Self-consistent GW Approximation Research Articles

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.

Electronic Structure Correspondence of Singlet-Triplet Scale Separation in Strained Sr2RuO4

At a temperature of roughly 1 K, Sr2RuO4 undergoes a transition from a normal Fermi liquid to a superconducting phase. Even while the former is relatively simple and well understood, the superconducting state has not even been understood after 25 years of study. More recently, it has been found that critical temperatures can be enhanced by the application of uniaxial strain, up to a critical strain, after which it falls off. In this work, we take an “instability” approach and seek divergences in susceptibilities. This provides an unbiased way to distinguish tendencies to competing ground states. We show that in the unstrained compound, the singlet and triplet instabilities of the normal Fermi liquid phase are closely spaced. Under uniaxial strain, electrons residing on all orbitals contributing to the Fermiology become more coherent, while the electrons of the Ru-dxy character become heavier, and the electrons of the Ru-dxz,yz characters become lighter. In the process, Im χ(q,ω) increases rapidly around q = (0.3,0.3,0)2π/a and q = (0.5,0.25,0)2π/a, while it gets suppressed at all other commensurate vectors, in particular at q = 0, which is essential for spin-triplet superconductivity. We observe that the magnetic anisotropy under strain drops smoothly, which is concomitant with the increment in singlet instability. Thus, the triplet superconducting instability remains the lagging instability of the system, and the singlet instability enhances under strain, leading to a large energy-scale separation between these competing instabilities. However, since this happens even without spin-orbit coupling, we believe it is primarily the enhancement in the spin fluctuation glue around quasi-anti-ferromagnetic vectors that drives the Cooper pairing instead of the magnetic anisotropy. At large strain, an instability to a spin density wave overtakes the superconducting one. The analysis relies on a high-fidelity, ab initio description of the one-particle properties and two-particle susceptibilities, based on the quasiparticle self-consistent GW approximation augmented by dynamical mean field theory. This approach is described and its high fidelity confirmed by comparing to observed one- and two-particle properties.

Evening out the spin and charge parity to increase {T}_{c} in {{rm{Sr}}}_{2}{{rm{RuO}}}_{4}

Unconventional superconductivity in {{rm{Sr}}}_{2}{{rm{RuO}}}_{4} has been intensively studied for decades. However, the nature of pairing continues to be widely debated. Here we develop a detailed ab initio theory, coupling quasiparticle self-consistent GW approximation with dynamical mean field theory (DMFT), including both local and non-local correlations to address the subtle interplay among spin, charge and orbital degrees of freedom. We report that the superconducting instability has multiple triplet and singlet components. In the unstrained case the triplet eigenvalues are larger than the singlets. Under uniaxial strain, the triplet eigenvalues drop and the singlet components increase. This is concomitant with our observation of spin and charge fluctuations shifting closer to wave-vectors favoring singlet pairing. We identify a complex mechanism where charge fluctuations and spin fluctuations co-operate in the even-parity channel under strain leading to increment in critical temperature (Tc), thus proposing a novel mechanism for pushing the frontier of critical temperature (Tc) in unconventional ‘triplet’ superconductors.

Quasiparticle self-consistent GW band structures of Mg-IV-N2 compounds: The role of semicore d states

We present improved band structure calculations of the Mg-IV-N2 compounds in the quasiparticle self-consistent GW approximation. Compared to previous calculations (Phys. Rev. B 94, 125201 (2016)) we here include the effects of the Ge-3d and Sn-4d semicore states and find that these tend to reduce the band gap significantly. This places the band gap of MgSnN2 in the difficult to reach green region of the visible spectrum. The stability of the materials with respect to competing binary compounds is also evaluated and details of the valence band maximum manifold splitting and effective masses are provided.

Assessment of the Linearized GW Density Matrix for Molecules.

The GW approximation is well-known for the calculation of high-quality ionization potentials and electron affinities in solids and molecules. Recently, it has been identified that the density matrix that is obtained from the contraction of the GW Green's function allows one to include Feynman diagrams that are significant for the ionization potentials. However, the Green's function contains much more information than the mere quasi-particle energies. Here, we test and assess the quality of this so-called linearized GW density matrix for several molecular properties. First of all, we extend the original formulation to perform the linearization starting from any self-consistent mean-field approximation, and not only from Hartree-Fock. We then demonstrate the reliability and the stability of the linearized GW density matrix to evaluate the total energy out of a non-self-consistent GW calculation. Based on a comprehensive benchmark of 34 molecules, we compare the quality of the electronic density, Hartree energy, exchange energy, and the Fock operator expectation values against other well-established techniques. In particular, we show that the obtained linearized GW densities markedly differ from those calculated within the widespread quasi-particle self-consistent GW approximation.

Optical properties from photoelectron energy-loss spectroscopy of low-temperature aqueous chemically synthesized ZnO nanorods grown on Si

The optical properties of zinc oxide (ZnO) nanorods (NRs) synthesized by the low-temperature aqueous chemical method on top of silicon (Si) substrate have been investigated by means of photoelectron energy loss spectroscopy (PEELS). The ZnO NRs were obtained by the low temperature aqueous chemical synthesis on top of Si substrate. The measured valence band, the dynamical dielectric functions and optical absorption of the material show a reasonable agreement when the trending and shape of the theoretical calculations are considered. A first-principle calculation based on density functional theory (DFT) was performed using the partially self-consistent GW approximation (scGW0) and compared to the experimental results. The application of these two techniques brings a new analysis of the electronic properties of this material. The experimental results regarding the density of states (DOS) obtained for the valence band using x-ray photoelectron spectroscopy (XPS) was found to be consistent with the theoretical calculated value. Due to this consistency, the same wavefunctions was then employed to calculate the dielectric function of the ZnO NRs. The experimentally extracted dielectric function was also consistent with the calculated values.

Many-body perturbation theory study of type-II InAs/GaSb superlattices within the GW approximation

Recent studies suggest that the many-body perturbation theory in the partially self-consistent GW (GW0) approximation significantly improves the prediction of band gaps in various semiconductors. In this work, we employed GW formalism to study the electronic structure of type-II InAs/GaSb strained-layer superlattices (T2SLs). T2SLs considered in this study, denoted by (monolayers of InAs, monolayers of GaSb) are (), (), (), (), and (). The InSb-type interfacial layer was introduced in the structures to resemble the actual growth condition in our laboratories. The electronic band gaps are indirect in all the structures. The band gaps at the center of the Brillouin zone show good agreement with experimental data. This study is the first step to investigate the electronic, optical, and defect characteristics of T2SLs within a parameter-free ab initio method.

One-electron spectra and susceptibilities of the three-dimensional electron gas from self-consistent solutions of Hedin's equations

A few approximate schemes to solve the Hedin equations self-consistently introduced in (Phys. Rev. B 94, 155101 (2016)) are explored and tested for the 3D electron gas at metallic densities. We calculate one electron spectra, dielectric properties, compressibility, and correlation energy. Considerable reduction in the calculated band width (as compared to the self consistent GW result) has been found when vertex correction was used for both polarizability and self energy. Generally, it is advantageous to obtain the diagrammatic representation of polarizability from the definition of this quantity as a functional derivative of the electronic density with respect to the total field (external plus induced). For self energy, the first order vertex correction seems to be sufficient for the range of densities considered. Whenever it is possible, we compare the accuracy of our vertex-corrected schemes with the accuracy of the self-consistent quasi-particle GW approximation (QSGW), which is less expensive computationally. We show that QSGW approach performs poorly and we relate this poor performance with an inaccurate description of the screening in the QSGW method (with an error comprising a factor 2-3 in the physically important range of momenta).

Dielectric function and thermodynamic properties of jellium in the GW approximation

The fully self-consistent GW approximation is an established method for electronic structure calculations. Its most serious deficiency is known to be an incorrect prediction of the dielectric response. In this work we examine the GW approximation for the homogeneous electron gas and find that problems with the dielectric response are solved by enforcing the particle-number conservation law in the polarization function. Previously reported data for the ground-state energy were plainly contradicting each other well outside of reported error bounds. Some of these results created a false impression of how accurate the fully self-consistent GW approximation is. We resolve this controversy by confirming that only Ref. [15] was reporting correct energy data, and present values for other key Fermi-liquid properties.

Coulomb and electron-phonon interactions in metals

An accurate and consistent theory of phonons in metals requires that all long-range Coulomb interactions between charged particles (electrons and ions) be treated on equal footing. So far, all attempts to deal with this non-perturbative system were relying on uncontrolled approximations in the absence of small parameters. In this work, we develop the Diagrammatic Monte Carlo approach for a two-component Coulomb system that obtains the solution to this fundamental problem in an approximation free way by computing vertex corrections from higher-order skeleton graphs. The feasibility of the method is demonstrated by calculating the spectrum of longitudinal acoustic phonons in a simple cubic lattice, determining their sound velocity, and obtaining the phonon spectral densities by analytic continuation of the Matsubara Green's functions. Final results are checked against the lowest-order fully self-consistent GW-approximation in both adiabatic and non-adiabatic regimes.

Electronic structure of Na, K, Si, and LiF from self-consistent solution of Hedin's equations including vertex corrections

A few self-consistent schemes to solve the Hedin equations are presented. They include vertex corrections of different complexity. Commonly used quasiparticle approximation for the Green function and static approximation for the screened interaction are avoided altogether. Using alkali metals Na and K as well as semiconductor Si and wide gap insulator LiF as examples, it is shown that both the vertex corrections in the polarizability P and in the self energy $\Sigma$ are important. Particularly, vertex corrections in $\Sigma$ with proper treatment of frequency dependence of the screened interaction always reduce calculated band widths/gaps, improving the agreement with experiment. The complexity of the vertex included in P and in $\Sigma$ can be different. Whereas in the case of polarizability one generally has to solve the Bethe-Salpeter equation for the corresponding vertex function, it is enough (for the materials in this study) to include the vertex of the first order in the self energy. The calculations with appropriate vertices show remarkable improvement in the calculated band widths and band gaps as compared to the self-consistent GW approximation as well as to the self-consistent quasiparticle GW approximation.

First-principles treatment of Mott insulators: linearized QSGW+DMFT approach

AbstractThe theoretical understanding of emergent phenomena in quantum materials is one of the greatest challenges in condensed matter physics. In contrast to simple materials such as noble metals and semiconductors, macroscopic properties of quantum materials cannot be predicted by the properties of individual electrons. One of the examples of scientific importance is strongly correlated electron system. Neither localized nor itinerant behaviors of electrons in partially filled 3d, 4f, and 5f orbitals give rise to rich physics such as Mott insulators, high-temperature superconductors, and superior thermoelectricity, but hinder quantitative understanding of low-lying excitation spectrum. Here we present a new first-principles approach to strongly correlated solids. It is based on a combination of the quasiparticle self-consistent GW approximation and the dynamical mean-field theory. The sole input in this method is the projector to the set of correlated orbitals for which all local Feynman graphs are being evaluated. For that purpose, we choose very localized quasiatomic orbitals spanning large energy window, which contains most strongly hybridized bands, as well as upper and lower Hubbard bands. The self-consistency is carried out on the Matsubara axis. This method enables the first-principles study of Mott insulators in both their paramagnetic and antiferromagnetic phases. We illustrate the method on the archetypical charge transfer correlated insulators La2CuO4 and NiO, and obtain spectral properties and magnetic moments in good agreement with experiments.

Research Update: Relativistic origin of slow electron-hole recombination in hybrid halide perovskite solar cells

The hybrid perovskite CH3NH3PbI3 (MAPI) exhibits long minority-carrier lifetimes and diffusion lengths. We show that slow recombination originates from a spin-split indirect-gap. Large internal electric fields act on spin-orbit-coupled band extrema, shifting band-edges to inequivalent wavevectors, making the fundamental gap indirect. From a description of photoluminescence within the quasiparticle self-consistent GW approximation for MAPI, CdTe, and GaAs, we predict carrier lifetime as a function of light intensity and temperature. At operating conditions we find radiative recombination in MAPI is reduced by a factor of more than 350 compared to direct gap behavior. The indirect gap is retained with dynamic disorder.

A self-consistent GW approach to the van der Waals potential for a helium dimer.

van der Waals interaction between two helium (He) atoms is studied by calculating the total energy as a function of the He-He distance within the self-consistent GW approximation, which is expected to behave correctly in the long wavelength limit. In the Born-Oppenheimer (BO) approximation, the pair potential curve has its minimum value at 2.87 Å, which is somewhat larger than the local density approximation result, 2.40 Å, and is closer to previous quantum chemistry results. The expectation value for the interatomic distance, calculated by solving the Schrödinger equation for the two nuclei problem using the BO potential energy curve, is 30 Å, which is smaller but of the same order as previous experimental and theoretical results.

Fermi surface symmetry and evolution of the electronic structure across the paramagnetic-helimagnetic transition in MnSi/Si(111)

MnSi has been extensively studied for five decades, nonetheless detailed information on the Fermi surface (FS) symmetry is still lacking. This missed information prevented from a comprehensive understanding the nature of the magnetic interaction in this material. Here, by performing angle-resolved photoemission spectroscopy on high-quality MnSi films epitaxially grown on Si(111), we unveil the FS symmetry and the evolution of the electronic structure across the paramagnetic-helimagnetic transition at T$_C$ $\sim$ 40 K, along with the appearance of sharp quasiparticle emission below T$_C$. The shape of the resulting FS is found to fulfill robust nesting effects. These effects can be at the origin of strong magnetic fluctuations not accounted for by state-of-art quasiparticle self-consistent GW approximation. From this perspective, the unforeseen quasiparticle damping detected in the paramagnetic phase and relaxing only below T$_C$, along with the persistence of the d-bands splitting well above T$_C$, at odds with a simple Stoner model for itinerant magnetism, open the search for exotic magnetic interactions favored by FS nesting and affecting the quasiparticles lifetime.

Electronic structure calculations of delafossite Cu-based transparent conducting oxidesCuMO2(M=B,Al,Ga,In)by quasiparticle self-consistentGWapproximation and Tran-Blaha's modified Becke-Johnson exchange potential

In this work, band gaps of the delafossite Cu-based transparent conducting oxides $\mathrm{Cu}M{\mathrm{O}}_{2}$ $(M=\mathrm{B},\mathrm{Al},\mathrm{Ga},\mathrm{In})$ are calculated by density functional theory (DFT) implemented with many-body perturbation theory (MBPT) based on quasiparticle self-consistent GW approximation (QPscGW) and with Tran-Blaha's modified Becke-Johnson functional (DFT-TB09). Their band gaps are explicitly improved from DFT within local density approximation (LDA). Their optical absorption spectra are also calculated by solving Bethe-Salpeter equation (BSE) that includes the electron-hole correlation effect; they show strong excitonic peaks.

Validity of virial theorem in all-electron mixed basis density functional, Hartree-Fock, and GW calculations.

In this paper, we calculate kinetic and potential energy contributions to the electronic ground-state total energy of several isolated atoms (He, Be, Ne, Mg, Ar, and Ca) by using the local density approximation (LDA) in density functional theory, the Hartree-Fock approximation (HFA), and the self-consistent GW approximation (GWA). To this end, we have implemented self-consistent HFA and GWA routines in our all-electron mixed basis code, TOMBO. We confirm that virial theorem is fairly well satisfied in all of these approximations, although the resulting eigenvalue of the highest occupied molecular orbital level, i.e., the negative of the ionization potential, is in excellent agreement only in the case of the GWA. We find that the wave function of the lowest unoccupied molecular orbital level of noble gas atoms is a resonating virtual bound state, and that of the GWA spreads wider than that of the LDA and thinner than that of the HFA.

Stable spin states of boron, aluminum and silicon dimers in a self-consistent GW calculation

Some small clusters, in particular dimers (diatomic molecules), composed of nonmagnetic atoms exhibit intrinsic spin magnetic moments. In this paper, we discuss the most stable spin state of boron, aluminum and silicon dimers. In order to treat the dynamically screened exchange interaction between electrons correctly, we adopt the self-consistent GW approximation in many-body perturbation theory. We find that the energy gain of the triplet ground state from the singlet excited state as a reference is mainly caused by the dynamically screened exchange interaction, although other contributions to the total energy do not have the same tendency between the triplet and singlet states. We also explicitly show the resulting quasiparticle energy spectra which can be compared with the photoemission and inverse photoemission spectroscopy measurements.

Relativistic quasiparticle self-consistent electronic structure of hybrid halide perovskite photovoltaic absorbers

Solar cells based on a light absorbing layer of the organometal halide perovskite CH$_3$NH$_3$PbI$_3$ have recently reached 15% conversion efficiency, though how these materials work remains largely unknown. We analyse the electronic structure and optical properties within the quasiparticle self-consistent GW approximation. While this compound bears some similarity to conventional sp semiconductors, it also displays unique features. Quasiparticle self-consistency is essential for an accurate description of the band structure: bandgaps are much larger than what is predicted by the local density approximation (LDA) or GW based on the LDA. Valence band dispersions are modified in a very unusual manner. In addition, spin orbit coupling strongly modifies the band structure and gives rise to unconventional dispersion relations and a Dresselhaus splitting at the band edges. The average hole mass is small, which accounts for the long diffusion lengths recently observed. The surface ionisation potential (workfunction) is calculated to be 5.7 eV with respect to the vacuum level, explaining efficient carrier transfer to TiO$_2$ and Au electrical contacts.

Bilayer graphene spectral function in the random phase approximation and self-consistent GW approximation

We calculate the single-particle spectral function for doped bilayer graphene in the low energy limit, described by two parabolic bands with zero band gap and long range Coulomb interaction. Calculations are done using thermal Green's functions in both the random phase approximation (RPA) and the fully self-consistent GW approximation. RPA (in line with previous studies) yields a spectral function which apart from the Landau quasiparticle peaks shows additional coherent features interpreted as plasmarons, i.e. composite electron-plasmon excitations. In GW the plasmaron becomes incoherent and peaks are replaced by much broader features. The deviation of the quasiparticle weight and mass renormalization from their non-interacting values is small which indicates that bilayer graphene is a weakly interacting system. The electron energy loss function, $Im[-\epsilon^{-1}_q(\omega)]$ shows a sharp plasmon mode in RPA which in GW approximation becomes less coherent and thus consistent with the weaker plasmaron features in the corresponding single-particle spectral function.