Quasiparticle Self-consistent GW Research Articles

Fully Dynamic G3W2 Self-Energy for Finite Systems: Formulas and Benchmark.

Over the years, Hedin's GW self-energy has been proven to be a rather accurate and simple approximation to evaluate electronic quasiparticle energies in solids and in molecules. Attempts to improve over the simple GW approximation, the so-called vertex corrections, have been constantly proposed in the literature. Here, we derive, analyze, and benchmark the complete second-order term in the screened Coulomb interaction W for finite systems. This self-energy named G3W2 contains all the possible time orderings that combine 3 Green's functions G and 2 dynamic W. We present the analytic formula and its imaginary frequency counterpart, with the latter allowing us to treat larger molecules. The accuracy of the G3W2 self-energy is evaluated on well-established benchmarks (GW100, Acceptor 24, and Core 65) for valence and core quasiparticle energies. Its link with the simpler static approximation, named SOSEX for static screened second-order exchange, is analyzed, which leads us to propose a more consistent approximation named 2SOSEX. In the end, we find that neither the G3W2 self-energy nor any of the investigated approximations to it improve over one-shot G0W0 with a good starting point. Only quasi-particle self-consistent GW HOMO energies are slightly improved by addition of the G3W2 self-energy correction. We show that this is due to the self-consistent update of the screened Coulomb interaction, leading to an overall sign change of the vertex correction to the frontier quasiparticle energies.

Orbital-Selective Mott Transition Effects and Nontrivial Topology of Iron Chalcogenide.

The iron-based superconductor FeSe_{1-x}Te_{x} has recently gained significant attention as a host of two distinct physical phenomena: (i)Majorana zero modes that can serve as potential topologically protected qubits, and (ii)a realization of the orbital-selective Mott transition. In this Letter, we connect these two phenomena and provide new insights into the interplay between strong electronic correlations and nontrivial topology in FeSe_{1-x}Te_{x}. Using linearized quasiparticle self-consistent GW plus dynamical mean-field theory, we show that the topologically protected Dirac surface state has substantial Fe(d_{xy}) character. The proximity to the orbital-selective Mott transition plays a dual role: it facilitates the appearance of the topological surface state by bringing the Dirac cone close to the chemical potential but destroys the Z_{2} topological superconductivity when the system is too close to the orbital-selective Mott phase. We derive a reduced effective Hamiltonian that describes the topological band. Its parameters capture all the chemical trends found in the first principles calculation. Our findings provide a framework for further study of the interplay between strong electronic correlations and nontrivial topology in other iron-based superconductors.

Pressure-dependent multiplet-excitation energies of α-Al2O3:Cr3+ by the first-principles method

We apply a method [Phys. Rev. B 108, 035141 (2023)], which can treat the multiplet excitations in the first-principles method, to a typical pressure indicator α-Al2O3:Cr3+. After optimizing the crystal structure under hydrostatic pressure from 0.0 to 35.0 GPa in the usual first-prinicple calculations, we obtain the multiplet energies in the method. That is, we conduct the exact diagonalization of the crystal-field model Hamiltonian which is directly determined based on the result of the quasiparticle self-consistent GW method. Our method has no parameters by hand. The calculated pressure dependences of the excitation energies agree well with those of experiments.

Spinel LiGa5O8 prospects as ultra-wideband-gap semiconductor: Band structure, optical properties, and doping

LiGa5O8 in the spinel type structure is investigated as a potential ultra-wideband-gap semiconductor. The band structure is determined using the quasiparticle self-consistent GW method, and the optical properties are calculated at the Bethe Salpeter Equation level including electron-hole interaction effects. The optical gap including exciton effects and an estimate of the zero-point motion electron phonon coupling renormalizations is estimated to be about 5.2±0.1 eV with an exciton binding energy of about 0.4 eV. Si doping as potential n-type dopant is investigated and found to be a promising shallow donor.

Two-Component GW Calculations: Cubic Scaling Implementation and Comparison of Vertex-Corrected and Partially Self-Consistent GW Variants.

We report an all-electron, atomic orbital (AO)-based, two-component (2C) implementation of the GW approximation (GWA) for closed-shell molecules. Our algorithm is based on the space-time formulation of the GWA and uses analytical continuation (AC) of the self-energy, and pair-atomic density fitting (PADF) to switch between AO and auxiliary basis. By calculating the dynamical contribution to the GW self-energy at a quasi-one-component level, our 2C-GW algorithm is only about a factor of 2-3 slower than in the scalar relativistic case. Additionally, we present a 2C implementation of the simplest vertex correction to the self-energy, the statically screened G3W2 correction. Comparison of first ionization potentials (IPs) of a set of 67 molecules with heavy elements (a subset of the SOC81 set) calculated with our implementation against results from the WEST code reveals mean absolute deviations (MAD) of around 70 meV for G0W0@PBE and G0W0@PBE0. We check the accuracy of our AC treatment by comparison to full-frequency GW calculations, which shows that in the absence of multisolution cases, the errors due to AC are only minor. This implies that the main sources of the observed deviations between both implementations are the different single-particle bases and the pseudopotential approximation in the WEST code. Finally, we assess the performance of some (partially self-consistent) variants of the GWA for the calculation of first IPs by comparison to vertical experimental reference values. G0W0@PBE0 (25% exact exchange) and G0W0@BHLYP (50% exact exchange) perform best with mean absolute deviations (MAD) of about 200 meV. Explicit treatment of spin-orbit effects at the 2C level is crucial for systematic agreement with experiment. On the other hand, eigenvalue-only self-consistent GW (evGW) and quasi-particle self-consistent GW (qsGW) significantly overestimate the IPs. Perturbative G3W2 corrections increase the IPs and therefore improve the agreement with experiment in cases where G0W0 alone underestimates the IPs. With a MAD of only 140 meV, 2C-G0W0@PBE0 + G3W2 is in best agreement with the experimental reference values.

Quasiparticle band structures of Cs2B+B3+Br6 lead-free halide double perovskites

Recently, lead-free halide double perovskites (DPs) have been proposed to be great alternative materials for perovskite solar cell (PSC). Therefore, we present a detailed understanding of the electronic structures of Cs2B+B3+Br6, where B+ are Ag and Cu, B3+ are Bi and Sb, by using the high accuracy first-principle method called quasiparticle self-consistent GW (QSGW). As a result, all bandgaps are indirect between X and L symmetry points, spanning from 1.13 to 2.33 eV. The band edges are composed from Br-4p, B+-sd and B3+-sp orbitals. Moreover, band structures including spin-orbit coupling (SOC) reveal that there are energy gaps of 1.29 eV between the first and second conduction bands in Bi-based compounds, resulting from the hybridization of Br-4p and Bi- 6p. Finally, the conductivity effective masses of electron (m*e) and hole (m*h) were calculated. We found that m*e of all materials are about 0.27 me, while m*h range from 0.32 me to 0.47 me. Overall, the effective masses of Cs2B+B3+Br6 are comparable to those of MAPbI3. In conclusion, Cs2B+B3+Br6 are predicted to be potential materials for photovoltaics and optoelectronics due to their bandgaps covering IR to UV range and have qualified electrical conductivity due to their small effective masses. We expected that our results will motivate researchers to further synthesize and characterize Cs2B+B3+Br6 and their related materials.

A Similarity Renormalization Group Approach to Green's Function Methods.

The family of Green's function methods based on the GW approximation has gained popularity in the electronic structure theory thanks to its accuracy in weakly correlated systems combined with its cost-effectiveness. Despite this, self-consistent versions still pose challenges in terms of convergence. A recent study [Monino and Loos J. Chem. Phys. 2022, 156, 231101.] has linked these convergence issues to the intruder-state problem. In this work, a perturbative analysis of the similarity renormalization group (SRG) approach is performed on Green's function methods. The SRG formalism enables us to derive, from first-principles, the expression of a naturally static and Hermitian form of the self-energy that can be employed in quasiparticle self-consistent GW (qsGW) calculations. The resulting SRG-based regularized self-energy significantly accelerates the convergence of qsGW calculations, slightly improves the overall accuracy, and is straightforward to implement in existing code.

First-principles method justifying the Dieke diagram and beyond

We present a method to determine the model Hamiltonians to treat rare-earth multiplets in solids from the results of the quasiparticle self-consistent GW (QSGW) method. We apply the method to trivalent Eu compounds ${\mathrm{EuCl}}_{3}$, EuN, and Eu-doped GaN after examining free rare-earth ions. We solve the model Hamiltonian by the exact diagonalization. Our results justify applying the Dieke diagram to ions in solid, while its limitation is clarified. In particular, we show that the crystal fields cause sizable breaking of the Russell-Saunders coupling.

Gaussian-based quasiparticle self-consistent GW for periodic systems.

We present a quasiparticle self-consistent GW (QSGW) implementation for periodic systems based on crystalline Gaussian basis sets. Our QSGW approach is based on a full-frequency analytic continuation GW scheme with Brillouin zone sampling and employs the Gaussian density fitting technique. We benchmark our QSGW implementation on a set of weakly correlated semiconductors and insulators as well as strongly correlated transition metal oxides, including MnO, FeO, CoO, and NiO. The band gap, band structure, and density of states are evaluated using finite size corrected QSGW. We find that although QSGW systematically overestimates the bandgaps of the tested semiconductors and transition metal oxides, it completely removes the dependence on the choice of density functionals and provides a more consistent prediction of spectral properties than G0W0 across a wide range of solids. This work paves the way for utilizing QSGW in ab initio quantum embedding for solids.

Quasiparticle Self-Consistent GW Study of Simple Metals.

The method is a standard method to calculate the electronic band structure from first principles. It has been applied to a large variety of semiconductors and insulators but less often to metallic systems, in particular, with respect to a self-consistent employment of the method. In this work, we take a look at all-electron quasiparticle self-consistent (QS) calculations for simple metals (alkali and alkaline earth metals) based on the full-potential linearized augmented-plane-wave approach and compare the results to single-shot (i.e., non-selfconsistent) calculations, density-functional theory (DFT) calculations in the local-density approximation, and experimental measurements. We show that, while DFT overestimates the bandwidth of most of the materials, the quasiparticle renormalization corrects the bandwidths in the right direction, but a full self-consistent calculation is needed to consistently achieve good agreement with photoemission data. The results mainly confirm the common belief that simple metals can be regarded as nearly free electron gases with weak electronic correlation. The finding is particularly important in light of a recent debate in which this seemingly established view has been contested.

Electronic structure of representative band-gap materials by all-electron quasiparticle self-consistent GW calculations

In this work, we report results of the quasiparticle self-consistent GW method within the framework of the linearized augmented plane-wave method. The impact of self-consistency on the electronic structure is investigated with the examples of nine semiconductors and insulators, namely, Ar, Si, SiC, C, BN, LiF, MgO, CaO, and GaAs. Possible reasons for discrepancies between different studies and implementations are discussed. For LiF, MgO, and CaO, we assess the charge-density redistribution upon self-consistency. For a representative set of materials, we investigate and confirm the absence of (any) starting-point dependence. The off-diagonal terms in the self-energy matrix are found to considerably impact the electronic structure. For better reproducibility and quality assessment, we describe the implementation of QSGW in the all-electron full-potential code exciting.

First-principles study of excitons in optical spectra of silver chloride

Silver chloride is a material that has been investigated and used for many decades. Of particular interest are its optical properties, but only few fundamental theoretical studies exist. We present first-principles results for the optical properties of AgCl, obtained using time-dependent density functional theory and many-body perturbation theory. We show that optical properties exhibit strong excitonic effects, which are correctly captured only by solving the Bethe-Salpeter equation starting from quasiparticle self-consistent GW results. Numerical simulations are made feasible by using a model screening for the electron-hole interaction in a way that avoids the calculation of the static dielectric constant. A thorough analysis permits us to discuss localization in bright and dark excitons of silver chloride.

Development of data-driven spd tight-binding models of Fe—parameterisation based on QSGW and DFT calculations including information about higher-order elastic constants

Quantum-mechanical (QM) simulations, thanks to their predictive power, can provide significant insights into the nature and dynamics of defects such as vacancies, dislocations and grain boundaries. These considerations are essential in the context of the development of reliable, inexpensive and environmentally friendly alloys. However, despite significant progress in computer performance, QM simulations of defects are still extremely time-consuming with ab-initio/non-parametric methods. The two-centre Slater–Koster (SK) tight-binding (TB) models can achieve significant computational efficiency and provide an interpretable picture of the electronic structure. In some cases, this makes TB a compelling alternative to models based on abstraction of the electronic structure, such as the embedded atom model. The biggest challenge in the implementation of the SK method is the estimation of the optimal and transferable parameters that are used to construct the Hamiltonian matrix. In this paper, we will present results of the development of a data-driven framework, following the classical approach of adjusting parameters in order to recreate properties that can be measured or estimated using ab-initio or non-parametric methods. Distinct features include incorporation of data from QSGW (quasi-particle self-consistent GW approximation) calculations, as well as consideration of higher-order elastic constants. Furthermore, we provide a description of the optimisation procedure, omitted in many publications, including the design stage. We also apply modern optimisation techniques that allow us to minimise constraints on the parameter space. In summary, this paper introduces some methodological improvements to the semi-empirical approach while addressing associated challenges and advantages.

Low-Order Scaling Quasiparticle Self-Consistent GW for Molecules.

Low-order scaling GW implementations for molecules are usually restricted to approximations with diagonal self-energy. Here, we present an all-electron implementation of quasiparticle self-consistent GW for molecular systems. We use an efficient algorithm for the evaluation of the self-energy in imaginary time, from which a static non-local exchange-correlation potential is calculated via analytical continuation. By using a direct inversion of iterative subspace method, fast and stable convergence is achieved for almost all molecules in the GW100 database. Exceptions are systems which are associated with a breakdown of the single quasiparticle picture in the valence region. The implementation is proven to be starting point independent and good agreement of QP energies with other codes is observed. We demonstrate the computational efficiency of the new implementation by calculating the quasiparticle spectrum of a DNA oligomer with 1,220 electrons using a basis of 6,300 atomic orbitals in less than 4 days on a single compute node with 16 cores. We use then our implementation to study the dependence of quasiparticle energies of DNA oligomers consisting of adenine-thymine pairs on the oligomer size. The first ionization potential in vacuum decreases by nearly 1 electron volt and the electron affinity increases by 0.4 eV going from the smallest to the largest considered oligomer. This shows that the DNA environment stabilizes the hole/electron resulting from photoexcitation/photoattachment. Upon inclusion of the aqueous environment via a polarizable continuum model, the differences between the ionization potentials reduce to 130 meV, demonstrating that the solvent effectively compensates for the stabilizing effect of the DNA environment. The electron affinities of the different oligomers are almost identical in the aqueous environment.

Electronic structure of van der Waals ferromagnet CrI3 from self-consistent vertex corrected GW approaches

The electronic structure of layered van der Waals ferromagnet ${\mathrm{CrI}}_{3}$ is studied with self-consistent diagrammatic approaches beyond GW approximation. Considerable improvement in the calculated band gap as compared to the non-self-consistent ${G}_{0}{W}_{0}$ results has been found. Certain spectral features in the valence bands discovered recently by angle-resolved photoemission spectroscopy are reproduced better when we use full frequency-dependent self-energy. Density-functional theory and quasiparticle self-consistent GW method which are based on frequency-independent self-energy are unable to resolve these features. Nonlocality effects in the diagrams beyond GW approximation are large for both polarizability and self-energy. This finding can potentially have an impact on the development of methods like GW$+$dynamical mean field theory.

Electronic structure of LaNiO2 and CaCuO2 from a self-consistent vertex-corrected GW approach

Electronic structure of one of the nickelates (LaNiO$_{2}$) and one of the cuprates (CaCuO$_{2}$) is studied with three self consistent GW-based methods: scGW, sc(GW+Vertex), and quasiparticle self-consistent GW. Low energy features obtained in our study are in many respects similar to the features reported in previous DFT+DMFT studies. Consistent with the DFT+DMFT conclusion, we find LaNiO$_{2}$ as more correlated than CaCuO$_{2}$. However, correlation effects included in our study change the DFT Fermi surface near the $\Gamma$ point differently than it was reported in the DMFT studies. Features which are a few electron-volts away from the Fermi level are broader in our calculations than in the DFT+DMFT which reflects the differences between the DFT and the GW methods. Our results are in qualitative agreement with previous G0W0 results, but the self-consistency brings in the quantitative differences. Generally, correlation effects are found to be sufficiently weak in both materials which allows one to use totally ab-initio diagrammatic approaches like sc(GW+Vertex) and to avoid the methods with adjustable parameters (DFT+U or DFT+DMFT). However, the possibility of some strong correlations at low energy which cannot be captured by perturbative methods cannot be completely excluded. For instance, differences in the Fermi surface should be resolved: experimental studies are necessary.

Effect of electron localization in theoretical design of Ni-Mn-Ga based magnetic shape memory alloys

The precise determination of the stability of different martensitic phases is an essential task in the successful design of (magnetic) shape memory alloys. We evaluate the effect of electron delocalization correction on the predictive power of density functional theory for Ni-Mn-Ga, the prototype magnetic shape memory compound. Using the corrected Hubbard-model-based generalized gradient approximation (GGA+U), we varied the Coulomb repulsion parameter U from 0 eV to 3 eV to reveal the evolution of predicted material parameters. The increasing localization on Mn sites results in the increasing stabilization of 10M modulated structure in stoichiometric Ni2MnGa in agreement with experiment whereas uncorrected GGA and meta-GGA functional provide the lowest energy for 4O modulated structure and non-modulated structure, respectively. GGA+U calculations indicate that 10M structure is more stable than other martensitic structures for U > 1.2 eV.The key features of density of states (DOS) responsible for the stabilization or destabilization of particular martensitic phases calculated with GGA+U are found also in DOS calculated with advanced quasi-particle self-consistent GW (QSGW) method. It supports the physical background of Hubbard correction. Moreover, the calculations with U = 1.8 eV provide the best agreement with experimental data for lattice parameters of stoichiometric and off-stoichiometric alloys.

Electronic Structure of Water from Koopmans-Compliant Functionals.

Obtaining a precise theoretical description of the spectral properties of liquid water poses challenges for both molecular dynamics (MD) and electronic structure methods. The lower computational cost of the Koopmans-compliant functionals with respect to Green's function methods allows the simulations of many MD trajectories, with a description close to the state-of-art quasi-particle self-consistent GW plus vertex corrections method (QSGW + fxc). Thus, we explore water spectral properties when different MD approaches are used, ranging from classical MD to first-principles MD, and including nuclear quantum effects. We have observed that different MD approaches lead to up to 1 eV change in the average band gap; thus, we focused on the band gap dependence with the geometrical properties of a system to explain such spread. We have evaluated the changes in the band gap due to variations in the intramolecular O-H bond distance and HOH angle, as well as the intermolecular hydrogen bond O···O distance and the OHO angles. We have observed that the dominant contribution comes from the O-H bond length; the O···O distance plays a secondary role, and the other geometrical properties do not significantly influence the gap. Furthermore, we analyze the electronic density of states (DOS), where the KIPZ functional shows good agreement with the DOS obtained with state-of-art approaches employing quasi-particle self-consistent GW plus vertex corrections. The O-H bond length also significantly influences the DOS. When nuclear quantum effects are considered, broadening of the peaks driven by the broader distribution of the O-H bond lengths is observed, leading to a closer agreement with the experimental photoemission spectra.

Ultrathin 2D-oxides: A perspective on fabrication, structure, defect, transport, electron, and phonon properties

In the field of atomically thin 2D materials, oxides are relatively unexplored in spite of the large number of layered oxide structures amenable to exfoliation. There is an increasing interest in ultrathin film oxide nanostructures from applied points of view. In this Perspective paper, recent progress in understanding the fundamental properties of 2D oxides is discussed. Two families of 2D oxides are considered: (1) van der Waals bonded layered materials in which the transition metal is in its highest valence state (represented by V2O5 and MoO3) and (2) layered materials with ionic bonding between positive alkali cation layers and negatively charged transition metal oxide layers (LiCoO2). The chemical exfoliation process and its combination with mechanical exfoliation are presented for the latter. Structural phase stability of the resulting nanoflakes, the role of cation size, and the importance of defects in oxides are discussed. Effects of two-dimensionality on phonons, electronic band structures, and electronic screening are placed in the context of what is known on other 2D materials, such as transition metal dichalcogenides. The electronic structure is discussed at the level of many-body-perturbation theory using the quasiparticle self-consistent GW method, the accuracy of which is critically evaluated including effects of electron–hole interactions on screening and electron–phonon coupling. The predicted occurrence of a two-dimensional electron gas on Li-covered surfaces of LiCoO2 and its relation to topological aspects of the band structure and bonding is presented as an example of the essential role of the surface in ultrathin materials. Finally, some case studies of the electronic transport and the use of these oxides in nanoscale field-effect transistors are presented.

Experimental determination of the valence band offsets of ZnGeN2 and (ZnGe)0.94Ga0.12N2 with GaN

A predicted type-II staggered band alignment with an approximately 1.4 eV valence band offset at the ZnGeN2/GaN heterointerface has inspired novel band-engineered III-N/ZnGeN2 heterostructure-based device designs for applications in high performance optoelectronics. We report on the determination of the valence band offset between metalorganic chemical vapor deposition grown (ZnGe)1−x Ga2x N2, for x = 0 and 0.06, and GaN using x-ray photoemission spectroscopy. The valence band of ZnGeN2 was found to lie 1.45–1.65 eV above that of GaN. This result agrees well with the value predicted by first-principles density functional theory calculations using the local density approximation for the potential profile and quasiparticle self-consistent GW calculations of the band edge states relative to the potential. For (ZnGe)0.94Ga0.12N2 the value was determined to be 1.29 eV, ∼10%–20% lower than that of ZnGeN2. The experimental determination of the large band offset between ZnGeN2 and GaN provides promising alternative solutions to address challenges faced with pure III-nitride-based structures and devices.