GW Approximation Research Articles

Valley Zeeman effect and Landau levels in two-dimensional transition metal dichalcogenides

This paper presents a theoretical description of both the valley Zeeman effect (g-factors) and Landau levels in two-dimensional H-phase transition metal dichalcogenides (TMDs) using the Luttinger-Kohn approximation with spin-orbit coupling. At the valley extrema in TMDs, energy bands split into Landau levels with a Zeeman shift in the presence of a uniform out-of-plane external magnetic field. The Landau level indices are symmetric in the $K$ and $K'$ valleys. We develop a numerical approach to compute the single band g-factors from first principles without the need for a sum over unoccupied bands. Many-body effects are included perturbatively within the GW approximation. Non-local exchange and correlation self-energy effects in the GW calculations increase the magnitude of single band g-factors compared to those obtained from density functional theory. Our first principles results give spin- and valley-split Landau levels, in agreement with recent optical experiments. The exciton g-factors deduced in this work are also in good agreement with experiment for the bright and dark excitons in monolayer WSe$_2$, as well as the lowest-energy bright excitons in MoSe$_2$-WSe$_2$ heterobilayers with different twist angles.

DFT study of electronic and optical properties of CH3NH3SnI3 perovskite

ABSTRACT CH3NH3SnI3 perovskite is an interesting compound for optoelectronics applications. In this paper, we report the results of our investigations on the electronic and optical behavior of this structure by density functional theory. The calculations were performed using PW-LDA, GGA (PBE) and GW approximations. The band-gap values obtained by GGA (1.02 eV) is bigger than that obtained by LDA (0.77 eV) and the best band gap value for the CH3NH3SnI3 perovskite obtained by the GW approximation (1.38 eV), which is close to the experimental value. The calculated total- and partial density of states for this perovskite show that the Sn and I atoms has a direct effect on the electronic properties of this atomic compound. The results obtained on optical properties such as the low reflectivity rate and high absorption of the incident photon energy in 1.5–3 eV energy range indicate the CH3NH3SnI3 has a good optical property to absorb solar wavelengths as an active layer in the perovskite-based solar cells.

First principle study on hybrid organic-inorganic perovskite ASnBr3 (A = Formamidinium, Dimethylammonium and Azetidinium)

The Organic-Inorganic halide perovskites of ABX3 type (A: Organic cation, B: Metal cation, X: Halide anion) have exceptional electronic properties which attract broad interest. The widely studied Methylammonium Lead Iodide (MAPbI3) is toxic and less stable. Hence there is a need to find potential alternative materials. We report in this study, the density functional theory calculations for the tin-based hybrid perovskite ASnBr3 (where A is an organic molecule: Formamidinium, Dimethylammonium or Azetidinium). We considered 106 different combinations of the constituent element/molecules and shortlisted three potential structures based on the factors like material abundance, bandgap, toxicity and stability. The structures were systematically analysed for their structural and electronic properties based on Density Functional Theory (DFT) calculations using Generalized Gradient Approximation (GGA) functional and GW approximations. Wide tunable bandgap with the range of 2.09 to 4.9 eV and corresponding changes in the optical absorption properties obtained by substituting different organic cations. The tin-based organic-inorganic halide perovskite may find application in tandem solar cells, which may enhance the efficiency of solar energy conversion.

Nonlinear response in the cumulant expansion for core-level photoemission

Most currently used approximations for the one-particle Green's function G in the framework of many-body perturbation theory, such as Hedin's GW approximation or the cumulant GW+C approach, are based on a linear response approximation for the screened interaction W. The extent to which such a hypothesis is valid and ways to go beyond have been explored only very little. Here we show how to derive a cumulant Green's function beyond linear-response from the equation of motion of the Green's function in a functional derivative formulation. The results can be written in a compact form, which opens the possibility to calculate the corrections in a first principles framework using time-dependent density functional theory. In order to illustrate the potential importance of the corrections, numerical results are presented for a model system with a core level and two valence orbitals.

Remarkable Band-Gap Renormalization via Dimensionality of the Layered Material C3B

Layer-dependent electronic and structural properties of emerging graphitic carbon boron compound C3B are investigated using both density functional theory and the GW approximation. We discover that, in contrast to a moderate quasiparticle band gap of 2.55 eV for monolayer C3B, the calculated quasiparticle band gap of perfectly stacked bulk phase C3B is as small as 0.17 eV. Therefore, our results suggest that layered material C3B exhibits a remarkably large band gap renormalization of over 2.3 eV due to the interlayer coupling and screening effects, providing a single material with an extraordinary band gap tunability. The quasiparticle band gap of monolayer C3B is also over 1.0 eV larger than that of C3N, a closely related two-dimensional semiconductor. Detailed inspections of the near-edge electronic states reveal that the conduction and valence band edges of C3B are formed by out-of-plane and in-plane electronic states, respectively, suggesting an interesting possibility of tuning the band edges of such layered material separately by modulating the in-plane and out-of-plane interactions.

A combined theoretical and experimental investigation of the electronic and vibrational properties of red lead pigment

The electronic and vibrational properties of red lead pigment, the mixed valence lead oxide compound Pb3O4, known as minium, have been studied by means of first principle calculations based on Density Functional Theory (DFT) and Fourier Transform–Infra Red (FT-IR) and Raman spectroscopies. The aim of the present investigation is to validate an integrated theoretical-experimental approach for modelling the structural, electronic and spectroscopic properties of minium and to define its structure-properties relationships. The calculated band gap performed using GW approximation is in excellent agreement with the experimental one and improves previous results found in literature. The simulated vibrational IR and Raman spectra are able to reproduce the main features of the experimental spectra and to assign the normal modes related to the experimental bands. The combined theoretical and experimental study of the electronic and vibrational properties of Pb3O4 allows to clarify the mechanism of lead whitening as well as to interpret ambiguous Raman spectra of minium in terms of resonance effects.

Anisotropic Optical Properties of 2D Silicon Telluride

ABSTRACTSilicon telluride (Si2Te3) is a silicon-based 2D chalcogenide with potential applications in optoelectronics. It has a unique crystal structure where Si atoms form Si-Si dimers to occupy the “metal” sites. In this paper, we report an ab initio computational study of its optical dielectric properties using the GW approximation and the Bethe-Salpeter equation (BSE). Strong in-plane optical anisotropy is discovered. The imaginary part of the dielectric constant in the direction parallel to the Si-Si dimers is found to be much lower than that perpendicular to the dimers. The optical measurement of the absorption spectra of 2D Si2Te3 nanoplates shows modulation of the absorption coefficient under 90-degree rotation, confirming the computational results. We show the optical anisotropy originates from the particular compositions of the wavefunctions in the valence and conduction bands. Because it is associated with the Si dimer orientation, the in-plane optical anisotropy can potentially be dynamically controlled by electrical field and strain, which may be useful for new device design. In addition, BSE calculations reduce GW quasiparticle band gap by 0.3 eV in bulk and 0.6 eV in monolayer, indicating a large excitonic effect in Si2Te3. Furthermore, including electron-hole interaction in bulk calculations significantly reduces the imaginary part of the dielectric constant in the out-of-plane direction, suggesting strong interlayer exciton effect in Si2Te3 multilayers.

Extrapolating Unconverged GW Energies up to the Complete Basis Set Limit with Linear Regression.

The GW approximation to the electronic self-energy is now a well-recognized approach to obtain the electron quasiparticle energies of molecules and, in particular, their ionization potential and electron affinity. Though much faster than the corresponding wavefunction methods, the GW energies are still affected by slow convergence with respect to the basis completeness. This limitation hinders a wider application of the GW approach. Here, we show that we can reach the complete basis set limit for the cumbersome GW calculations solely based on fast preliminary calculations with an unconverged basis set. We introduce a linear model that correlates the molecular orbital characteristics and the basis convergence error for a large database of approximately 600 states in 104 organic molecules that contain H, C, O, N, F, P, S, and Cl. The model employs molecular-orbital-based non-linear descriptors that encode efficiently the chemical space offering outstanding transferability. Using a low number of descriptors (17) the performance of this extrapolation procedure is superior to that of the earlier more physically motivated approaches. The predictive power of the method is finally demonstrated for a selection of large acceptor molecules.

Correction of band-gap energy and dielectric function of BiOX bulk with GW and BSE

Using the DFT method and beyond with GW approximation, we investigate the electronic structures of bismuth oxyhalides BiOXs (where X = F, Cl, Br, and I). The optical properties such as dielectric function and absorption coefficient of BiOXs except BiOI are fully computed with different methods, i.e., DFT, ACFDT in RPA, and with BSE. Our results show that the band-gap nature of BiOF is direct, whereas the band-gaps of BiOCl, BiOBr, and BiOI are indirect. Also, our GW results indicate that the band-gaps of BiOX are very well agreement with the experimental values. Besides, we show that under an external electric field a semiconductor can be changed to a metal with a strong field of more than 0.5 V/Å. Further, we found that the BSE method is the best way to describe the optical properties of BiOXs.

Quasirelativistic two-component core excitations and polarisabilities from a damped-response formulation of the Bethe–Salpeter equation

A damped-response formalism in the GW approximation to the Bethe–Salpeter equation (BSE) is presented and implemented. It is based on a quasirelativistic two-component (2c) approach that includes scalar-relativistic and spin–orbit effects derived from the one-electron Dirac equation. A generalised solver, which also allows to calculate static, dynamic and damped-response polarisabilites, is discussed in detail. Throughout our implementation, the resolution-of-the-identity approximation is employed to reduce the computational effort. The performance of 2c GW-BSE is benchmarked against experimental and high-level ab initio data and compared to standard density-functional theory approaches, including modern local hybrid functionals for which a proper non-collinear kernel for Kramers-restricted systems is reported.

Electronic and optical properties of PbFCl and PbFI monolayers using density functional theory and beyond

In the two years, the TMDs materials perform a hugely great role in that they represent other resources of getting a material with bandgap energy and stable dynamically for electronics purposes. Many subjects have confirmed that TMDs mono or bi-layer could offer properties superior to those of graphene. Astonishingly, few of them have synthesized. Based on the density functional theory and beyond, we study the electronic, vibrational, and optical properties of new 2D materials, i.e., the alkaline-earth fluoro-halides monolayers such as PbFCl and PbFI. By computing the phonon spectra of PbFCl and PbFI monolayers, we have shown that they are dynamically stable. We obtained the bandgaps of these monolayers as achieved with the GW approximation are 6.38 and 6.64 eV. Also, we found that the strength of the electric field decreases the bandgap energy of our compounds and modifies the location of CBM and VBM. Further, we obtained by employing the picture marks seen in the calculated STM images and their accompanying geometries as creating slabs it is probable to build these 2D monolayers.

Origin of nonlinear current-voltage curves for suspended zigzag edge graphene nanoribbons

The structure-dependent electronic properties of suspended graphene nanoribbon (GNR) have still been important issues. However, these properties have been rarely investigated experimentally due to technical difficulties to produce high-quality suspended GNRs and the identification of atomic structures. Here, we report the electronic properties of suspended GNRs by in situ transmission electron microscopy observations to simultaneously obtain the structural information while measuring the current-voltage (I-V) curves. The suspended GNRs could be obtained by convergent electron beam nanosculpting after careful cleaning by current annealing. The I-V curves were measured for GNRs with a mixture of both zigzag and armchair edges (MGNR) with widths of 3.7 to 1.9 nm and also zigzag edge GNRs (ZGNR) with widths of 1.7 to 1.2 nm. The I-V curves for the ZGNRs were different from those of the MGNRs, as follows. (1) The ZGNRs showed a sharp increase at the threshold voltage in differential conductance-voltage curves. (2) The band gaps measured for ZGNRs were smaller than the band gaps calculated using the GW approximation. (3) The threshold voltage increased with the GNR length. These findings support magnetic-insulator and nonmagnetic-metal nonequilibrium phase transitions as theoretically predicted. Narrow and short ZGNR represents the potential for further nanosized switching devices.

Pros and Cons of the Bethe-Salpeter Formalism for Ground-State Energies.

The combination of the many-body Green's function GW approximation and the Bethe-Salpeter equation (BSE) formalism has shown to be a promising alternative to time-dependent density functional theory (TD-DFT) for computing vertical transition energies and oscillator strengths in molecular systems. The BSE formalism can also be employed to compute ground-state correlation energies thanks to the adiabatic-connection fluctuation-dissipation theorem (ACFDT). Here, we study the topology of the ground-state potential energy surfaces (PESs) of several diatomic molecules near their equilibrium bond length. Using comparisons with state-of-art computational approaches (CC3), we show that ACFDT@BSE is surprisingly accurate and can even compete with lower-order coupled cluster methods (CC2 and CCSD) in terms of total energies and equilibrium bond distances for the considered systems. However, we sometimes observe unphysical irregularities on the ground-state PES in relation with difficulties in the identification of a few GW quasiparticle energies.

ABINIT: Overview and focus on selected capabilities.

abinit is probably the first electronic-structure package to have been released under an open-source license about 20 years ago. It implements density functional theory, density-functional perturbation theory (DFPT), many-body perturbation theory (GW approximation and Bethe-Salpeter equation), and more specific or advanced formalisms, such as dynamical mean-field theory (DMFT) and the "temperature-dependent effective potential" approach for anharmonic effects. Relying on planewaves for the representation of wavefunctions, density, and other space-dependent quantities, with pseudopotentials or projector-augmented waves (PAWs), it is well suited for the study of periodic materials, although nanostructures and molecules can be treated with the supercell technique. The present article starts with a brief description of the project, a summary of the theories upon which abinit relies, and a list of the associated capabilities. It then focuses on selected capabilities that might not be present in the majority of electronic structure packages either among planewave codes or, in general, treatment of strongly correlated materials using DMFT; materials under finite electric fields; properties at nuclei (electric field gradient, Mössbauer shifts, and orbital magnetization); positron annihilation; Raman intensities and electro-optic effect; and DFPT calculations of response to strain perturbation (elastic constants and piezoelectricity), spatial dispersion (flexoelectricity), electronic mobility, temperature dependence of the gap, and spin-magnetic-field perturbation. The abinit DFPT implementation is very general, including systems with van der Waals interaction or with noncollinear magnetism. Community projects are also described: generation of pseudopotential and PAW datasets, high-throughput calculations (databases of phonon band structure, second-harmonic generation, and GW computations of bandgaps), and the library libpaw. abinit has strong links with many other software projects that are briefly mentioned.

Excited-state electronic structure of molecules using many-body Green's functions: Quasiparticles and electron-hole excitations with VOTCA-XTP.

We present the open-source VOTCA-XTP software for the calculation of the excited-state electronic structure of molecules using many-body Green's function theory in the GW approximation with the Bethe-Salpeter equation (BSE). This work provides a summary of the underlying theory and discusses the details of its implementation based on Gaussian orbitals, including resolution-of-identity techniques and different approaches to the frequency integration of the self-energy or acceleration by offloading compute-intensive matrix operations using graphics processing units in a hybrid OpenMP/Cuda scheme. A distinctive feature of VOTCA-XTP is the capability to couple the calculation of electronic excitations to a classical polarizable environment on an atomistic level in a coupled quantum- and molecular-mechanics (QM/MM) scheme, where a complex morphology can be imported from Molecular Dynamics simulations. The capabilities and limitations of the GW-BSE implementation are illustrated with two examples. First, we study the dependence of optically active electron-hole excitations in a series of diketopyrrolopyrrole-based oligomers on molecular-architecture modifications and the number of repeat units. Second, we use the GW-BSE/MM setup to investigate the effect of polarization on localized and intermolecular charge-transfer excited states in morphologies of low-donor content rubrene-fullerene mixtures. These showcases demonstrate that our implementation currently allows us to treat systems with up to 2500 basis functions on regular shared-memory workstations, providing accurate descriptions of quasiparticle and coupled electron-hole excited states of various characters on an equal footing.

Ultrafast Formation of the Charge Transfer State of Prodan Reveals Unique Aspects of the Chromophore Environment.

Lipophilic dyes such as laurdan and prodan are widely used in membrane biology due to a strong bathochromic shift in emission that reports the structural parameters of the membrane such as area per molecule. Disentangling of the factors which control the spectral shift is complicated by the stabilization of a charge-transfer-like excitation of the dye in polar environments. Predicting the emission therefore requires modeling both the relaxation of the environment and the corresponding evolution of the excited state. Here, an approach is presented in which (i) the local environment is sampled by a classical molecular dynamics (MD) simulation of the dye and solvent, (ii) the electronically excited state of prodan upon light absorption is predicted by numerical quantum mechanics (QM), (iii) the iterative relaxation of the environment around the excited dye by MD coupled with the evolution of the excited state is performed, and (iv) the emission properties are predicted by QM. The QM steps are computed using the many-body Green's function in the GW approximation and the Bethe-Salpeter equation with the environment modeled as fixed point charges, sampled in the MD simulation steps. The comparison to ultrafast time-resolved transient absorption measurements demonstrates that the iterative molecular mechanics (MM)/QM approach agrees quantitatively with both the polarity-dependent shift in emission and the time scale over which the charge transfer state is stabilized. Together the simulations and experimental measurements suggest that the evolution into the charge transfer state is slower in amphiphilic solvents.

Reproducibility in [formula omitted] calculations for solids

Ab initio many-body perturbation theory within the GW approximation is a Green’s function formalism widely used in the calculation of quasiparticle excitation energies of solids. In what has become an increasingly standard approach, Kohn–Sham eigenenergies, generated from a DFT calculation with a strategically-chosen exchange–correlation functional “starting point”, are used to construct G and W, and then perturbatively corrected by the resultant GW self-energy. In practice, there are several ways to construct the GW self-energy, and these can lead to variations in predicted quasiparticle energies. For example, for ZnO and TiO2, the GW fundamental gaps reported in the literature can vary by more than 1 eV depending on the GW code used. In this work, we calculate and analyze GW quasiparticle (QP) energies of these and other systems with three different GW codes: BerkeleyGW, Abinit and Yambo. Through a systematic analysis of the GW implementation of these three codes, we identify the primary origin of major discrepancies between codes reported in prior literature to be the different implementations the Coulomb divergence in the Fock exchange term and the frequency integration scheme of the GW self-energy. We then eliminate these discrepancies by using common numerical methods and algorithms, demonstrating that the same quasiparticle energies for a given material can be obtained with different codes, within numerical differences ascribable to the technical details of the underling implementations. This work will be important for users and developers in assessing the precision of future GW applications and methods.

Multiscale simulations of singlet and triplet exciton dynamics in energetically disordered molecular systems based on many-body Green's functions theory

We present a multiscale model based on many-body Green’s functions theory in the GW approximation and the Bethe–Salpeter equation (GW-BSE) for the simulation of singlet and triplet exciton transport in molecular materials. Dynamics of coupled electron–hole pairs are modeled as a sequence of incoherent tunneling and decay events in a disordered morphology obtained at room temperature from molecular dynamics. The ingredients of the rates associated to the events, i.e. reorganization energies, site energies, lifetimes, and coupling elements, are determined from a combination of GW-BSE and classical polarizable force field techniques. Kinetic Monte Carlo simulations are then employed to evaluate dynamical properties such as the excitonic diffusion tensor and diffusion lengths. Using DCV5T-Me(3,3), a crystalline organic semiconductor, we demonstrate how this multiscale approach provides insight into the fundamental factors driving the transport processes. Comparing the results obtained via different calculation models, we investigate in particular the effects of charge-transfer mediated high exciton coupling and the influence of internal site energy disorder due to conformational variations. We show that a small number of high coupling elements indicative of delocalized exciton states does not impact the overall dynamics perceptively. Molecules with energies in the tail of the excitonic density of states dominate singlet decay, independent of the level of disorder taken into account in the simulation. Overall, our approach yields singlet diffusion lengths on the order of 10 nm as expected for energetically disordered molecular materials.

First-principles investigation on the stability and material properties of all-inorganic cesium lead iodide perovskites CsPbI3 polymorphs

Cesium metal halide perovskites are very promising light absorbing materials for solar cells, due to their good thermal stability compared to other organometallic perovskites. Cesium lead iodide perovskite CsPbI3 is one the most promising compound from this family because of its band gap of 1.7eVsuitable for a top cell in silicon tandem solar cell. Herein, we systematically investigate the structural, electronic, elastic, optical properties and some carrier transport properties of CsPbI3 perovskites polymorphs using pseudo-potential plane wave method implemented in CASTEP and ABINIT codes. We use hybrid functional within the GW approximation (GW-HSE06) and the spin-orbit coupling (GGA-PBE + SOC) to estimate the band gaps. The elastic properties indicate the flexibility and softness of CsPbI3 perovskites, they also have a high absorption coefficient values (α = 104–105 cm−1) and low exciton binding energy which make them potential candidate for solar cells application.

A comprehensive theoretical picture of E centers in silicon: From optical properties to vacancy-mediated dopant diffusion

Among the common vacancy-related point defects in silicon, the E center is one of the most prominent due to its degrading effect in silicon-based technology. Even though it has been the subject of extensive experimental and theoretical studies, a comprehensive theoretical model capable of reproducing the experimental evidence for all three dopants (P, As, and Sb) is still missing. Guided by a Jahn-Teller model, we are able to reproduce the absorption bands and the transition probability between equivalent geometries of the defect at low temperatures by including many-body-perturbation corrections based on the GW approximation on top of the density functional theory. At higher temperatures, vacancies become mobile centers, enabling the reorientation of the whole defect and contributing to the dopant diffusion. The underlying mechanisms of the vacancy-mediated dopant diffusion are revisited, characterizing the activation energies of such technologically relevant processes and obtaining quantitative results in good agreement with experiment.