Competing stripe and magnetic phases in the cuprates from first principles

Advancing DFT predictions in Cu-chalcogenides with full-yet-shallow 3d-orbitals: Meta-GGA plus Hubbard-like U correction

The technologically important Cu-chalcogenides, such as Cu2Se and CuInSe2, usually have relatively small band gaps. Achieving a reliable yet efficient description of the electronic properties has proven to be quite challenging for the popular exchange-correlation functionals of density functional theory, primarily due to the involvement of full-yet-shallow Cu-3d orbitals. In this study, we evaluate the applicability of several meta-generalized gradient approximation (GGA) functionals that have been recently developed. We find that the r2SCAN (regularized-restored strongly constrained and appropriately normed) functional significantly improves upon conventional local density approximation and GGA in terms of geometry and electronic band structure; however, there is still a notable discrepancy with experimental results due to the remaining delocalization error. This error is mitigated by combining r2SCAN with a Hubbard-like U correction applied to the Cu-3d orbitals. For predicting band gaps, both the TASK functional and the mBJ potential, when combined with the U correction, demonstrate similar accuracies with a mean absolute error of 0.17-0.19 eV. This accuracy is lower than that achieved with the many-body Hedin's GW approximation method but more accurate than that of hybrid functionals. Moreover, the r2SCAN+U approach well reproduces the phonon dispersion in CuInSe2, revealing a neglected computational problem in previous reports. We conclude that the meta-GGA+U approach represents a significant advancement by striking a balance between reliability and computational effort, and further efforts are still required to describe the Cu-3d orbitals more accurately.

Emergence of Competing Stripe Phases in Undoped Infinite-Layer Nickelates

Recent discovery of superconductivity in infinite-layer nickelates has ignited renewed theoretical and experimental interest in the role of electronic correlations in their properties. Here, using first-principles simulations, we show that the parent compound of the nickelate family, LaNiO_{2}, hosts competing low-energy stripe phases, similar to doped cuprates. The stripe states are shown to be driven by multiorbital electronic mechanisms and Peierls distortions. Our study indicates that both strong correlations and electron-phonon coupling effects play a key role in the physics of infinite-layer nickelates, and sheds light on the microscopic origin of electronic inhomogeneity and the lack of long-range order in the nickelates.

Exploring unconventional ferromagnetism in hole-doped LaCrAsO: insights into charge-transfer and magnetic interactions

Itinerant ferromagnetism due to the canonical double exchange (CDE) mechanism always occurs at low doping concentrations. Here we demonstrate the occurrence of robust itinerant ferromagnetism that can persist high doping concentrations. Using experimentally synthesized LaCrAsO as an illustrative example, we study the effects of hole doping via first-principles calculations and observe that the parent G-type antiferromagnetism vanishes quickly at a low doping concentration (∼0.20) and the system becomes a ferromagnetic metal due to the CDE mechanism. As the doping concentration continues to increase, the As 4p orbitals are gradually pushed up to the Fermi level and doped with holes. These ligand holes participate in the exchange interactions and drive the system toward ferromagnetism. Therefore, itinerant ferromagnetism doesn't terminate at an intermediate doping concentration as the CDE mechanism usually predicts. Furthermore, our results reveal that both the nearest and the next-nearest ferromagnetic exchange coupling strengths keep growing with doping concentration monotonically, showing that the emergent ferromagnetism mediated by As 4p orbitals is "stronger" than that of the CDE picture. Our work unlocks a new mechanism of itinerant ferromagnetism and potentially paves the way towards novel magneto-transport properties.

Challenges for density functional theory in simulating metal-metal singlet bonding: A case study of dimerized VO2

VO2 is renowned for its electric transition from an insulating monoclinic (M1) phase, characterized by V-V dimerized structures, to a metallic rutile (R) phase above 340 K. This transition is accompanied by a magnetic change: the M1 phase exhibits a non-magnetic spin-singlet state, while the R phase exhibits a state with local magnetic moments. Simultaneous simulation of the structural, electric, and magnetic properties of this compound is of fundamental importance, but the M1 phase alone has posed a significant challenge to the density functional theory (DFT). In this study, we show none of the commonly used DFT functionals, including those combined with on-site Hubbard U to treat 3d electrons better, can accurately predict the V-V dimer length. The spin-restricted method tends to overestimate the strength of the V-V bonds, resulting in a small V-V bond length. Conversely, the spin-symmetry-breaking method exhibits the opposite trends. Each of these two bond-calculation methods underscores one of the two contentious mechanisms, i.e., Peierls lattice distortion or Mott localization due to electron-electron repulsion, involved in the metal-insulator transition in VO2. To elucidate the challenges encountered in DFT, we also employ an effective Hamiltonian that integrates one-dimensional magnetic sites, thereby revealing the inherent difficulties linked with the DFT computations.

Comparing first-principles density functionals plus corrections for the lattice dynamics of YBa2Cu3O6

The enigmatic mechanism underlying unconventional high-temperature superconductivity, especially the role of lattice dynamics, has remained a subject of debate. Theoretical insights have long been hindered due to the lack of an accurate first-principles description of the lattice dynamics of cuprates. Recently, using the r2SCAN meta-generalized gradient approximation (meta-GGA) functional, we have been able to achieve accurate phonon spectra of an insulating cuprate YBa2Cu3O6 and discover significant magnetoelastic coupling in experimentally interesting Cu-O bond stretching optical modes [Ning et al., Phys. Rev. B 107, 045126 (2023)]. We extend this work by comparing Perdew-Burke-Ernzerhof and r2SCAN performances with corrections from the on-site Hubbard U and the D4 van der Waals (vdW) methods, aiming at further understanding on both the materials science side and the density functional side. We demonstrate the importance of vdW and self-interaction corrections for accurate first-principles YBa2Cu3O6 lattice dynamics. Since r2SCAN by itself partially accounts for these effects, the good performance of r2SCAN is now more fully explained. In addition, the performances of the Tao-Mo series of meta-GGAs, which are constructed in a different way from the strongly constrained and appropriately normed (SCAN) meta-GGA and its revised version r2SCAN, are also compared and discussed.

Stretching Bonds without Breaking Symmetries in Density Functional Theory

Kohn-Sham density functional theory (KS-DFT) stands out among electronic structure methods due to its balance of accuracy and computational efficiency. However, to achieve chemically accurate energies, standard density functional approximations in KS-DFT often need to break underlying symmetries, a long-standing "symmetry dilemma". By employing fragment spin densities as the main variables in calculations (rather than total molecular densities, as in KS-DFT), we present an embedding framework in which this symmetry dilemma is understood and partially resolved. The spatial overlap between fragment densities is used as the main ingredient to construct a simple, physically motivated approximation to a universal functional of the fragment densities. This "overlap approximation" is shown to significantly improve semilocal KS-DFT binding energies of molecules without artificially breaking either charge or spin symmetries. The approach is shown to be applicable to covalently bonded molecules and to systems of the "strongly correlated" type.

My life in science: Lessons for yours?

Because of an acquired obsession to understand as much as possible in a limited but important area of science and because of optimism, luck, and help from others, my life in science turned out to be much better than I or others could have expected or planned. This is the story of how that happened, and also the story of the groundstate density functional theory of electronic structure, told from a personal perspective.

Comparative Density Functional Theory Study of Magnetic Exchange Couplings in Dinuclear Transition-Metal Complexes

Multicenter transition-metal complexes (MCTMs) with magnetically interacting ions have been proposed as components for information-processing devices and storage units. For any practical application of MCTMs as magnetic units, it is crucial to characterize their magnetic behavior, and in particular, the isotropic magnetic exchange coupling, J, between its magnetic centers. Due to the large size of typical MCTMs, density functional theory is the only practical electronic structure method for evaluating the J coupling. Here, we assess the accuracy of different density functional approximations for predicting the magnetic couplings of eight dinuclear transition-metal complexes, including five dimanganese, two dicopper, and one divanadium with known reliable experimental J couplings spanning from ferromagnetic to strong antiferromagnetic. The density functionals considered include global hybrid functionals which mix semilocal density functional approximations and exact exchange with a fixed admixing parameter, six local hybrid functionals where the admixing parameters are extended to be spatially dependent, the SCAN and r2SCAN meta-generalized gradient approximations (GGAs), and two widely used GGAs. We found that global hybrids tested in this work have a tendency to over-correct the error in magnetic coupling parameters from the Perdew-Burke-Ernzerhof (PBE) GGA as seen for manganese complexes. The performance of local hybrid density functionals shows no improvement in terms of bias and is scattered without a clear trend, suggesting that more efforts are needed for the extension from global to local hybrid density functionals for this particular property. The SCAN and r2SCAN meta-GGAs are found to perform as well as benchmark global hybrids on most tested complexes. We further analyze the charge density redistribution of meta-GGAs as well as global and local hybrid density functionals with respect to that of PBE, in connection to the self-interaction error or delocalization error.

Correlation versus hybridization gap in CaMn[Formula: see text]Bi[Formula: see text]

We study the interplay between electronic correlations and hybridization in the low-energy electronic structure of CaMn[Formula: see text]Bi[Formula: see text], a candidate hybridization-gap semiconductor. By employing a DFT+U approach we find both the antiferromagnetic Néel order and band gap in good agreement with the corresponding experimental values. Under hydrostatic pressure, we find a crossover from hybridization gap to charge-transfer insulting physics due to the delicate balance of hybridization and correlations. Increasing the pressure above [Formula: see text] GPa we find a simultaneous pressure-induced volume collapse, plane-to-chain, insulator to metal transition. Finally, we have also analyzed the topology in the antiferromagnetic CaMn[Formula: see text]Bi[Formula: see text] for all pressures studied.

Testing the r2SCAN Density Functional for the Thermodynamic Stability of Solids with and without a van der Waals Correction

A central aim of materials discovery is an accurate and numerically reliable description of thermodynamic properties, such as the enthalpies of formation and decomposition. The r2SCAN revision of the strongly constrained and appropriately normed (SCAN) meta-generalized gradient approximation (meta-GGA) balances numerical stability with high general accuracy. To assess the r2SCAN description of solid-state thermodynamics, we evaluate the formation and decomposition enthalpies, equilibrium volumes, and fundamental band gaps of more than 1000 solids using r2SCAN, SCAN, and PBE, as well as two dispersion-corrected variants, SCAN+rVV10 and r2SCAN+rVV10. We show that r2SCAN achieves accuracy comparable to SCAN and often improves upon SCAN's already excellent accuracy. Although SCAN+rVV10 is often observed to worsen the formation enthalpies of SCAN and makes no substantial correction to SCAN's cell volume predictions, r2SCAN+rVV10 predicts marginally less accurate formation enthalpies than r2SCAN, and slightly more accurate cell volumes than r2SCAN. The average absolute errors in predicted formation enthalpies are found to decrease by a factor of 1.5 to 2.5 from the GGA level to the meta-GGA level. Smaller decreases in error are observed for decomposition enthalpies. For formation enthalpies r2SCAN improves over SCAN for intermetallic systems. For a few classes of systems-transition metals, intermetallics, weakly bound solids, and enthalpies of decomposition into compounds-GGAs are comparable to meta-GGAs. In total, r2SCAN and r2SCAN+rVV10 can be recommended as stable, general-purpose meta-GGAs for materials discovery.

Symmetry Breaking with the SCAN Density Functional Describes Strong Correlation in the Singlet Carbon Dimer

The SCAN (strongly constrained and appropriately normed) meta-generalized gradient approximation (meta-GGA), which satisfies all 17 exact constraints that a meta-GGA can satisfy, accurately describes equilibrium bonds that are normally correlated. With symmetry breaking, it also accurately describes some sd equilibrium bonds that are strongly correlated. While sp equilibrium bonds are nearly always normally correlated, the C₂ singlet ground state is known from correlated wave function theory to be a rare case of strong correlation in an sp equilibrium bond. Earlier work that calculated atomization energies of the molecular sequence B₂, C₂, O₂, and F₂ in the local spin density approximation (LSDA), the Perdew-Burke-Ernzerhof (PBE) GGA, and the SCAN meta-GGA, without symmetry breaking in the molecule, found that only SCAN was accurate enough to reveal an anomalous under-binding for C₂. This work shows that spin symmetry breaking in singlet C₂, which involves the appearance of net up- and down-spin densities on opposite sides (not ends) of the bond, corrects that underbinding, with a small SCAN atomization-energy error more like that of the other three molecules, suggesting that symmetry breaking with an advanced density functional might reliably describe strong correlation. This article also discusses some general aspects of symmetry breaking and the insights into strong correlation that symmetry breaking can bring. The normally correlated low-lying triplet excited state has the right vertical excitation energy in SCAN but not in LSDA or PBE, where the triplet is a false ground state. Fractional occupation numbers are found only for the symmetry-unbroken singlet and only in LSDA and PBE GGA.

Topology and Symmetry in Quantum Materials

Interest in topological materials continues to grow unabated in view of their conceptual novelties as well as their potential as platforms for transformational new technologies. Electronic states in a topological material are robust against perturbations and support unconventional electromagnetic responses. The first-principles band-theory paradigm has been a key player in the field by providing successful prediction of many new classes of topological materials. This perspective presents a cross section through the recent work on understanding the role of geometry and topology in generating topological states and their responses to external stimuli, and as a basis for connecting theory and experiment within the band theory framework. In this work, effective strategies for topological materials discovery and impactful directions for future topological materials research are also commented.

Re-examining the giant magnetization density in α''-Fe16N2 with the SCAN+U method

We present an in-depth discussion of the magnetic ground state of α''-Fe₁₆N₂ within the framework of the density functional theory (DFT). The exchange-correlation effects are treated using a variety of schemes, including the local-spin-density approximation, the generalized-gradient approximation, and the Strongly-Constrained-and-Appropriately-Normed (SCAN) scheme. We also delineate effects of adding an on-site interaction parameter U on the Fe sites. Among all the schemes considered, only SCAN+U is found to capture the surprisingly large magnetization density in α''-Fe₁₆N₂ that has been observed experimentally. Our study shows how the combination of SCAN and self-interaction corrections applied on different Fe sites through the parameter U can reproduce both the correct equilibrium volume and the giant magnetization density of α''-Fe₁₆N₂.

Pushing the frontiers of density functionals by solving the fractional electron problem

[Figure: see text].

Artificial intelligence "sees" split electrons

[Figure: see text].

Improved electronic structure prediction of chalcopyrite semiconductors from a semilocal density functional based on Pauli kinetic energy enhancement factor

The correct treatment ofdelectrons is of prime importance in order to predict the electronic properties of the prototype chalcopyrite semiconductors. The effect ofdstates is linked with the anion displacement parameteru, which in turn influences the bandgap of these systems. Semilocal exchange-correlation functionals which yield good structural properties of semiconductors and insulators often fail to predict reasonableubecause of the underestimation of the bandgaps arising from the strong interplay betweendelectrons. In the present study, we show that the meta-generalized gradient approximation (meta-GGA) obtained from the cuspless hydrogen density (MGGAC) (2019Phys. Rev.B 100 155140) performs in an improved manner in apprehending the key features of the electronic properties of chalcopyrites, and its bandgaps are comparative to that obtained using state-of-art hybrid methods. Moreover, the present assessment also shows the importance of the Pauli kinetic energy enhancement factor,α= (τ-τ^W)/τ^unifin describing thedelectrons in chalcopyrites. The present study strongly suggests that the MGGAC functional within semilocal approximations can be a better and preferred choice to study the chalcopyrites and other solid-state systems due to its superior performance and significantly low computational cost.

Restored strange metal phase through suppression of charge density waves in underdoped YBa2Cu3O7-δ

[Figure: see text].

Interpretations of ground-state symmetry breaking and strong correlation in wavefunction and density functional theories

Strong correlations within a symmetry-unbroken ground-state wavefunction can show up in approximate density functional theory as symmetry-broken spin densities or total densities, which are sometimes observable. They can arise from soft modes of fluctuations (sometimes collective excitations) such as spin-density or charge-density waves at nonzero wavevector. In this sense, an approximate density functional for exchange and correlation that breaks symmetry can be more revealing (albeit less accurate) than an exact functional that does not. The examples discussed here include the stretched H2 molecule, antiferromagnetic solids, and the static charge-density wave/Wigner crystal phase of a low-density jellium. Time-dependent density functional theory is used to show quantitatively that the static charge-density wave is a soft plasmon. More precisely, the frequency of a related density fluctuation drops to zero, as found from the frequency moments of the spectral function, calculated from a recent constraint-based wavevector- and frequency-dependent jellium exchange-correlation kernel.

Magnetic Interactions in ZnMnO3: Active Role of Zn 3d10 Orbitals, in Comparison with MgMnO3

The ilmenite-type MgMnO₃ and ZnMnO₃ with honeycomb Mn layers exhibit distinctive magnetic ground states. In experiments, MgMnO₃ exhibits a Néel antiferromagnetic alignment, in which both nearest-neighbor (NN) J₁ and next-nearest-neighbor (NNN) J₂ exchange interactions are antiferromagnetic, while ZnMnO₃ has zigzag antiferromagnetic ordering with NN ferromagnetic and NNN antiferromagnetic coupling. On the basis of ab initio band structure calculations, we explain the deviation of NN J₁ exchange coupling from antiferromagnetic (MgMnO₃) to ferromagnetic (ZnMnO₃) as originating from the intensive hybridization between the occupied Zn 3d¹⁰ orbitals with those of the bridging O 2p states, strongly depending on the position of the orbitals. In addition, our results indicate that, in combination with the NN J₁ coupling, the considerably large third-nearest-neighbor (TNN) J₃ exchange interaction plays an important role in erecting the magnetic ground states, rather than the experimentally proposed NNN J₂. Furthermore, our findings highlight the important role of not only the electronic configurations but also the positions of the nonmagnetic cations in determining the essence of the magnetic exchange interactions. Therefore, the hybridization effect of nonmagnetic cations should not be dismissed in an analysis of the magnetic properties of transition-metal oxides.

Accurate and Numerically Efficient r2SCAN Meta-Generalized Gradient Approximation

The recently proposed rSCAN functional [ J. Chem. Phys. 2019 150, 161101] is a regularized form of the SCAN functional [ Phys. Rev. Lett. 2015 115, 036402] that improves SCAN's numerical performance at the expense of breaking constraints known from the exact exchange-correlation functional. We construct a new meta-generalized gradient approximation by restoring exact constraint adherence to rSCAN. The resulting functional maintains rSCAN's numerical performance while restoring the transferable accuracy of SCAN.

Topological Dirac Semimetal Phase in Bismuth Based Anode Materials for Sodium-Ion Batteries

Bismuth has recently attracted interest in connection with Na-ion battery anodes due to its high volumetric capacity. It reacts with Na to form Na 3 Bi which is a prototypical Dirac semimetal with a nontrivial electronic structure. Density-functional-theory based first-principles calculations are playing a key role in understanding the fascinating electronic structure of Na 3 Bi and other topological materials. In particular, the strongly-constrained-and-appropriately-normed (SCAN) meta-generalized-gradient-approximation (meta-GGA) has shown significant improvement over the widely used generalized-gradient-approximation (GGA) scheme in capturing energetic, structural, and electronic properties of many classes of materials. Here, we discuss the electronic structure of Na 3 Bi within the SCAN framework and show that the resulting Fermi velocities and s-band shift around the Γ point are in better agreement with experiments than the corresponding GGA predictions. SCAN yields a purely spin-orbit-coupling (SOC) driven Dirac semimetal state in Na 3 Bi in contrast with the earlier GGA results. Our analysis reveals the presence of a topological phase transition from the Dirac semimetal to a trivial band insulator phase in Na 3 Bi x Sb 1 − x alloys as the strength of the SOC varies with Sb content, and gives insight into the role of the SOC in modulating conduction properties of Na 3 Bi.