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Ternary ABX3 perovskites made of corner-sharing BX6 octahedra have long featured prominently in solid-state chemistry and condensed matter physics. Still, the joint understanding of their two main subgroups—halides and oxides—has not been fully developed. Indeed, unlike the case in simpler compounds having a single, robust repeated motif (“monomorphous”), certain cubic perovskites can manifest a non-thermal (= intrinsic) distribution of local motifs (“polymorphous networks”). Such static deformations can include positional degrees of freedom (e.g., atomic displacements and octahedral tilting) or magnetic moment degrees of freedom in paramagnets. Unlike thermal motion, such static distortions do not time-average to zero, being an expression of the intrinsic symmetry breaking preference of the chemical bonding. The present study compares electronic structure features of oxide and halide perovskites starting from the static polymorphous distribution of motifs described by Density Functional Theory (DFT) minimization of the internal energy, continuing to finite temperature thermal disorder modeled via finite temperature DFT molecular dynamics. We find that (i) different oxide vs. halide ABX3 compounds adopt different energy-lowering symmetry-breaking modes. The calculated pair distribution function (PDF) of SrTiO3 from the first-principles agrees with recently measured PDF. (ii) In both oxides and halides, such static distortions lead to band gap blueshifts with respect to undistorted cubic Pm-3m structure. (iii) For oxide perovskites, high-temperature molecular dynamics simulations initiated from the statically distorted polymorphous structures reveal that the thermally-induced distortions can lead to a band gap redshift. (iv) In contrast, for cubic halide perovskite CsPbI3, both the intrinsic distortions and the thermal distortions contribute in tandem to band gap blueshift, the former, intrinsic effect being dominant. (v) In the oxide SrTiO3 and CaTiO3 (but not in halide) perovskites, octahedral tilting leads to the emergence of a distinct Γ–Γ direct band gap component as a secondary valley minimum to the well-known indirect R–Γ gap. Understanding such intrinsic vs. thermal effects on oxide vs. halide perovskites holds the potential for designing target electronic properties.

Many textbook physical effects in crystals are enabled by some specific symmetries. In contrast to such "apparent effects", "hidden effect X" refers to the general condition where the nominal global system symmetry would disallow the effect X, whereas the symmetry of local sectors within the crystal would enable effect X. Known examples include the hidden Rashba and/or hidden Dresselhaus spin polarization that require spin orbit coupling, but (unlike the apparent Rashba and Dresselhaus counterparts) can exist even in inversion-symmetric non-magnetic crystals. Here we point out that the spin splitting effect that does not require spin-orbit coupling (SOC) can have a hidden spin polarization counterpart in antiferromagnets. We show that such hidden, SOC-independent effects reflect intrinsic properties of the perfect crystal rather than an effect due to imperfections, opening the possibility for experimental realization, and offering a potential way to switch antiferromagnetic ordering., 16 pages, 5 figures

Trove of exotic topoloid structures has recently been predicted by searching for compounds whose calculated band structure crossing points fulfill specific symmetry requirements. Discovery of exciting physical phenomena by experimental studies of such predicted compounds is just around the corner. Yet, the examination of some of these assumed high-symmetry structures suggests that not always will assembly of atoms in a configuration that yields exotic topological properties be protected against energy-lowering symmetry breaking modes. Indeed, although bulk topological characteristics lead to protected surface/edge states, nothing protects bulk states from structural instability. The burden of proof for theoretical predictions of exciting physical phenomena should include some compelling hints that such phenomena can live in thermodynamically stable (or near stable) compounds. Herein, we illustrate how the use of the calculated total (electron + ion) energies of candidate structures can remove false-positive predicted topoloids from the list of likely realizable compounds, to the benefit of the much-cherished iterative process of theory-experiment materials discovery.

Describing the (a) electronic and magnetic properties (EMPs) of compounds generally requires the specification of (b) the type of spin configurations one is considering [e.g., antiferromagnetic (AFM) or paramagnetic (PM) phases, with or without spin short-range order (SRO)] and lattice structure (e.g., atomic displacements, possible symmetry breaking) of such phases at a given temperature. Indeed, studying the interplay between the spin configuration and lattice structure (SCLS) and the ensuing EMPs has been an outstanding challenge in the theory of matter. The traditional approach of electronic phases of matter has generally focused on the interelectronic interactions, regarding the lattice structure as a spectator degree of freedom (DOF), often fixed from an external source (experiment or model assumptions). However, one expects that the EMPs of a compound can generally respond self-consistently to changes in SCLS (including symmetry), and at the same time, the SCLS can change in response to different electron and spin distributions visited during the calculation of the EMPs. This ping-pong-like interplay where structure affects electronic properties and the latter affect structure is indeed a cornerstone of much of the intricacy of understanding quantum materials. However, there is a limited understanding of the theory required to determine the SCLS at finite temperature in a way that can affect the EMPs and vice versa. We use here a practical, density functional theory (DFT)-based approach that provides the SCLS as a function of temperature, involving the description of spin, lattice, and spin-lattice dynamics of AFM and PM phases, thus providing the required ping-pong partners to the description of the EMPs of different phases. We distinguish three levels of dynamics: (I) dynamics of the spin DOFs treated via noncollinear Heisenberg Monte Carlo solved with exchange energies obtained from first-principles DFT cluster expansion, (II) dynamics of the lattice DOFs treated by ab initio molecular dynamics (AIMD) employing a fixed, representative spin configuration from Level I at the simulated temperature, and (III) coupling of spin and lattice dynamics via Landau-Lifshitz-Gilbert spin dynamics combined with AIMD. Such SCLSs at each of the three levels are used as inputs to DFT supercell calculations, providing the EMPs at each temperature. The results of this sequence include electronic band structures, bandgaps, density of states, as well as the statistical distribution of local moments and the SRO parameters, each as a function of temperature. Herein, we define a path to include temperature in magnetic insulators at different levels of spin dynamics by intercommunication between electronic structure theory and statistical mechanics. Using NiO as a test case, we address the separability of the DOFs in magnetic insulators for a minimal description of EMPs, demonstrating that inclusion of spin dynamics and, to some level, lattice dynamics is enough to explain the EMPs. Funding Agencies|Swedish Foundation for Strategic Research through the Future Research Leaders 6 program [FFL 15-0290]; Swedish Research Council (VR) [2019-05403]; Knut and Alice Wallenberg Foundation (Wallenberg Scholar Grant) [KAW-2018.0194]; Swedish Government Strategic Research Area in Materials Science on Functional Materials at Linkoping University [2009 00971]; Swedish Research Council [2018-05973]; U.S. National Science Foundation, Division of Materials Research (DMR), Condensed Matter and Materials Theory Grant [DMR 2113922]; National Science Foundation [ACI-1548562]

Crystallographic point group symmetry (CPGS) such as polar and nonpolar crystal classes have long been known to classify compounds that have spin-orbit-induced spin splitting. While taking a journey through the Brillouin zone (BZ) from one $k$-point to another for a fixed CPGS, it is expected that the wave vector point group symmetry (WPGS) can change, and consequently, a qualitative change in the texture of the spin polarization can occur [the expectation value of spin operator ${\stackrel{P\vec}{S}}_{n{k}_{0}}$ in Bloch state $u(n,k)$ and the wave vector ${k}_{0}$]. However, the nature of the spin texture (ST) change is generally unsuspected. In this paper, we determine a full classification of the linear-in-$k$ ST patterns based on the polarity and chirality reflected in the WPGS at ${k}_{0}$. The spin-polarization vector ${\stackrel{P\vec}{S}}_{n{k}_{0}}$ controlling the ST is bound to be parallel to the rotation axis and perpendicular to the mirror planes, and hence, symmetry operation types in WPGSs impose symmetry restriction to the ST. For instance, the ST is always parallel to the wave vector $k$ in nonpolar chiral WPGSs since they contain only rotational symmetries. Some consequences of the ST classification based on the symmetry operations in the WPGS include the observation of ST patterns that are unexpected according to the symmetry of the crystal. For example, it is usually established that spin-momentum locking effect (spin vector always perpendicular to the wave vector) requires the crystal inversion symmetry breaking by an asymmetric electric potential. However, we find that polar WPGS can have this effect even in compounds without electric dipoles or external electric fields. We use the determined relation between WPGS and ST as a design principle to select compounds with multiple STs near band edges at different $k$ valleys. Based on high-throughput calculations for 1481 compounds, we find 37 previously fabricated materials with different STs near band edges. The ST classification as well as the predicted compounds with multiple STs can be a platform for potential application for spin-valleytronics and the control of the ST by accessing different valleys.

Summary We highlight a class of materials representing an exception to the Daltonian view that compounds maintain integer stoichiometry at low temperatures and use this behavior to select ordered vacancy compounds (OVCs) striking a wanted compromise between carrier concentration, transparency, and phase stability, crucial for transparent conductors (TCs). We show that carriers in the conduction band (CB) of degenerate gapped BaNbO3, Ca6Al7O16, and Ag3Al22O34 compounds can cause a self-regulating instability, whereby cation vacancies form exothermically because a fraction of the CB electrons decays into the hole states formed by such vacancies, and this electron-hole recombination offsets the positive energy associated with vacancy bond breaking. This Fermi level-induced spontaneous non-stoichiometry can lead to the formation of OVCs with different optoelectronic properties and stable in different ranges of chemical potentials. Thus, we demonstrate how a window of opportunity can be determined between opposing tendencies of transparency, conductivity, and stability to design TCs.

Distinct shortcomings of individual halide perovskites for solar applications, such as restricted range of band gaps, propensity of ABX3 to decompose into AX + BX2, or oxidation of 2ABX3 into A2BX6, have led to the need to consider alloys of individual perovskites such as [FA,Cs][Pb,Sn][Br,I]3. This proposition creates a nontrivial material selection problem associated with a six-component structure, spanning a continuum of three sets of compositions (one for each sublattice) and requiring control of phase separation or ordering in each alloyed subfield. Not surprisingly, material and structure choices were made thus far mostly via trial-and-error explorations among a large number of arrangements. Here, we use ideas from solid-state theory of semiconductor alloys to analyze the behaviors of the canonical [FA,Cs][Pb,Sn]I3 alloy system, where FA is formamidinium. Density functional calculations utilizing specially constructed supercells are used to calculate the composition dependence of band gaps, energy o...

Whereas low-temperature ferroelectrics have a well understood ordered spatial dipole arrangement, the fate of these dipoles in paraelectric phases remains poorly understood. Using density functional theory (DFT), we find that unlike the case in conventional non-polar ABO$_3$ compounds illustrated here for cubic BaZrO$_3$, the origin of the distribution of the B site off-centering in cubic paraelectric such as BaTiO$_3$ is an intrinsic, energy stabilizing symmetry breaking. Minimizing the internal energy E of a constrained cubic phase already reveals the formation of a distribution of intrinsic local displacements that (i) mimic the symmetries of the low temperature phases, while (ii) being the precursors of what finite temperature DFT Molecular Dynamics finds as thermal motifs. The implications of such symmetry breaking on the microscopic structures and anomalous properties in these kinds of PE materials are discussed., 3 figures, 10 pages

Recent studies have shown that the non-relativistic antiferromagnetic ordering could generate momentum-dependent spin splitting analogous to the Rashba effect, but free from the requirement of relativistic spin-orbit coupling. Whereas the classification of such compounds can be illustrated by different spin-splitting prototypes (SSTs) from symmetry analysis and density functional theory calculations, the significant variation in bonding and structure of these diverse compounds representing different SSTs clouds the issue of how much of the variation in spin splitting can be traced back to the symmetry-defined characteristics, rather to the underlining chemical and structural diversity. The alternative model Hamiltonian approaches do not confront the issues of chemical and structural complexity, but often consider only the magnetic sublattice, dealing with the all-important effects of the non-magnetic ligands via renormalizing the interactions between the magnetic sites. To this end we constructed a 'DFT model Hamiltonian' that allows us to study SSTs at approximate 'constant chemistry', while retaining the realistic atomic scale structure including ligands. This is accomplished by using a single, universal magnetic skeletal lattice (Ni2+ ions in Rocksalt NiO) and designing small displacements of the non-magnetic (oxygen) sublattice which produce, by design, the different SSTs magnetic symmetries. We show that (i) even similar crystal structures having very similar band structures can lead to contrasting behavior of spin splitting vs. momentum, and (ii) even subtle deformations of the non-magnetic ligand sublattice could cause a giant spin splitting in AFM-induced SST. This is a paradigm shift relative to the convention of modeling magnets without considering the non-magnetic ligand that mediate indirect magnetic interaction (e.g., super exchange)., Comment: 23 pages, 5. figures

In some $d$-electron oxides, the measured effective mass ${m}_{\mathrm{exptl}}^{*}$ has long been known to be significantly larger than the model effective mass ${m}_{\mathrm{model}}^{*}$ deduced from mean-field band theory, i.e., ${m}_{\mathrm{exptl}}^{*}=\ensuremath{\beta}{m}_{\mathrm{model}}^{*}$, where $\ensuremath{\beta}g1$ is the ``mass-enhancement'' or ``mass-renormalization'' factor. Previous applications of density functional theory (DFT), based on a symmetry-restricted structure with the smallest number of possible magnetic, orbital, and structural degrees of freedom, missed such mass enhancement. This fact has been taken as evidence of strong electronic correlation, often described via the symmetry-restricted dynamic mean-field approach of the many-body theory, being the exclusive enabling physics. This paper uses instead a static density functional approach that does not restrict positional or spin degrees of freedom (symmetry-broken structures). This approach analyzes the contributions of different symmetry-broken modalities to mass enhancement for a few nominally highly correlated $d$-electron perovskites as well as the nominally uncorrelated, closed-shell $s\text{\ensuremath{-}}p$ bonding perovskites. It shows that the energy-lowering symmetry-broken spin effects (e.g., nonzero local moment in the paramagnetic phase) and structural effects (e.g., atomic displacement) as described in mean-field DFT already manifest mass enhancement for both electrons and holes in a range of $d$-electron perovskites $\mathrm{SrV}{\mathrm{O}}_{3}, \mathrm{SrTi}{\mathrm{O}}_{3}, \mathrm{BaTi}{\mathrm{O}}_{3}$, and $\mathrm{LaMn}{\mathrm{O}}_{3}$, as well as $p$-electron perovskites $\mathrm{CsPb}{\mathrm{I}}_{3}$ and $\mathrm{SrBi}{\mathrm{O}}_{3}$, including both metals ($\mathrm{SrV}{\mathrm{O}}_{3}$) and insulators (the rest). This is revealed only when enlarged unit cells of the same parent global symmetry, which are large enough to allow for symmetry-breaking distortions and concomitant variations in spin order, are explored for their ability to lower the total energy. Positional symmetry breaking that leads to mass enhancement includes octahedral rotation in halide perovskites such as $\mathrm{CsPb}{\mathrm{I}}_{3}$, Jahn-Teller-like ${Q}_{2}^{+}$ distortion in $\mathrm{LaMn}{\mathrm{O}}_{3}$, and bond disproportionation in $\mathrm{SrBi}{\mathrm{O}}_{3}$, while magnetic symmetry breaking resulting in mass enhancement includes the formation of a distribution of local moments in $\mathrm{SrV}{\mathrm{O}}_{3}$ that averages to zero in the paramagnetic phase. Not all symmetry breaking leads to significant mass enhancement, e.g., the rather small octahedral rotations in the nearly perfectly cubic $\mathrm{SrTi}{\mathrm{O}}_{3}$ cause negligible mass enhancement, as do the paraelectric displacements in $\mathrm{BaTi}{\mathrm{O}}_{3}$. In principle, by ergodicity, the two descriptions, i.e., the symmetry-restricted dynamic approach with a single time-fluctuating magnetic moment and the symmetry-broken mean-field approach with a static distribution of spatially fluctuated local moments, are not mutually exclusive but are a choice of representation and consequently, a choice of computational efficiency. In approximate implementations, the symmetry-broken mean-field approach appears to remove much of what was strong correlation in dynamically correlated symmetry-restricted solutions, leaving smaller (``weak'') residual correlation with respect to the exact solution.

Inorganic Halide perovskites (HP's) of the CsPbX3 (X=I, Br, Cl) type have reached prominence in photovoltaic solar cell efficiencies. Peculiarly, they have shown, however, an asymmetry in their ability to be doped by holes rather than by electrons. Indeed, both structural defect-induced doping as well as extrinsic impurity-induced doping strangely result in a unipolar doping (dominantly p-type) with low free carriers concentration. This raises the question whether such doping limitations presents just a temporary setback due to insufficient optimization of the doping process, or perhaps this represents an intrinsic, physically-mandated bottleneck. In this paper we study three fundamental Design Principles (DP's) for ideal doping, applying them via density functional doping theory to these HP's, thus identifying the violated DP that explains the doping limitations and asymmetry in these HP's. Here, the target DP are: (i) requires that the thermodynamic transition level induced by the dopants must ideally be energetically shallow both for donors (n-type) or acceptors (p-type); DP-(ii) requires that the 'Fermi level pinning energies' for electrons and holes (being the limiting values of the Fermi level before a structural defect that compensate the doping forms spontaneously) should ideally be located inside the conduction band for n-type doping and inside the valence band for p-type doping. DP-(iii) requires that the doping-induced equilibrium Fermi energy shifts towards the conduction band for n-type doping (shift towards the valence band, for p-type doping) to be sufficiently large. We find that, even though in HP's based on Br and Cl there are numerous shallow level dopants that satisfy DP-(i), in contrast DP-(ii) is satisfied only for holes and DP-(iii) fail for both holes and electrons, being the ultimate bottleneck for the n-type doping in Iodine HP's.

Exploring hidden effects that have been overlooked given the nominal global crystal symmetry but are indeed visible in solid-state materials has been a fascinating subject of research recently. Here, we introduce a novel hidden Zeeman-type spin polarization (HZSP) in nonmagnetic bulk crystals with sublattice structures. In the momentum space of these crystals, the doubly degenerate bands formed in a certain plane can exhibit a uniform spin configuration with opposite spin orientations perpendicular to this plane, whereas such degenerate states are spatially separated in a pair of real-space sectors. Interestingly, we find that HZSP can manifest itself in both centrosymmetric and non-centrosymmetric materials. We further demonstrate the important role of nonsymmorphic twofold screw-rotational symmetry played in the formation of HZSP. Moreover, two representative material examples, i.e., centrosymmetric WSe$_2$ and noncentrosymmetric BaBi$_4$O$_7$, are identified to show HZSP via first-principles calculations. Our finding thus not only opens new perspectives for hidden spin polarization research but also significantly broadens the range of materials towards spintronics applications., Comment: 5 pages, 3 figures

Understanding the controlling principles of band gaps trends in d electron perovskites is needed both for gauging metal-insulator transitions, as well as their application in catalysis and doping. The magnitude of this band gap is rather different for different magnetic spin configurations. We find via electronic structure theory that the factors that connect gapping magnitudes to magnetism depend on the nature of the band edge orbital character (BEOC) and surprisingly scale with the number of antiferromagnetic contacts z$_i$ between neighboring transition metal ions. The dependence is weak when the BEOC are (d,d)-like ("Mott insulators"), whereas this dependence is rather strong in (p,d)-like ("charge transfer" insulators). These unexpected rules are traced to the reduced orbital interactions through the increase in the number of antiferromagnetic contacts between transition metal ions. The impact of magnetic order is not limited to the band gap magnitude and includes also the magnitude of lattice distortions connected to the electronic structure. These results highlight the importance of establishing in electronic structure theory of gap-related phenomena (doping, transport, metal-insulator transitions, conductive interfaces) the appropriate magnetic order.

Cofunctionality---the coexistence of different (possibly even contraindicated) properties in the same compound---is an exciting prospect that never fails to deliver interesting surprises, as in transparent while electrically conducting compounds, topological insulators having Rashba spin split bands, or electrically conducting while thermally insulating (thermoelectric) compounds. Here we study a cofunctionality of ferroelectricity and Rashba effect that combines the directional helical spin-polarization characteristic of the energy bands of bulk Rashba compounds with the existence of two opposite electric polarization states, characteristic of atomic displacements in displacive ferroelectrics. Flipping of the ferroelectric polarization (e.g., via an applied electric field) would result in the reversal of the Rashba spin polarization. However, thus far, only very few (essentially one) compounds have been found to be ferroelectric Rashba semiconductors (FERSCs), e.g., GeTe ($R3m$). In this paper, we propose a general strategy for the identification of compounds that possess cofunctionalities and apply it to perform an inverse design, finding compounds that simultaneously have ferroelectricity and Rashba spin splitting. The inverse design combining functionality ${f}_{1}$ with ${f}_{2}$ involves definition and utilization of causal factors that enable the said functionalities, and involves three steps: (1) screening materials that satisfy the enabling DPs common to the two functionalities ${f}_{1}$ and ${f}_{2}$; (2) filtering the materials according to DPs that are unique to each of the individual functionalities ${f}_{1}$ and ${f}_{2}$; and (3) by using the ensuing two compound lists of compounds $C({f}_{1})$ and $C({f}_{2})$ identifying the intersection between them, i.e., compounds $C({f}_{1},{f}_{2})$ possessing simultaneous ${f}_{1}$ and ${f}_{2}$. Based on this process, we design 52 atomic combinations not suspected to be FERSCs that were previously synthesized. Of these 52 compounds, we find 24 FERSCs that are thermodynamically stable (i.e., reside on the convex hull) and, at the same time, feature larger spin splitting (large than 25 meV). These include ${\mathrm{BrF}}_{5}(Cmc{2}_{1})$, $\mathrm{TlI}{\mathrm{O}}_{3}(R3m)$, $\mathrm{Zn}{\mathrm{I}}_{2}{\mathrm{O}}_{6}(P{2}_{1})$, $\mathrm{LaTa}{\mathrm{O}}_{4}(Cmc{2}_{1})$, ${\mathrm{Tl}}_{3}{\mathrm{S}}_{3}\mathrm{Sb}(R3m)$, ${\mathrm{Sn}}_{2}{\mathrm{P}}_{2}{\mathrm{Se}}_{6}$ (Pc), and ${\mathrm{Bi}}_{2}\mathrm{Si}{\mathrm{O}}_{5}(Cmc{2}_{1})$ that have Rashba spin splitting of 31, 57, 111, 40, 90, 67, and 76 meV, respectively. Density functional theory calculations illustrate the reversal of the spin texture when the electric polarization is flipped. This paper validates a general approach for the search of other cofunctionalities based on causal enabling design principles rather than uncovering machine correlations.

Recent study (Yuan et. al., Phys. Rev. B 102, 014422 (2020)) revealed a SOC-independent spin splitting and spin polarization effect induced by antiferromagnetic ordering which do not necessarily require breaking of inversion symmetry or the presence of SOC, hence can exist even in centrosymmetric, low-Z light element compounds, considerably broadening the material base for spin polarization. In the present work we develop the magnetic symmetry conditions enabling such effect, dividing the 1651 magnetic space groups into 7 different spin splitting prototypes (SST-1 to SST-7). We use the 'Inverse Design' approach of first formulating the target property (here, spin splitting in low-Z compounds not restricted to low symmetry structures), then derive the enabling physical design principles to search realizable compounds that satisfy these a priori design principles. This process uncovers 422 magnetic space groups (160 centrosymmetric and 262 non-centrosymmetric) that could hold AFM-induced, SOC-independent spin splitting and spin polarization. We then search for stable compounds following such enabling symmetries. We investigate the electronic and spin structures of some selected prototype compounds by density functional theory (DFT) and find spin textures that are different than the traditional Rashba-Dresselhaus patterns. We provide the DFT results for all antiferromagnetic spin splitting prototypes (SST-1 to SST-4) and concentrate on revealing of the AFM-induced spin splitting prototype (SST-4). The symmetry design principles along with their transformation into an Inverse Design material search approach and DFT verification could open the way to their experimental examination.M). The symmetry design principles along with their transformation into an Inverse Design material search approach and DFT verification could open the way to their experimental examination., 29 pages, 8 figures, 1 table

Spin splitting of energy bands can be induced by relativistic spin-orbit interactions in materials without inversion symmetry. Whereas polar space group symmetries permit Rashba (R-1) spin splitting with helical spin textures in momentum space, which could be reversed upon switching a ferroelectric polarization via applied electric fields, the ordinary Dresselhaus effect (D-1A) is ac-tive only in materials exhibiting nonpolar noncentrosymmetric crystal classes with atoms occupy-ing exclusively non-polar lattice sites. Consequently, the spin-momentum locking induced by D-1A is not electric field-switchable. An alternative type of Dresselhaus symmetry, referred to as D-1B, exhibits crystal class constraints similar to D-1A (all dipoles add up to zero), but unlike D-1A, at least one polar site is occupied. We find that this behavior exists in a class of ferri-chiral crys-tals, which in principle could be reversed upon a change in chirality. Focusing on alkali metal chalcogenides, we identify NaCu5S3 in the nonentiamorphic ferri-chiral structure, which exhibits CuS3 chiral units differing in the magnitude of their Cu displacements. We then synthesize NaCu5S3 (space group P6322) and confirm its ferri-chiral structure with power x-ray diffraction. Our electronic structure calculations demonstrate it exhibits D-1B spin splitting as well as a ferri-chiral phase transition, revealing spin splitting interdependent on chirality. Our electronic struc-ture calculations show that a few percent biaxial tensile strain can reduce (or nearly quench) the switching barrier separating the monodomain ferri-chiral P6322 states. We discuss what type of external stimuli might switch the chirality so as to reverse the (non-helical) Dresselhaus D-1B spin texture, offering an alternative to the traditional reversal of the (helical) Rashba spin texture., 27 pages, 12 figures

In standard doping, adding charge carrier to a compound results in a shift of the Fermi level towards the conduction band for electron doping and towards the valence band for hole doping. We discuss the curious case of antidoping, where the direction of band movements in response to doping is reversed. Specifically, $p$-type antidoping moves the previously occupied bands to the principal conduction band resulting in an increase of band gap energy and reduction of electronic conductivity. We find that this is a generic behavior for a class of materials: early transition and rare-earth metal (e.g., Ti, Ce) oxides where the sum of composition-weighed formal oxidation states is positive; such compounds tend to form the well-known electron-trapped intermediate bands localized on the reduced cation orbitals. What is less known is that doping by a hole annihilates a single trapped electron on a cation. The latter thus becomes electronically inequivalent with respect to the normal cation in the undoped lattice, thus representing a symmetry-breaking effect. We give specific theoretical predictions for target compounds where hole antidoping might be observed experimentally: Magn\'eli-like phases (i.e., $\mathrm{Ce}{\mathrm{O}}_{2\text{\ensuremath{-}}x}$ and $\mathrm{Ti}{\mathrm{O}}_{2\text{\ensuremath{-}}x}$) and ternary compounds (i.e., $\mathrm{B}{\mathrm{a}}_{2}\mathrm{T}{\mathrm{i}}_{6}{\mathrm{O}}_{13}$ and $\mathrm{B}{\mathrm{a}}_{4}\mathrm{T}{\mathrm{i}}_{12}{\mathrm{O}}_{27}$), and note that this unique behavior opens the possibility of unconventional control of materials conductivity by doping.

Doping mobile carriers into ordinary semiconductors such as Si, GaAs, and ZnO was the enabling step in the electronic and optoelectronic revolutions. The recent emergence of a class of "Quantum Materials", where uniquely quantum interactions between the components produce specific behaviors such as topological insulation, unusual magnetism, superconductivity, spin-orbit-induced and magnetically-induced spin splitting, polaron formation, and transparency of electrical conductors, pointed attention to a range of doping-related phenomena associated with chemical classes that differ from the traditional semiconductors. These include wide-gap oxides, compounds containing open-shell d electrons, and compounds made of heavy elements yet having significant band gaps. The atomistic electronic structure theory of doping that has been developed over the past two decades in the sub-field of semiconductor physics has recently been extended and applied to quantum materials. The present review focuses on explaining the main concepts needed for a basic understanding of the doping phenomenology and indeed peculiarities in quantum materials from the perspective of condensed matter theory, with the hope of forging bridges to the chemists that have enabled the synthesis of some of the most interesting compounds in this field.

The spin-orbit -induced spin splitting of energy bands in low symmetry compounds (the Rashba Effect) has a long-standing relevance to spintronic applications and to the fundamental understanding of symmetry breaking in solids, yet the knowledge of what controls its magnitude in different materials is difficult to anticipate. Indeed, rare discoveries of compounds with large Rashba coefficients are invariably greeted as pleasant surprises. We advance the understanding of the "Rashba Scale" using the "inverse design" approach by formulating theoretically the relevant design principle and then identifying compounds that satisfy it. We show that the presence of energy band anti-crossing provides a causal design principle of compounds with large Rashba coefficients, leading to the identification via first-principles calculations of 34 rationally designed strong-Rashba compounds. Since topological insulators must have band anti crossing, this leads us to establish an interesting cross functionality of "Topological Rashba Insulators" (TRI) that may provide a platform for the simultaneous control of spin splitting and spin-polarization., Comment: 24 pages and 9 figures

This paper deals with a significant family of compounds predicted by simplistic electronic structure theory to be metals but are, in fact, insulators. This false metallic state has been traditionally attributed in the literature to reflect the absence of proper treatment of electron-electron correlation ("Mott insulators") whereas, in fact, even mean-field like density functional theory describes the insulating phase correctly if the restrictions posed on the simplistic theory are avoided. Such unwarranted restrictions included different forms of disallowing symmetry breaking described in this article. As science and technology of conductors have transitioned from studying simple elemental metals such as Al or Cu to compound conductors such as binary or ternary oxides and pnictides, a special class of degenerate but gapped metals has been noticed. Their presumed electronic configurations show the Fermi level inside the conduction band or valence band, yet there is an "internal band gap" between the principal band edges. The significance of this electronic configuration is that it might be unstable towards the formation of states inside the internal band gap when the formation of such states costs less energy than the energy gained by transferring carriers from the conduction band to these lower energy acceptor states, changing the original (false) metal to an insulator., Comment: 43 pages, 14 figures

Real materials rarely behave like their digital counterparts. Stability of the compounds must be part of the burden of proof for predicting the complex properties of matter, urges Alex Zunger. Real materials rarely behave like their digital counterparts. Stability of the compounds must be part of the burden of proof for predicting the complex properties of matter, urges Alex Zunger.

To realize the fundamental limits of photovoltaic device efficiency, solar absorbers must exhibit strong absorption and abrupt absorption onsets. Ideally, onsets to maximum absorption (α > 105 cm–1) occur over a few tenths of an electronvolt. First-principles calculations predict CuTaS3 represents a potentially new class of materials with such absorption characteristics. Narrow metallic d bands in both the initial and final states present high joint densities of states and, therefore, strong absorption. Specifically, a mixture of metal d (Cu1+, d10) and S p characterizes states near the valence band maximum, and metal d (Ta5+, d0) dominates near the conduction band minimum. Optical absorption measurements on thin films confirm the abrupt onset to strong absorption α > 105 cm–1 at Eg + 0.4 eV (Eg = 1.0 eV). Theoretical CuTaS3 solar cell efficiency is predicted to be 28% for a 300 nm film based on the metric of spectroscopic limited maximum efficiency, which exceeds that of CuInSe2. This sulfide may offer n...

The energy vs. crystal momentum E(k) diagram for a solid (band structure) constitutes the road map for navigating its optical, magnetic, and transport properties. By selecting crystals with specific atom types, composition and symmetries, one could design a target band structure and thus desired properties. A particularly attractive outcome would be to design energy bands that are split into spin components with a momentum-dependent splitting, as envisioned by Pekar and Rashba [Zh. Eksperim. i Teor. Fiz. 47 (1964)], enabling spintronic application. The current paper provides "design principles" for wavevector dependent spin splitting (SS) of energy bands that parallels the traditional Dresselhaus and Rashba spin-orbit coupling (SOC) - induce splitting, but originates from a fundamentally different source -- antiferromagnetism. We identify a few generic AFM prototypes with distinct SS patterns using magnetic symmetry design principles. These tools allow also the identification of specific AFM compounds with SS belonging to different prototypes. A specific compound -- centrosymmetric tetragonal MnF2 -- is used via density functional band structure calculations to quantitatively illustrate one type of AFM SS. Unlike the traditional SOC-induced effects restricted to non-centrosymmetric crystals, we show that antiferromagnetic-induced spin splitting broadens the playing field to include even centrosymmetric compounds, and gives SS comparable in magnitude to the best known ('giant') SOC effects, even without SOC, and consequently does not rely on the often-unstable high atomic number elements required for high SOC. We envision that use of the current design principles to identify an optimal antiferromagnet with spin-split energy bands would be beneficial for efficient spin-charge conversion and spin orbit torque applications without the burden of requiring compounds containing heavy elements., 20 pages, 5 figures

The authors identify the modalities enabling an electronically induced distortion, which is identical across the board of 3d elements showing electronic degenerate states in the high symmetry cubic cell. This constitutes the fingerprint of a Jahn-Teller effect. Materials without electronic instabilities such as LaMnO3 display an alternate lattice distortion simply resulting from lattice mode couplings with the sterically induced distortions.

Traditional band theory of perfect crystalline solids often uses as input the structure deduced from diffraction experiments; when modeled by the minimal unit cell this often produces a spatially averaged model. The present study illustrates that this is not always a safe practice unless one examines if the intrinsic bonding mechanism is capable of benefiting from the formation of a distribution of lower symmetry local environments that differ from the macroscopically averaged structure. This can happen either due to positional or to magnetic symmetry breaking. By removing the constraint of a small crystallographic cell, the energy minimization in the density functional theory finds atomic and spin symmetry breaking, not evident in conventional diffraction experiments but being found by local probes such as atomic pair distribution function analysis. Here we report that large atomic and electronic anomalies in bulk tetragonal FeSe emerge from the existence of distributions of local positional and magnetic moment motifs. The found symmetry-broken motifs obtained by minimization of the internal energy represent what chemical bonding in the tetragonal phase prefers as intrinsic energy lowering (stabilizing) static distortions. This explains observations of band renormalization, predicts orbital order and enhanced nematicity, and provides unprecedented close agreement with spectral function measured by photoemission and local atomic environment revealed by the pair distribution function. While the symmetry-restricted strong correlation approach has been argued previously to be the exclusive theory needed for describing the main peculiarities of FeSe, we show here that the symmetry-broken mean-field approach addresses numerous aspects of the problem, provides intuitive insight into the electronic structure, and opens the door for large-scale mean-field calculations for similar $d$-electron quantum materials.

The existence of band gaps in Mott insulators such as perovskite oxides with partially filled 3d shells has been traditionally explained in terms of strong, dynamic interelectronic repulsion codified by the on-site repulsion energy U in the Hubbard Hamiltonian. The success of the ``DFT+U approach'' where an empirical on-site potential term U is added to the exchange- and correlation density functional theory (DFT) raised questions on whether U in DFT+U represents interelectronic correlation in the same way as it does in the Hubbard Hamiltonian, and if empiricism in selecting U can be avoided. Here we illustrate that ab initio DFT without any U is able to predict gapping trends and structural symmetry breaking (octahedra rotations, Jahn-Teller modes, bond disproportionation) for all $3d\phantom{\rule{0.16em}{0ex}}AB{\mathrm{O}}_{3}$ perovskites from titanates to nickelates in both spin-ordered and spin-disordered paramagnetic phases. Thus, the mechanism of gap formation due to the Hubbard Hamiltonian dynamic interelectronic correlation is not a requirement in these $3d$ electron compounds. We describe the paramagnetic phases as a supercell where individual sites can have different local environments thereby allowing DFT to develop finite moments on different sites as long as the total cell has zero moment. We use the recently developed strongly constrained appropriately normed exchange and correlation functional (SCAN) that is sanctioned by the usual single-determinant, mean-field DFT paradigm with static correlations, but has a more precise rendering of self-interaction cancelation. Our results suggest that strong dynamic electronic correlations are not playing a universal role in gapping of $3d\phantom{\rule{0.16em}{0ex}}AB{\mathrm{O}}_{3}$ Mott insulators, and opens the way for future applications of DFT for studying a plethora of complexity effects that depend on the existence of gaps, such as doping, defects, and band alignment in $AB{\mathrm{O}}_{3}$ oxides.

It has been long known that numerous halide and oxide perovskites can have non-ideal octahedra, showing tilting, rotation, and metal atom displacements. It has also been known that compounds that have at low temperatures a single structural motif ("monomorphous structures") could become disordered at higher temperatures, resulting in non-ideal octahedra as an entropy effect. What is shown here is that in many cubic halide perovskites and some oxides compounds a distribution of different low-symmetry octahedra ("polymorphous networks") emerge already from the minimization of the systems internal energy, i.e., they represent the intrinsic, preferred low temperature pattern of chemical bonding. Thermal disorder effects build up at elevated temperatures on top of such low temperature polymorphous networks. Compared with the monomorphous counterparts, the polymorphous networks have lower predicted total energies (enhanced stability), larger band gaps and dielectric constants now dominated by the ionic part, and agrees much more closely with the observed pair distribution functions. The nominal cubic perovskites (Pm-3m) structure deduced from X-Ray diffraction is actually a macroscopically averaged, high symmetry configuration, which should not be used to model electronic properties, given that the latter reflect a low symmetry local configuration., 20 pages; 7 figures; 94 references

Interest in substitutional disordered alloys has recently reemerged with focus on the symmetry-sensitive properties in the alloy such as topological insulation and Rashba effect. A substitutional random alloy manifests a distribution of local environments, creating a polymorphous network. While the macroscopic average (monomorphous) structure may have the original high symmetry of the constituent compounds, many observable physical properties are sensitive to local symmetry, and are hence $$ rather than $P(S_0)$=$P()$. The fundamental difference between polymorphous $$ and monomorphous $P(S_0)$ led to the often-diverging results and the missing the atomic-scale resolution needed to discern symmetry-related physics. A natural approach capturing the polymorphous aspect is supercell model, which however suffers the difficulty of band folding ('spaghetti bands'), rendering the E vs k dispersion needed in topology and Rashba physics and seen in experiments, practically inaccessible. A solution that retains the polymorphous nature but restores the E vs k relation is to unfold the supercell bands. This yields alloy Effective Band Structure (EBS), providing a 3D picture of spectral density consisting of E- and k-dependent spectral weight with coherent and incoherent features, all created naturally by the polymorphous distribution of many local environments. We illustrate this EBS approach for CdTe-HgTe, PbSe-SnSe and PbS-PbTe alloys. We found properties that are critical for e.g. topological phase transition and Rashba splitting but totally absent in conventional monomorphous approaches, including (1) co-existing, wavevector- and energy-dependent coherent band splitting and incoherent band broadening, (2) coherent-incoherent transition along different k space directions, and (3) Rashba-like band splitting having both coherent and incoherent features., Comment: 17 pages, 8 figures, 1 table

Hidden Rashba and Dresselhaus spin splittings in centrosymmetric crystals with subunits/sectors having non-centrosymmetric symmetries (the R-2 and D-2 effects) have been predicted theoretically and then observed experimentally, but the microscopic mechanism remains unclear. Here we demonstrate that the spin splitting in the R-2 effect is enforced by specific symmetries, such as non-symmorphic symmetry in the present example, which ensures that the pertinent spin wavefunctions segregate spatially on just one of the two inversion-partner sectors and thus avoid compensation. We further show that the effective Hamiltonian for the conventional Rashba (R-1) effect is also applicable for the R-2 effect, but applying a symmetry-breaking electric field to a R-2 compound produces a different spin-splitting pattern than applying a field to a trivial, non-R-2, centrosymmetric compound. This finding establishes a common fundamental source for the R-1 effect and the R-2 effect, both originating from local sector symmetries rather than from the global crystal symmetry per se., The Dresselhaus and Rashba effects have traditionally been expected only in non-centrosymmetric systems but recent work has shown that they can exist in some centrosymmetric materials. Here the authors show that the so-called hidden Rashba effect originates from wavefunction segregation enforced by local symmetries.

With their broad range of properties, ABO3 transition metal perovskite oxides have long served as a platform for device applications and as a testing bed for different condensed matter theories. Their insulating character and structural distortions are often ascribed to dynamical electronic correlations within a universal, symmetry-conserving paradigm. This view restricts predictive theory to complex computational schemes, going beyond density functional theory (DFT). Here, we show that, if one allows symmetry-breaking energy-lowering crystal symmetry reductions and electronic instabilities within DFT, one successfully and systematically recovers the trends in the observed band gaps, magnetic moments, type of magnetic and crystallographic ground state, bond disproportionation and ligand hole effects, Mott vs. charge transfer insulator behaviors, and the amplitude of structural deformation modes including Jahn-Teller in low temperature spin-ordered and high temperature disordered paramagnetic phases. We then provide a classification of the four mechanisms of gap formation and establish DFT as a reliable base platform to study the ground state properties in complex oxides., It is often stated that first principles studies of transition metal oxides require dynamically correlated methods to correctly produce gap formation, magnetism and structural distortions. Varignon et al. show instead that static correlations are sufficient to capture these features in the ABO3 oxide series.

Correlated materials with open-shell d- and f-ions having degenerate band edge states show a rich variety of interesting properties ranging from metal-insulator transition to unconventional superconductivity. The textbook view for the electronic structure of these materials is that mean-field approaches are inappropriate, as the interelectronic interaction U is required to open a band gap between the occupied and unoccupied degenerate states while retaining symmetry. We show that the latter scenario often defining what Mott insulators are, is in fact not needed for the 3d binary oxides MnO, FeO, CoO, and NiO. The mean-field band theory can indeed lift such degeneracies in the binaries when nontrivial unit cell representations (polymorphous networks) are allowed to break symmetries, in conjunction with a recently developed non-empirical exchange and correlation density-functional without an on-site interelectronic interaction U. We explain how density-functional theory (DFT) in the polymorphous representation achieves band gap opening in correlated materials through a separate mechanism to the Mott-Hubbard approach. We show the method predicts magnetic moments and gaps for the four binary monoxides in both the antiferromagnetic and paramagnetic phases, offering an effective alternative to symmetry-conserving approaches for studying a range of functionalities in open d- and f-shell complex materials., Comment: 20 pages, 7 figures

Carrier doping of quantum spin liquids is a long-proposed route to the emergence of high-temperature superconductivity. Electrochemical intercalation in kagome hydroxyl halide materials shows that samples remain insulating across a wide range of electron counts. Here we demonstrate through first-principles density-functional calculations, corrected for self-interaction, the mechanism by which electrons remain localized in various Zn-Cu hydroxyl halides, independent of the chemical identity of the dopant-the formation of polaronic states with attendant lattice displacements and a dramatic narrowing of bandwidth upon electron addition. The same theoretical method applied to electron doping in cuprate Nd_{2}CuO_{4} correctly produces a metallic state when the initially formed polaron dissolves into an extended state. Our general findings explain the insulating behavior in a wide range of "doped" quantum magnets and demonstrate that new quantum spin liquid host materials are needed to realize metallicity borne of a spin liquid.

Some $AB{X}_{3}$ perovskites exhibit different local environments (DLE) for the same $B$ atoms in the lattice, an effect referred to as disproportionation, distinguishing such compounds from common perovskites that have single local environments (SLE). The basic phenomenology associated with such disproportionation involves the absence of $B$-atom charge ordering, the creation of different B-X bond length (``bond alternation'') for different local environments, the appearance of metal (in SLE) to insulator (in DLE) transitions, and the formation of ligand holes. We point out that this phenomenology is common to a broad range of chemical bonding patterns in $AB{X}_{3}$ compounds, either with s-p electron $B$-metal cations (${\mathrm{BaBiO}}_{3}$, ${\mathrm{CsTlF}}_{3}$) or with noble-metal cations (${\mathrm{CsAuCl}}_{3}$), as well as with $d$-electron cations (${\mathrm{SmNiO}}_{3}$, ${\mathrm{CaFeO}}_{3}$). We show that underlying much of this phenomenology is the ``self-regulating response,'' whereby in strongly bonded metal-ligand systems with high-lying ligand orbitals, the system protects itself from creating highly charged cations by transferring ligand electrons to the metal, thus preserving a nearly constant metal charge in different local environments, while creating $B$-ligand bond alternation and ligand-like conduction band (``ligand hole'' states). We are asking what are the minimal theory ingredients needed to explain the main features of this SLE-to-DLE phenomenology, such as its energetic driving force, bond length changes, possible modifications in charge density, and density of state changes. Using as a guide the lowering of the total energy in DLE relative to SLE, we show that density functional calculations describe this phenomenology across the whole chemical bonding range without resort to special strong correlation effects, beyond what DFT naturally contains. In particular, lower total energy configurations (DLE) naturally develop bond alternation, gapping of the metallic SLE state, and absence of charge ordering with ligand hole formation.

We apply machine learning (ML) methods to a database of 390 experimentally reported $AB{\mathrm{O}}_{3}$ compounds to construct two statistical models that predict possible new perovskite materials and possible new cubic perovskites. The first ML model classified the 390 compounds into 254 perovskites and 136 that are not perovskites with a 90% average cross-validation (CV) accuracy; the second ML model further classified the perovskites into 22 known cubic perovskites and 232 known noncubic perovskites with a 94% average CV accuracy. We find that the most effective chemical descriptors affecting our classification include largely geometric constructs such as the $A$ and $B$ Shannon ionic radii, the tolerance and octahedral factors, the $A$-O and $B$-O bond length, and the $A$ and $B$ Villars' Mendeleev numbers. We then construct an additional list of $625AB{\mathrm{O}}_{3}$ compounds assembled from charge conserving combinations of $A$ and $B$ atoms absent from our list of known compounds. Then, using the two ML models constructed on the known compounds, we predict that 235 of the 625 exist in a perovskite structure with a confidence greater than 50% and among them that 20 exist in the cubic structure (albeit, the latter with only $\ensuremath{\sim}50%$ confidence). We find that the new perovskites are most likely to occur when the $A$ and $B$ atoms are a lanthanide or actinide, when the $A$ atom is an alkali, alkali earth, or late transition metal atom, or when the $B$ atom is a $p$-block atom. We also compare the ML findings with the density functional theory calculations and convex hull analyses in the Open Quantum Materials Database (OQMD), which predicts the $T=0$ K ground-state stability of all the $AB{\mathrm{O}}_{3}$ compounds. We find that OQMD predicts 186 of 254 of the perovskites in the experimental database to be thermodynamically stable within 100 meV/atom of the convex hull and predicts 87 of the 235 ML-predicted perovskite compounds to be thermodynamically stable within 100 meV/atom of the convex hull, including 6 of these to be in cubic structures. We suggest these 87 as the most promising candidates for future experimental synthesis of novel perovskites.