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We combine synchrotron-based near-field infrared spectroscopy and first principles lattice dynamics calculations to explore the vibrational response of CrPS4 in bulk, few-, and single-layer form. Analysis of the mode pattern reveals a C2 polar + chiral space group, no symmetry crossover as a function of layer number, and a series of non-monotonic frequency shifts in which modes with significant intralayer character harden on approach to the ultra-thin limit whereas those containing interlayer motion or more complicated displacement patterns soften and show inflection points or steps. This is different from MnPS3 where phonons shift as 1/size2 and are sensitive to the three-fold rotation about the metal center that drives the symmetry crossover. We discuss these differences as well as implications for properties such as electric polarization in terms of presence or absence of the P–P dimer and other aspects of local structure, sheet density, and size of the van der Waals gap.

Using the ab initio embedded dynamical mean-field theory (eDMFT) approach, we study the effect of long-range magnetic ordering on the spectral properties in the binary transition metal oxides, and find that the most significant changes appear in the momentum resolved spectral functions, which sharpen into quite well-defined bands in the antiferromagnetic (AFM) phase. The strongest change across the transition is found at the topmost valence-band edge (VBE), which is commonly associated with the Zhang-Rice bound state. This VBE state strengthens in the AFM phase, but only for the minority spin component, which is subject to stronger fluctuations. A similar hybridized VBE state also appears in the DFT single-particle description of the AFM phase, but gets much stronger and acquires a well-defined energy in the eDMFT description.

The anomalous Hall effect (AHE) is a non-linear Hall effect appearing in magnetic conductors, boosted by internal magnetism beyond what is expected from the ordinary Hall effect. With the recent discovery of the quantized version of the AHE, the quantum anomalous Hall effect (QAHE), in Cr- or V-doped topological insulator (TI) (Sb,Bi)$_2$Te$_3$ thin films, the AHE in magnetic TIs has been attracting significant interest. However, one of the puzzles in this system has been that while Cr- or V-doped (Sb,Bi)$_2$Te$_3$ and V-doped Bi$_2$Se$_3$ exhibit AHE, Cr-doped Bi$_2$Se$_3$ has failed to exhibit even ferromagnetic AHE, the expected predecessor to the QAHE, though it is the first material predicted to exhibit the QAHE. Here, we have successfully implemented ferromagnetic AHE in Cr-doped Bi$_2$Se$_3$ thin films by utilizing a surface state engineering scheme. Surprisingly, the observed ferromagnetic AHE in the Cr-doped Bi$_2$Se$_3$ thin films exhibited only positive slope regardless of the carrier type. We show that this sign problem can be explained by the intrinsic Berry curvature of the system as calculated from a tight-binding model combined with a first-principles method., Comment: 24 pages, 5 figures

The polarization and piezoelectric response of the BiTe$X$ ($X$=Cl, Br, and I) layered tellurohalides are computed from first principles. The results confirm a mixed ionic-covalent character of the bonding, and demonstrate that the internal structure within each triple layer is only weakly affected by the external stress, while the changes in the charge distribution with stress produce a substantial negative piezoelectric response. This suggests a new mechanism for negative piezoelectric response that should remain robust even in ultra-thin film form in this class of materials.

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 SrTiO$_3$., Comment: 15 pages, 5 figures, 4 tables, 1 appendix

We report a comprehensive study on the surface structural and electronic properties of $\mathrm{TaT}{\mathrm{e}}_{2}$ at room temperature. The surface structure was investigated using both low energy electron diffraction intensity versus voltage and density functional theory calculations. The relaxed structures obtained from the two methods are in good agreement, which is very similar to the bulk, maintaining double zigzag trimer chains. The calculated density of states indicates that such structure originates from the trimer bonding states of the Ta ${d}_{xz}$ and ${d}_{xy}$ orbitals. This work will further provide new insights towards the understanding of the charge density wave phase transition in $\mathrm{TaT}{\mathrm{e}}_{2}$ at low temperature.

Over the past twenty-five years, mathematical concepts associated with geometric phases have come to occupy a central place in our modern understanding of the physics of electrons in solids. These 'Berry phases' describe the global phase acquired by a quantum state as the Hamiltonian is changed. Beginning at an elementary level, this book provides a pedagogical introduction to the important role of Berry phases and curvatures, and outlines their great influence upon many key properties of electrons in solids, including electric polarization, anomalous Hall conductivity, and the nature of the topological insulating state. It focuses on drawing connections between physical concepts and provides a solid framework for their integration, enabling researchers and students to explore and develop links to related fields. Computational examples and exercises throughout provide an added dimension to the book, giving readers the opportunity to explore the central concepts in a practical and engaging way.

In this study, we investigated theoretically the Mott-insulating phase of a deficient spinel chalcogenide GaV$_4$S$_8$, which is known to form a tetrahedral V$_4$S$_4$ cluster unit that results in molecular orbitals (MOs) with a narrow bandwidth in the noninteracting limit. We used a cluster extension of charge self-consistent embedded dynamical mean-field theory to study the impact of strong intra-cluster correlations on the spectral properties as well as the structural degrees of freedom of the system. We found that the strong tetrahedral clustering renders the atomic Mott picture ineffective, and that the resulting MO picture is essential to describe the Mott phase. It was also found that, while the spectral properties can be qualitatively described by the truncation of the Hilbert space down to the lowest-energy MO, a proper description of the structural degrees of freedom requires the inclusion of multi-MO correlations that span a larger energy window. Specifically, we found that the lowest-energy MO description overemphasizes the clustering tendency, while the inclusion of the Hund's coupling between the lower- and higher-energy MOs corrects this tendency, bringing the theoretically predicted crystal structure into good agreement with the experiment., 5 pages, 5 figures

Iridates abound with interesting magnetic behaviours because of their strong spin-orbit coupling. Sr$_3$NiIrO$_6$ brings together the spin-orbital entanglement of the Ir$^{4+}$ ion with a 3$d$ Ni cation and a one-dimensional crystal structure. It has a ferrimagnetic ground state with a 55 T coercive field. We perform a theoretical study of the magnetic interactions in this compound, and elucidate the role of anisotropic symmetric exchange as the source of its strong magnetic anisotropy. Our first-principles calculations reproduce the magnon spectra of this compound and predict a signature in the cross sections that can differentiate the anisotropic exchange from single-ion anisotopy., Comment: 7 pages, 5 figures

We report $\textit{ab-initio}$ density functional theory calculation and Raman scattering results to explore the electronic structure of Ba$_5$CuIr$_3$O$_{12}$ single crystals. This insulating iridate, consisting of face-sharing IrO$_6$ octahedra forming quasi-one-dimensional chains, cannot be described by the local $j_{\rm eff}$=1/2 moment picture commonly adopted for discussing electronic and magnetic properties of iridate compounds with IrO$_6$ octahedra. The shorter Ir-Ir distance in the face-sharing geometry, compared to corner- or edge-sharing structures, leads to strong covalency between neighboring Ir. Then this strong covalency results in the formation of molecular orbitals (MO) at each Ir trimers as the low-energy electronic degree of freedom. The theoretically predicted three-peak structure in the joint density of states, a distinct indication of deviation from the $j_{\rm eff}$=1/2 picture, is verified by observing the three-peak structure in the electronic excitation spectrum by Raman scattering., 5 pages, 5 figures, with a Supplementary Information

Transition metal phosphorous trichalcogenides, $M{\rm P}X_3$ ($M$ and $X$ being transition metal and chalcogen elements respectively), have been the focus of substantial interest recently because of their possible magnetism in the two-dimensional limit. Here we investigate material properties of the compounds with $M$ = Mn and Ni employing $\textit{ab-initio}$ density functional and dynamical mean-field calculations, especially their electronic behavior under external pressure in the paramagnetic phase. Mott metal-insulator transitions (MIT) are found to be a common feature for both compounds, but their lattice structures show drastically different behaviors depending on the relevant orbital degrees of freedom, i.e. $t_{\rm 2g}$ or $e_{g}$. MnPS$_3$ undergoes an isosymmetric structural transition by forming Mn-Mn dimers due to the strong direct overlap between the neighboring $t_{\rm 2g}$ orbitals, accompanied by a significant volume collapse and a spin-state transition. In contrast, NiPS$_3$ and NiPSe$_3$, with their active $e_g$ orbital degrees of freedom, do not show a structural change at the MIT pressure or deep in the metallic phase. Hence NiPS$_3$ and NiPSe$_3$ become rare examples of materials hosting electronic bandwidth-controlled Mott MITs, thus showing promise for ultrafast resistivity switching behavior., 5 pages, 4 figures

We construct a general metric-tensor framework for treating inhomogenous adiabatic deformations applied to crystalline insulators, by deriving an effective time-dependent Schr\"odinger equation in the undistorted frame. The response can be decomposed into "static" and "dynamic" terms that correspond, respectively, to the amplitude and the velocity of the distortion. We then focus on the dynamic contributon, which takes the form of a gauge field entering the effective Hamiltonian, in the linear-response limit. We uncover an intimate relation between the dynamic response to the rotational component of the inhomogeneous deformation and the diamagnetic response to a corresponding inhomogeneous magnetic field. We apply this formalism to the theory of flexoelectric response, where we resolve a previous puzzle by showing that the currents generated by the dynamic term, while real, generate no bound charges even at surfaces, and so may be dropped from a practical theory of flexoelectricity., Comment: 21 pages, 2 figures

Nexus metals represent a new type of topological material in which nodal lines merge at nexus points. Here, we propose novel networks in nexus systems through intertwining between nexus fermions and additional nodal lines. These nexus networks can be realized in several recently synthesized carbon honeycomb materials. In these carbon honeycombs, we demonstrate a phase transition between a nexus network and a system with triply-degenerate points and additional nodal lines. The Landau level spectra show unusual magnetic transport properties in the nexus networks. Our results pave the way toward realizations of new topological materials with novel transport properties beyond standard Weyl/Dirac semimetals.

Using the semiclassical theory of electron dynamics, we derive a gauge-invariant expression for the spin toroidization in a periodical crystal. We show that the spin toroidization is comprised of two contributions: one is due to the configuration of a classical spin array, while the other comes from the coordinate shift of the electron as spin carrier in response to the inhomogeneous magnetic field. We then establish a direct and elengant relation between our spin toroidization and the antisymmetric magnetoelectric polarizability in insulators. Finally, we demonstrate our spin toroidization in a tight-binding model and show that it is a genuine bulk quantity.

The flexoelectric effect refers to polarization induced in an insulator when a strain gradient is applied. We have developed a first-principles methodology based on density-functional perturbation theory to calculate the elements of the bulk, clamped-ion flexoelectric tensor. In order to determine the transverse and shear components directly from a unit cell calculation, we calculate the current density induced by the adiabatic atomic displacements of a long-wavelength acoustic phonon. Previous implementations based on the charge-density response required supercells to capture these components. Our density-functional-theory implementation requires the development of an expression for the current density that is valid for the case of nonlocal pseudopotentials, and long-wavelength phonon perturbations. We benchmark our methodology on simple systems of isolated noble gas atoms, and apply it to calculate the clamped-ion flexoelectric constants for a variety of technologically important cubic oxides. We also discuss some technical issues that are associated with the definition of current density in a nonlocal pseudopotential context, and their relevance to the calculation of macroscopic response properties of crystals., 23 pages, 3 figures

Axion insulators are magnetic topological insulators in which the non-trivial $\mathbb{Z}_2$ index is protected by inversion symmetry instead of time-reversal symmetry. The naturally gapped surfaces of axion insulators give rise to a half-quantized surface anomalous Hall conductivity (AHC), but the sign of the surface AHC cannot be determined from topological arguments. In this paper, we consider topological phenomena at the surface of an axion insulator. To be explicit, we construct a minimal tight-binding model on the pyrochlore lattice and investigate the all-in-all-out (AIAO) and ferromagnetic (FM) spin configurations. We also implement a recently proposed approach for calculating the surface AHC directly, which allows us to explore how the interplay between surface termination and magnetic ordering determines the sign of the half-quantized surface AHC. In the case of AIAO ordering, we show that it is possible to construct a topological state with no protected metallic states on boundaries of any dimension (surfaces, hinges, or corners), although chiral hinge modes do occur for many surface configurations. In the FM case, rotation of the magnetization by an external field offers a promising means of control of chiral hinge modes, which can also appear on surface steps or where bulk domain walls emerge at the surface., Comment: 13 pages, 10 figures

Recent developments in topological semimetals open a way to realize relativistic dispersions in condensed matter systems. One recently studied type of topological feature is the "triple nodal point" where three bands become degenerate. In contrast to Weyl and Dirac nodes, triple nodal points, which are protected by a rotational symmetry, have nodal lines attached, so that a characterization in terms of a chirality is not possible. Previous studies of triple nodal points considered nonmagnetic systems, although an artificial Zeeman splitting was used to probe the topological nature. Here instead we treat a ferromagnetic material, half-metallic GdN, where the splitting of the triple nodal points comes from the spin-orbit coupling. The size of the splitting ranges from 15 to 150 meV depending on the magnetization orientation, enabling a transition between a Weyl-point phase and a "nearly triple nodal point" phase that exhibits very similar surface spectra and transport properties compared to a true triple-node system. The rich topological surface states, manipulable via the orientation of the magnetization, make half-metallic GdN a promising platform for future investigations and applications.

A static electric field generates circulating currents at the surfaces of a magnetoelectric insulator. The anomalous Hall part of the surface conductivity tensor describing such bound currents can change by multiples of e2/h depending on the insulating surface preparation, and a bulk calculation does not fix its quantized part. To resolve this ambiguity, we develop a formalism for calculating the full surface anomalous Hall conductivity in a slab geometry. We identify a Berry-curvature term, closely related to the expression for the bulk anomalous Hall conductivity, whose value can change by quantized amounts by adjusting the surface Hamiltonian. In addition, the surface anomalous Hall conductivity contains a nongeometric part that does not depend on the surface preparation., This work was supported by the Forschungsstipendium Grant No. RA 3025/1-1 from the Deutsche Forschungsgemeinschaft (T.R.), by Grant No. FIS2016-77188-P from the Spanish Ministerio de Economía y Competitividad (T.R. and I.S.), and by NSF Grant No. DMR-1629059 (D. V.).

The unique properties of topological semimetals have strongly driven efforts to seek for new topological phases and related materials. Here, we identify a critical condition for the existence of intersecting nodal rings (INRs) in symmorphic crystals, and further classify all possible kinds of INRs which can be obtained in the layered semiconductors with Amm2 and Cmmm space group symmetries. Several honeycomb structures are suggested to be topological INR semimetals, including layered and "hidden" layered structures. Transitions between the three types of INRs, named as α, β, and γ type, can be driven by external strains in these structures. The resulting surface states and Landau-level structures, more complicated than those resulting from a simple nodal loop, are also discussed.

We introduce antiferroelectric topological insulators as a new class of functional materials in which an electric field can be used to control topological order and induce topological phase transitions. Using first principles methods, we predict that several alkali-MgBi orthorhombic members of an $ABC$ family of compounds are antiferroelectric topological insulators. We also show that epitaxial strain and hydrostatic pressure can be used to tune the topological order and the band gap of these $ABC$ compounds. Antiferroelectric topological insulators could enable precise control of topology using electric fields, enhancing the applicability of topological materials in electronics and spintronics.

We introduce antiferroelectric topological insulators as a new class of functional materials in which an electric field can be used to control topological order and induce topological phase transitions. Using first principles methods, we predict that several alkali-MgBi orthorhombic members of an ABC family of compounds are antiferroelectric topological insulators. We also show that epitaxial strain and hydrostatic pressure can be used to tune the topological order and the band gap of these ABC compounds. Antiferroelectric topological insulators could enable precise control of topology using electric fields, enhancing the applicability of topological materials in electronics and spintronics.

We study the temperature dependence of the Rashba-split bands in the bismuth tellurohalides BiTe$X$ $(X=$ I, Br, Cl) from first principles. We find that increasing temperature reduces the Rashba splitting, with the largest effect observed in BiTeI with a reduction of the Rashba parameter of $40$% when temperature increases from $0$ K to $300$ K. These results highlight the inadequacy of previous interpretations of the observed Rashba splitting in terms of static-lattice calculations alone. Notably, we find the opposite trend, a strengthening of the Rashba splitting with rising temperature, in the pressure-stabilized topological-insulator phase of BiTeI. We propose that the opposite trends with temperature on either side of the topological phase transition could be an experimental signature for identifying it. The predicted temperature dependence is consistent with optical conductivity measurements, and should also be observable using photoemission spectroscopy, which could provide further insights into the nature of spin splitting and topology in the bismuth tellurohalides., Comment: 10 pages, 5 figures

We study adatom-covered single layers of ${\mathrm{CrSiTe}}_{3}$ and ${\mathrm{CrGeTe}}_{3}$ using first-principles calculations based on hybrid functionals. We find that the insulating ground state of a monolayer of La (Lu) deposited on single-layer ${\mathrm{CrSiTe}}_{3}$ (${\mathrm{CrGeTe}}_{3}$) carries spontaneously generated current loops around the Cr sites. These ``flux states'' induce antiferromagnetically ordered orbital moments on the Cr sites and are also associated with nontrivial topological properties. The calculated Chern numbers for these systems are predicted to be $\ifmmode\pm\else\textpm\fi{}1$ even in the absence of spin-orbit coupling, with sizable gaps on the order of 100 meV. The flux states and the associated topological phases result from spontaneous time-reversal symmetry breaking due to the presence of nonlocal Coulomb interactions.

We study the effects of temperature on the band structure of the Bi$_2$Se$_3$ family of topological insulators using first-principles methods. Increasing temperature drives these materials towards the normal state, with similar contributions from thermal expansion and from electron-phonon coupling. The band gap changes with temperature reach $0.3$ eV at $600$ K, of similar size to the changes caused by electron correlation. Our results suggest that temperature-induced topological phase transitions should be observable near critical points of other external parameters., 5 pages, 3 figures

We present a general technique for capturing various non-trivial topologies in the band structure of materials, which often arise from spin-orbit coupling. The technique is aimed at insulators and semimetals. Of insulators, Chern, Z2, and crystalline topological insulators can be identified. Of semimetals, the technique captures non-trivial topologies associated with the presence of Weyl and Dirac points in the spectrum. A public software package -- Z2Pack -- based on this technique will be presented. Z2Pack is an easy-to-use, well documented Python package that computes topological invariants and illustrates non-trivial features of Berry curvature. It works as a post-processing tool with all major first-principles codes, as well as with tight-binding models. As such, it can be used to investigate materials with strong spin-orbit coupling.

The intense theoretical and experimental interest in topological insulators and semimetals has established band structure topology as a fundamental material property. Consequently, identifying band topologies has become an important, but often challenging problem, with no exhaustive solution at the present time. In this work we compile a series of techniques, some previously known, that allow for a solution to this problem for a large set of the possible band topologies. The method is based on tracking hybrid Wannier charge centers computed for relevant Bloch states, and it works at all levels of materials modeling: continuous k.p models, tight-binding models and ab initio calculations. We apply the method to compute and identify Chern, Z2 and crystalline topological insulators, as well as topological semimetal phases, using real material examples. Moreover, we provide a numerical implementation of this technique (the Z2Pack software package) that is ideally suited for high-throughput screening of materials databases for compounds with non-trivial topologies. We expect that our work will allow researchers to: (a) identify topological materials optimal for experimental probes, (b) classify existing compounds and (c) reveal materials that host novel, not yet described, topological states., The supplementary files (Z2Pack source and documentation) can be downloaded from http://z2pack.ethz.ch/supplementary.tar.gz

We combined high field optical spectroscopy and first principles calculations to analyze the electronic structure of ${\mathrm{Ni}}_{3}{\mathrm{TeO}}_{6}$ across the 53 K and 9 T magnetic transitions, both of which are accompanied by large changes in electric polarization. The color properties are sensitive to magnetic order due to field-induced changes in the crystal field environment, with those around Ni1 and Ni2 most affected. These findings advance the understanding of magnetoelectric coupling in materials in which magnetic $3d$ centers coexist with nonmagnetic heavy chalcogenide cations.

By means of density functional theory based calculations, we study the role of spin-orbit coupling in the new family of ABC hyperferroelectrics [Phys. Rev. Lett. 112, 127601 (2014)]. We unveil an extremely rich physics strongly linked to ferroelectric properties, ranging from the electric control of bulk Rashba effect to the existence of a three dimensional topological insulator phase, with concomitant topological surface states even in the ultrathin film limit. Moreover, we predict that the topological transition, as induced by alloying, is followed by a Weyl semi-metal phase of finite concentration extension, which is robust against disorder, putting forward hyperferroelectrics as promising candidates for spin-orbitronic applications., 5 pages, 3 figures

We study adatom-covered single layers of CrSiTe_{3} and CrGeTe_{3} using first-principles calculations based on hybrid functionals. We find that the insulating ground state of a monolayer of La (Lu) deposited on single-layer CrSiTe_{3} (CrGeTe_{3}) carries spontaneously generated current loops around the Cr sites. These "flux states" induce antiferromagnetically ordered orbital moments on the Cr sites and are also associated with nontrivial topological properties. The calculated Chern numbers for these systems are predicted to be ±1 even in the absence of spin-orbit coupling, with sizable gaps on the order of 100 meV. The flux states and the associated topological phases result from spontaneous time-reversal symmetry breaking due to the presence of nonlocal Coulomb interactions.

Based on first-principles calculations and an effective Hamiltonian analysis, we systematically investigate the electronic and topological properties of alkaline-earth compounds $AX_2$ ($A$=Ca, Sr, Ba; $X$=Si, Ge, Sn). Taking BaSn$_2$ as an example, we find that when spin-orbit coupling is ignored, these materials are three-dimensional topological nodal-line semimetals characterized by a snake-like nodal loop in three-dimensional momentum space. Drumhead-like surface states emerge either inside or outside the loop circle on the (001) surface depending on surface termination, while complicated double-drumhead-like surface states appear on the (010) surface. When spin-orbit coupling is included, the nodal line is gapped and the system becomes a topological insulator with Z$_2$ topological invariants (1;001). Since spin-orbit coupling effects are weak in light elements, the nodal-line semimetal phase is expected to be achievable in some alkaline-earth germanides and silicides., 13 pages, 5 figures

The search for new ferroelectric (FE) materials holds promise for broadening our understanding of FE mechanisms and extending the range of application of FE materials. Here we investigate a class of ABO3 and A2BB'O6 materials that can be derived from the X2O3 corundum structure by mixing two or three ordered cations on the X site. Most such corundum derivatives have a polar structure, but it is unclear whether the polarization is reversible, which is a requirement for a FE material. In this paper, we propose a method to study the FE reversal path of materials in the corundum derivative family. We first categorize the corundum derivatives into four classes and show that only two of these allow for the possibility of FE reversal. We then calculate the energy profile and energy barrier of the FE reversal path using first-principles density functional methods with a structural constraint. Furthermore, we identify several empirical measures that can provide a rule of thumb for estimating the energy barriers. Finally, the conditions under which the magnetic ordering is compatible with ferroelectricity are determined. These results lead us to predict several potentially new FE materials., 7 pages, 6 figures

NTRODUCTION The reproducibility of results is one of the underlying principles of science. An observation can only be accepted by the scientific community when it can be confirmed by independent studies. However, reproducibility does not come easily. Recent works have painfully exposed cases where previous conclusions were not upheld. The scrutiny of the scientific community has also turned to research involving computer programs, finding that reproducibility depends more strongly on implementation than commonly thought. These problems are especially relevant for property predictions of crystals and molecules, which hinge on precise computer implementations of the governing equation of quantum physics. RATIONALE This work focuses on density functional theory (DFT), a particularly popular quantum method for both academic and industrial applications. More than 15,000 DFT papers are published each year, and DFT is now increasingly used in an automated fashion to build large databases or apply multiscale techniques with limited human supervision. Therefore, the reproducibility of DFT results underlies the scientific credibility of a substantial fraction of current work in the natural and engineering sciences. A plethora of DFT computer codes are available, many of them differing considerably in their details of implementation, and each yielding a certain “precision” relative to other codes. How is one to decide for more than a few simple cases which code predicts the correct result, and which does not? We devised a procedure to assess the precision of DFT methods and used this to demonstrate reproducibility among many of the most widely used DFT codes. The essential part of this assessment is a pairwise comparison of a wide range of methods with respect to their predictions of the equations of state of the elemental crystals. This effort required the combined expertise of a large group of code developers and expert users. RESULTS We calculated equation-of-state data for four classes of DFT implementations, totaling 40 methods. Most codes agree very well, with pairwise differences that are comparable to those between different high-precision experiments. Even in the case of pseudization approaches, which largely depend on the atomic potentials used, a similar precision can be obtained as when using the full potential. The remaining deviations are due to subtle effects, such as specific numerical implementations or the treatment of relativistic terms. CONCLUSION Our work demonstrates that the precision of DFT implementations can be determined, even in the absence of one absolute reference code. Although this was not the case 5 to 10 years ago, most of the commonly used codes and methods are now found to predict essentially identical results. The established precision of DFT codes not only ensures the reproducibility of DFT predictions but also puts several past and future developments on a firmer footing. Any newly developed methodology can now be tested against the benchmark to verify whether it reaches the same level of precision. New DFT applications can be shown to have used a sufficiently precise method. Moreover, high-precision DFT calculations are essential for developing improvements to DFT methodology, such as new density functionals, which may further increase the predictive power of the simulations.

In typical topological insulator (TI) systems the TI is bordered by a non-TI insulator, and the surrounding conventional insulators, including vacuum, are not generally treated as part of the TI system. Here, we implement a material system where the roles are reversed, and the topological surface states form around the non-TI (instead of the TI) layers. This is realized by growing a layer of the tunable non-TI ${(\mathrm{B}{\mathrm{i}}_{1\ensuremath{-}x}\mathrm{I}{\mathrm{n}}_{x})}_{2}\mathrm{S}{\mathrm{e}}_{3}$ in between two layers of the TI $\mathrm{B}{\mathrm{i}}_{2}\mathrm{S}{\mathrm{e}}_{3}$ using the atomically precise molecular beam epitaxy technique. On this tunable inverse topological platform, we systematically vary the thickness and the composition of the ${(\mathrm{B}{\mathrm{i}}_{1\ensuremath{-}x}\mathrm{I}{\mathrm{n}}_{x})}_{2}\mathrm{S}{\mathrm{e}}_{3}$ layer and show that this tunes the coupling between the TI layers from strongly coupled metallic to weakly coupled, and finally to a fully decoupled insulating regime. This system can be used to probe the fundamental nature of coupling in TI materials and provides a tunable insulating layer for TI devices.

We review the role that first-principles calculations have played in understanding the effects of substrate-imposed misfit strain on epitaxially grown perovskite ferroelectric films. We do so by analyzing the case of BaTiO$_3$, complementing our previous publications on this subject with unpublished data to help explain in detail how these calculations are done. We also review similar studies in the literature for other perovskite ferroelectric-film materials., Comment: 14 pages, submitted to Phase Transitions

Domain walls are the topological defects that mediate polarization reversal in ferroelectrics, and they may exhibit quite different geometric and electronic structures compared to the bulk. Therefore, a detailed atomic-scale understanding of the static and dynamic properties of domain walls is of pressing interest. In this work, we use first-principles methods to study the structures of $180^{\circ}$ domain walls, both in their relaxed state and along the ferroelectric reversal pathway, in ferroelectrics belonging to the family of corundum derivatives. Our calculations predict their orientation, formation energy, and migration energy, and also identify important couplings between polarization, magnetization, and chirality at the domain walls. Finally, we point out a strong empirical correlation between the height of the domain-wall mediated polarization reversal barrier and the local bonding environment of the mobile $A$ cations as measured by bond valence sums. Our results thus provide both theoretical and empirical guidance to future searches for ferroelectric candidates in materials of the corundum derivative family., Comment: 8 pages, 7 figures

Accurate values for polarization discontinuities between pyroelectric materials are critical for understanding and designing the electronic properties of heterostructures. For wurtzite materials, the zincblende structure has been used in the literature as a reference to determine the effective spontaneous polarization constants. We show that, because the zincblende structure has a nonzero formal polarization, this method results in a spurious contribution to the spontaneous polarization differences between materials. In addition, we address the correct choice of "improper" versus "proper" piezoelectric constants. For the technologically important III-nitride materials GaN, AlN, and InN, we determine polarization discontinuities using a consistent reference based on the layered hexagonal structure and the correct choice of piezoelectric constants, and discuss the results in light of available experimental data.

We propose a new method for calculating the Chern-Simons orbital magnetoelectric coupling, conventionally parametrized in terms of a phase angle $\theta$. According to previous theories, $\theta$ can be expressed as a 3D Brillouin-zone integral of the Chern-Simons 3-form defined in terms of the occupied Bloch functions. Such an expression is valid only if a smooth and periodic gauge has been chosen in the entire Brillouin zone, and even then, convergence with respect to the $\mathbf{k}$-space mesh density can be difficult to obtain. In order to solve this problem, we propose to relax the periodicity condition in one direction (say, the $k_z$ direction) so that a gauge discontinuity is introduced on a 2D $\mathbf{k}$ plane normal to $k_z$. The total $\theta$ response then has contributions from both the integral of the Chern-Simons 3-form over the 3D bulk BZ and the gauge discontinuity expressed as a 2D integral over the $\mathbf{k}$ plane. Sometimes the boundary plane may be further divided into subregions by 1D "vortex loops" which make a third kind of contribution to the total $\theta$, expressed as a combination of Berry phases around the vortex loops. The total $\theta$ thus consists of three terms which can be expressed as integrals over 3D, 2D and 1D manifolds. When time-reversal symmetry is present and the gauge in the bulk BZ is chosen to respect this symmetry, both the 3D and 2D integrals vanish; the entire contribution then comes from the vortex-loop integral, which is either 0 or $\pi$ corresponding to the $\mathbb{Z}_2$ classification of 3D time-reversal invariant insulators. We demonstrate our method by applying it to the Fu-Kane-Mele model with an applied staggered Zeeman field., Comment: 16 pages, 5 figures, submitted to PRB

We combined high field optical spectroscopy and first principles calculations to analyze the electronic structure of Ni_{3}TeO_{6} across the 53 K and 9 T magnetic transitions, both of which are accompanied by large changes in electric polarization. The color properties are sensitive to magnetic order due to field-induced changes in the crystal field environment, with those around Ni1 and Ni2 most affected. These findings advance the understanding of magnetoelectric coupling in materials in which magnetic 3d centers coexist with nonmagnetic heavy chalcogenide cations.

A Chern insulator (quantum anomalous Hall insulator) phase is demonstrated to exist in a typical semi-Dirac system, the TiO2/VO2 heterostructure. By combining first-principles calculations with Wannier-based tight-binding model, we calculate the Berry curvature distribution, finding a Chern number of -2 for the valence bands, and demonstrate the existence of gapless chiral edge states, ensuring quantization of the Hall conductivity to 2e^2/h. A new semi-Dirac model, where each semi-Dirac cone is formed by merging three conventional Dirac points, is proposed to reveal how the nontrivial topology with finite Chern number is compatible with a semi-Dirac electronic spectrum., 12 pages, 3 figures

We report the discovery of a metamagnetic phase transition in a polar antiferromagnet Ni_{3}TeO_{6} that occurs at 52 T. The new phase transition accompanies a colossal magnetoelectric effect, with a magnetic-field-induced polarization change of 0.3 μC/cm^{2}, a value that is 4 times larger than for the spin-flop transition at 9 T in the same material, and also comparable to the largest magnetically induced polarization changes observed to date. Via density-functional calculations we construct a full microscopic model that describes the data. We model the spin structures in all fields and clarify the physics behind the 52 T transition. The high-field transition involves a competition between multiple different exchange interactions which drives the polarization change through the exchange-striction mechanism. The resultant spin structure is rather counterintuitive and complex, thus providing new insights on design principles for materials with strong magnetoelectric coupling.

Magnetoelectric (ME) materials are of fundamental interest and show broad potential for technological applications. Commonly the dominant contribution to the ME response is the lattice-mediated one, which is proportional to both the Born electric charge $Z^{\rm e}$ and its analogue, the dynamical magnetic charge $Z^{\rm m}$. Our previous study has shown that exchange striction acting on noncollinear spins induces much larger magnetic charges than those that depend on spin-orbit coupling. The hexagonal manganites $R$MnO$_3$ and ferrites $R$FeO$_3$ ($R$ = Sc, Y, In, Ho-Lu) exhibit strong couplings between electric, magnetic and structural degrees of freedom, with the transition-metal ions in the basal plane antiferromagnetically coupled through super-exchange so as to form a 120$^\circ$ noncollinear spin arrangement. Here we present a theoretical study of the magnetic charges, and of the spin-lattice and spin-electronic ME constants, in these hexagonal manganites and ferrites, clarifying the conditions under which exchange striction leads to an enhanced $Z^{\rm m}$ values and anomalously large in-plane spin-lattice ME effects.

We first review earlier work in which we computed the first-principles structural, vibrational, and lattice dielectric properties of the cubic, tetragonal, and monoclinic phases of ZrO 2 and HfO 2 . We then discuss two approaches to the construction of realistic models of amorphous ZrO 2 : a “melt-and-quench” ab-initio molecular dynamics approach, and an “activation–relaxation technique”. The structural, vibrational, and dielectric properties of the resulting models are then analyzed in detail. The overall average dielectric constant is computed and found to be comparable to that of the monoclinic phase. These techniques show promise for future modeling of high-K dielectric ultrathin films and interfaces.