems. Upon a gradual change of a parameter in the system, the polarization always varies smoothly as long as the gap remains open. In this paper, we focus on the two-dimensional Weyl semimetal, which hosts Weyl nodes protected by symmetries, and study the behavior of the polarization when a symmetry-breaking term $M$ is introduced and a gap opens. We show that there can be a jump between $M\ensuremath{\rightarrow}{0}^{+}$ and ${0}^{\ensuremath{-}}$ limits. We find that the jump is universally described by the ``Weyl dipole'' representing how the Weyl nodes with monopole charges are displaced in the reciprocal space. Our result is applicable to general two-dimensional Weyl semimetals.

First-principles study on unidirectional proton transfer on anatase TiO2 (101) surface induced by external electric fields.

The electric field (EF) effect on hydrogen or proton transfer (PT) via hydroxyl groups on an anatase TiO2 (101) surface is examined using first-principles density functional theory and the modern theory of polarization. This study focuses on unidirectional surface PT caused by external EFs at various orientations toward the surface. The preferred PT pathway can change depending on the magnitude and direction of the EF. Detailed analysis reveals that the variation in the energy profile with the EF is significantly different from that determined by the classical electric work of an EF carrying a point charge. The EF effect on the energy profile of the PT is governed by the rearrangement of the chemical bond network at the interface between the water molecules and the surface.

Real-space many-body marker for correlated Z2 topological insulators

Taking the clue from the modern theory of polarization [R. Resta, Rev. Mod. Phys. {\bf 66}, 899 (1994)], we identify an operator to distinguish between ${\mathbb Z}_2$-even (trivial) and ${\mathbb Z}_2$-odd (topological) insulators in two spatial dimensions. Its definition extends the position operator [R. Resta and S. Sorella, Phys. Rev. Lett. {\bf 82}, 370 (1999)], which was introduced in one-dimensional systems. We first show a few examples of non-interacting models, where single-particle wave functions are defined and allow for a direct comparison with standard techniques on large system sizes. Then, we illustrate its applicability for an interacting model on a small cluster, where exact diagonalizations are available. Its formulation in the Fock space allows a direct computation of expectation values over the ground-state wave function (or any approximation of it), thus allowing us to investigate generic interacting systems, such as strongly-correlated topological insulators.

First-principles study on structural, electronic and ferroelectric properties of Bi2VO5.5 compound

A first-principles investigation of the origin of ferroelectricity in the Aurivillius compound Bi2VO5.5 is presented. Calculations with the density functional theory, in conjunction with the modern theory of polarization, allowed us to study the structural, electronic, and polar properties of two configurations built with oxygen vacancies, causing a charge imbalance and a subsequent displacement of the ions, generating two maximum polarizations, one of 14.75 μC/cm2 and one of 4.31 μC/cm2 along [011] direction. Electron localization function schemes were used to identify the asymmetry of charges in (001), (010) and (100) planes. The results obtained in this study establish that the origin of ferroelectricity is due to the displacement of the ions caused by oxygen vacancies and the asymmetric distribution of the isolated pair of Bi ions. On the other hand, the bandgap calculations and the results of Ps establish that Bi2VO5.5 is a candidate ferro-photovoltaic material.

Large Exciton-Driven Linear and Nonlinear Optical Processes in Monolayers of Nitrogen Arsenide and Nitrogen Antimonide

We demonstrate that atomically thin nitrogen-based binary group V wide band gap indirect semiconductors (β-NX (X = As, Sb)) embody 3-fold valley degenerated band structures and strong linear and nonlinear optical activities. Contrary to NAs, the fundamental optical absorption in NSb is quite resilient toward the temperature variations between 0 and 450 K. In the absence of lattice vibrations, exciton in NSb is, however, less strongly bound (1.30 eV) compared to the tighter case in NAs (1.62 eV), leading to a more delocalized Mott–Wannier-type texture. The inhomogeneous excitonic line widths for both monolayers within these temperatures are within the 100–400 meV range. The most significant nonlinear second harmonic optical coefficients (2ω resonances) in NAs and NSb monolayers are obtained as ∼636 and 270 pm/V at 3.2 eV (387 nm) and 2.6 eV (477 nm), respectively. We also present a detailed analysis of in-plane biaxial strain on these structures and found that tensile strain dynamically stabilizes structures with no loss in absorbance spectra (and does not influence exciton binding energy in NAs). The nonlinear coefficient also significantly improves at the two most important 810 and 1560 nm wavelengths compared to the cases offered by the monolayer transitional metal dichalcogenides. Our analyses originate from a fully ab initio G0W0+Bethe-Salpeter excited-state theory. The temperature-dependent linear absorption spectra are evaluated by including the electron–phonon self-energies, whereas the nonlinear spectra are treated using the modern theory of polarization within the same perturbative approach. Our reference findings provide important advanced characteristics for applications of two-dimensional β-NX (X = As, Sb) materials and should motivate further theoretical and experimental investigations of these interesting materials.

First-principles LCPAO approach for insulators under finite electric fields with forces

We propose a linear-combination-of-pseudo-atomic-orbitals scheme for a finite electric field method based on the modern theory of polarization. We derive the matrix elements of the effective potential for the static and homogeneous field and the corresponding terms of the forces on atoms. In addition, we successfully evaluated the static and electronic dielectric constants and Born effective charges of typical semiconducting and insulating materials. Our formalism will aid in the study of materials under electric fields.

First-principles indicators of ferroic parameters in epitaxial BiFeO3 and BiCrO3

Density-functional theory is used to validate spin-resolved and orbital-resolved metrics of localized electronic states to anticipate ferroic and dielectric properties of BiFeO3 and BiCrO3 under epitaxial strain. Using previous investigations of epitaxial phase stability in these systems, trends in properties such as spontaneous polarization and bandgap are compared to trends in atomic orbital occupation derived from projected density of states. Based on first principles theories of ferroic and dielectric properties, such as the Modern Theory of Polarization for spontaneous polarization or Goodenough–Kanamori theory for magnetic interactions, this work validates the sufficiency of metrics of localized electronic states to predict trends in multiple ferroic and dielectric properties. Capabilities of these metrics include the anticipation of the transition from G-Type to C-Type antiferromagnetism in BiFeO3 under 4.2% compressive epitaxial strain and the interval of C-Type antiferromagnetism from 3% to 7% tensile epitaxial strain in BiCrO3. The results of this work suggest a capability of localized electronic metrics to predict multiferroic characteristics in the BiXO3 systems under epitaxial strain, with single or mixed B-site occupation.

Electron accumulation and distribution at interfaces of hexagonal ScxAl1−xN/GaN- and ScxAl1−xN/InN-heterostructures

Electron charges and distribution profiles induced by polarization gradients at the interfaces of pseudomorphic, hexagonal ScxAl1−xN/GaN- and ScxAl1−xN/InN-heterostructures are simulated by using a Schrödinger–Poisson solver across the entire range of random and metal-face ScxAl1−xN-alloys, considering the transition from wurtzite to hexagonal layered crystal structure. In contrast to previous calculations of polarization-induced sheet charges, we use Dryer’s modern theory of polarization, which allows for consideration of the spontaneous polarization measured on ferroelectric ScxAl1−xN-layers. Because the sheet density of the electrons accumulating at the heterostructure interfaces can strongly depend both on the data set of the piezoelectric and structural coefficients and on the alloying region of the ScxAl1−xN-layers in which the transition from the wurtzite to the hexagonal layered crystal structure occurs, we have calculated the charge carrier sheet densities and profiles for three representative data sets and evaluated their relevance for devices. We predict electron sheet densities of (2.26±0.20)×1014cm−2 and (6.25±0.20)×1014cm−2 for all three sets of data for Ni/AlN/InN- and Ni/ScN/InN-heterostructures, respectively. We demonstrate that the polarization-induced interface charges of Ni/ScxAl1−xN/InN-heterostructures are always positive, tend to increase with increasing Sc-content, and can cause electron accumulations that lead to flooding of the triangular quantum wells at the semiconductor interface. We identify Ni/ScxAl1−xN/GaN-heterostructures with 0.13≤x≤0.19 as particularly promising candidates for the processing of energy-efficient high electron mobility transistors due to their missing or low mechanical strain and their large electron sheet densities between (4.11±0.20)×1013cm−2 and (6.37±0.20)×1013cm−2. Furthermore, we present simulation results of highly strained Ni/ScxAl1−xN/GaN-heterostructures for 0.81≤x≤1.0, which point to electron accumulations of up to (8.02±0.40)×1014cm−2. These heterostructures are not suitable for transistor devices, but they may be of great interest for the implementation of low impedance contacts.

Tuning the dielectric response in a nanocomposite material through nanoparticle morphology.

Ceramic materials such as metal oxides, mixed metal oxides and silicates, constitute a broadly-used, high-performance technology for electronic insulators. The introduction of metal cluster dopants and molecular-scale inclusions in a dielectric matrix provides an opportunity for manufacturing new high-κ solid-state dielectrics with tunable field–response properties. The quantum properties of these metallic nanoparticles depend strongly on their size and shape, a characteristic that can be exploited in changing the response properties of a material, whereas the small nanoparticle size can help limit the issues of conduction and current leakage. Here, we model the polarization of molecular-scale silver inclusions in a magnesium oxide matrix, using the Modern Theory of Polarization and Car–Parrinello Molecular Dynamics (CPMD). Details of the implementation are laid out, including handling of current jumps due to the distortion of the matrix during the simulation. Several trends in the dielectric response are considered in this work, including the effects of nanoparticle size, shape and orientation relative to the applied field. Dielectric permittivity enhancements of 30–100% are observed with inclusion sizes varying from 8 to 32 atoms, considering both rod-like and disk-like inclusions, with alignment either parallel or perpendicular to the external field.

Modeling of Ferroelectric Oxide Perovskites: From First to Second Principles

Taking a historical perspective, we provide a brief overview of the first-principles modeling of ferroelectric perovskite oxides over the past 30 years. We emphasize how the work done by a relatively small community on the fundamental understanding of ferroelectricity and related phenomena has been at the origin of consecutive theoretical breakthroughs, with an impact going often well beyond the limit of the ferroelectric community. In this context, we first review key theoretical advances such as the modern theory of polarization, the computation of functional properties as energy derivatives, the explicit treatment of finite fields, or the advent of second-principles methods to extend the length and timescale of the simulations. We then discuss how these have revolutionized our understanding of ferroelectricity and related phenomena in this technologically important class of compounds.

Unique Features of Polarization in Ferroelectric Ionic Conductors

AbstractFerroelectrics that are also ionic conductors offer possibilities for novel applications with high tunability, especially if the same atomic species causes both phenomena. In particular, at temperatures just below the Curie temperature, polarized states may be sustainable as the mobile species is driven in a controlled way over the energy barrier that governs ionic conduction, resulting in unique control of the polarization. This possibility is recently demonstrated in CuInP2S6, a layered ferroelectric ionic conductor in which Cu ions cause both ferroelectricity and ionic conduction. Here, it is shown that the commonly used approach to calculate the polarization of evolving atomic configurations in ferroelectrics using the modern theory of polarization, namely concerted (synchronous) migration of the displacing ions, is not well suited to describe the polarization evolution as the Cu ions cross the van der Waals gaps. An asynchronous Cu‐migration scheme is introduced, which reflects the physical process by which Cu ions migrate, resolves the difficulties, and describes the polarization evolution both for normal ferroelectric switching and for transitions across the van der Waals gaps, providing a single framework to discuss ferroelectric ionic conductors.

Polarization of arbitrary charge distributions: The classical electrodynamics perspective

The conventional definition of electric polarization as the “dipole moment per unit volume” is valid only for the special case of well-separated dipoles. An alternative general approach is to view polarization as a characteristic not of a single charge distribution but rather of an adiabatic transition between two nearby states. Polarization can then be rigorously defined as the integral of the current density over that transition. In contrast with the “Modern Theory of Polarization,” which is fully quantum-mechanical, in this paper polarization is considered from the classical perspective. Such treatment is less fundamental but simpler, has pedagogical advantages and, importantly, is subject to fewer constraints. Polarization can be rigorously and unambiguously defined for periodic or nonperiodic charge distributions, finite or infinite, microscale or macroscale, electrically neutral or non-neutral, continuous or discrete, at any temperature; polarization can be spontaneous or induced. A previous classical (non-quantum) analysis by Russakoff (Am J Phys 1970) was (i) limited to the Clausius–Mossotti/Lorenz–Lorentz model of molecular dipoles, and (ii) involves multipole expansions, which the analysis of this paper shows to be redundant. The traditional dipole model of polarization is a straightforward special case of the proposed definition. A number of illustrative examples are presented. • Review of models of electric polarization, with an emphasis on generality and rigor. • The definition of polarization as “the dipole moment per unit volume” is flawed. • Polarization is rigorously defined for a transition between two states, not for a single state. • Trade-offs between classical and quantum-mechanical theories are examined. • The classical theory is less fundamental but is subject to much fewer constraints. • A variety of examples are presented.

The Concept of Negative Capacitance in Ionically Conductive Van der Waals Ferroelectrics

Adv. Energy Mater. 2020, 10, 2001726 DOI: 10.1002/aenm.202001726 The polarization P(z) shown in Figure 1c in the original paper and reproduced here as Figure 1A was calculated by moving the Cu-atom sheets in a synchronous (concerted) way. The modern theory of polarization (MTP)[1] however, yields the two curves shown in Figure 1B, defined by P(z) = Pcalc(z) − Pref, where Pref are the polarizations for the Cu sheets at the mid-layer and mid-gap planes. In constructing Figure 1A, the red curve was mistakenly plotted as P(z) = Pref − Pcalc(z), which reversed its slope. Here it shown that a form of asynchronous Cu migration (ACM) is more appropriate to describe the experimental observations and results in the P(z) curve shown in Figure 1C. The markedly different behavior of the calculated synchronous Cu migration (SCM) and ACM P(z)'s can be traced to differences in the evolution of the Cu ions relative to the InP2S6 cages in the pertinent sequences of periodic unit cells. Midgap-to-midgap unit cells are adopted and the black curves in Figure 1B are compared with the ACM curve in Figure 1C. In the SCM, the Cu sheets always move from left to right relative to the stationary InP2S6 cages. Thus, P(z) rises monotonically in the entire unit cell and is then repeated periodically both on the z axis, as shown in Figure 1B, featuring a discontinuity from +25 to -25 μC/cm−2, and on the P axis without discontinuities (the MTP's polarization quanta,[1] not shown). In the ACM, as viewed in each unit cell, the average position of the Cu ions is identical to the actual positions of the SCM Cu sheets only while transiting within the layers from −HP to +HP. Thus, the SCM and ACM P(z)'s are identical only from −HP to +HP. From +HP on, however, the Cu ions transit across the vdW-gaps a fraction at a time, into the adjacent unit cells on the right. By periodicity, the same fractions of Cu ions enter each unit cell on the left. Thus, within each unit cell, the average position of the Cu ions appears to move from right to left, which leads to the calculated negative-slope P(z) in Figure 1C. Note that the negative-slope P(z) in effect replaces the discontinuity in the black curve in Figure 1B at the midgap planes with a gradual transition from +HP to −HP, in accord with the experimental data. Like the SCM curves, the ACM curve is also repeated periodically on the z and P axes. For a more detailed discussion of the asynchronous scheme and insights into the results, see Ref. [6]. The contents of this correction do not affect the analysis of the experimental data, and the conclusions in the original paper. The authors apologize for any inconvenience caused, they would also like to thank David Vanderbilt for inquiring about the slope of the red curve in Figure 1A and Raffaele Resta for valuable discussions.

Local approaches for electric dipole moments in periodic systems and their application to real-time time-dependent density functional theory.

Within periodic boundary conditions, the traditional quantum mechanical position operator is ill-defined, necessitating the use of alternative methods, most commonly the Berry phase formulation in the modern theory of polarization. Since any information about local properties is lost in this change of framework, the Berry phase formulation can only determine the total electric polarization of a system. Previous approaches toward recovering local electric dipole moments have been based on applying the conventional dipole moment operator to the centers of maximally localized Wannier functions (MLWFs). Recently, another approach to local electric dipole moments has been demonstrated in the field of subsystem density functional theory (DFT) embedding. We demonstrate in this work that this approach, aside from its use in ground state DFT-based molecular dynamics, can also be applied to obtain electric dipole moments during real-time propagated time-dependent DFT (RT-TDDFT). Moreover, we present an analogous approach to obtain local electric dipole moments from MLWFs, which enables subsystem analysis in cases where DFT embedding is not applicable. The techniques were implemented in the quantum chemistry software CP2K for the mixed Gaussian and plane wave method and applied to cis-diimide and water in the gas phase, cis-diimide in aqueous solution, and a liquid mixture of dimethyl carbonate and ethylene carbonate to obtain absorption and infrared spectra decomposed into localized subsystem contributions.

Universal properties of boundary and interface charges in multichannel one-dimensional models without symmetry constraints

The boundary charge that accumulates at the edge of a one-dimensional single-channel insulator is known to possess the universal property, that its change under a lattice shift towards the edge by one site is given by the sum of the average bulk electronic density and a topologically invariant contribution, restricted to the values $0$ and $-1$ [Phys. Rev. B 101, 165304 (2020)]. This quantized contribution is associated with particle-hole duality, ensures charge conservation and fixes the mod(1) ambiguity appearing in the Modern Theory of Polarization. In the present work we generalize the above-mentioned single-channel results to the multichannel case by employing the technique of boundary Green's functions. We show that the topological invariant associated with the change in boundary charge under a lattice shift in multichannel models can be expressed as a winding number of a certain combination of components of bulk Green's functions as function of the complex frequency, as it encircles the section of the energy axis that corresponds to the occupied part of the spectrum. We observe that this winding number is restricted to values ranging from $-N_c$ to $0$, where $N_c$ is the number of channels (orbitals) per site. Furthermore, we consider translationally invariant one-dimensional multichannel models with an impurity and introduce topological indices which correspond to the quantized charge that accumulates around said impurity. These invariants are again given in terms of winding numbers of combinations of components of bulk Green's functions. Through this construction we provide a rigorous mathematical proof of the so called nearsightedness principle formulated by W. Kohn [Phys. Rev. Lett. 76, 3168 (1996)] for noninteracting multichannel lattice models.

Giant Linear and Nonlinear Excitonic Responses in an Atomically Thin Indirect Semiconductor Nitrogen Phosphide

Large linear and nonlinear optical responses can be obtained from two-dimensional semiconductors with an indirect electronic gap. Here, we demonstrate exceptionally large exciton-driven responses such as the fundamental exciton binding energy (2 eV), zero-point band-gap renormalization (200 meV), and nonlinear second and third harmonic coefficients (800 pm/V and 1.4 × 10–18 m2/V2, respectively) from an atomically thin binary group-V nitrogen phosphide (NP) semiconductor. The influence of lattice vibrations on the absorption spectra unfolds strong electronic couplings to both LA and ZO-TO phonon modes. All the linear process analyses were computed using a fully ab initio-based G0W0 + Bethe–Salpeter equation approach that also includes the electron–phonon self-energies. The nonlinear processes were instead obtained using a real-time ab initio process flow after creating a coupling between the time-dependent external electric field and the correlated electrons within the modern theory of polarization and the same electron–hole interaction level.