GW Approach Research Articles

One-shot calculation of temperature-dependent optical spectra and phonon-induced band-gap renormalization

Recently, Zacharias et al [Phys. Rev. Lett. 115, 177401 (2015)] developed a new ab initio theory of temperature-dependent optical absorption spectra and band gaps in semiconductors and insulators. In that work the zero-point renormalization and the temperature dependence were obtained by sampling the nuclear wavefunctions using a stochastic approach. In the present work, we show that the stochastic sampling can be replaced by fully deterministic supercell calculations based on a single optimal configuration of the atomic positions. We demonstrate that a single calculation is able to capture the temperature-dependent band gap renormalization including quantum nuclear effects in direct and indirect-gap semiconductors, as well as phonon-assisted optical absorption in indirect-gap semiconductors. In order to demonstrate this methodology we calculate from first principles the temperature-dependent optical absorption spectra and the renormalization of direct and indirect band gaps in Si, C, and GaAs, and we obtain good agreement with experiment and with previous calculations. In this work we also establish the formal connection between the Williams-Lax theory of optical transitions and the related theories of indirect absorption by Hall, Bardeen, and Blatt, and of temperature-dependent band structures by Allen and Heine. Furthermore, we identify an additional band gap renormalization that arises in the case of degenerate band extrema, and which has not been considered in previous work. The present methodology enables systematic ab initio calculations of optical absorption spectra at finite temperature, including both direct and indirect transitions. This feature will be useful for high-throughput calculations of optical properties at finite temperature, and for calculating temperature-dependent optical properties using high-level theories such as GW and Bethe-Salpeter approaches.

On the combined use of GW approximation and cumulant expansion in the calculations of quasiparticle spectra: The paradigm of Si valence bands

Since the earliest implementations of the various GW approximations and cumulant expansion in the calculations of quasiparticle propagators and spectra, several attempts have been made to combine the advantageous properties and results of these two theoretical approaches. While the GW plus cumulant approach has proven successful in interpreting photoemission spectroscopy data in solids, the formal connection between the two methods has not been investigated in detail. By introducing a general bijective integral representation of the cumulants, we can rigorously identify at which point these two approximations can be connected for the paradigmatic model of quasiparticle interaction with the dielectric response of the system that has been extensively exploited in recent interpretations of the satellite structures in photoelectron spectra. We establish a protocol for consistent practical implementation of the thus established GW+cumulant scheme, and illustrate it by comprehensive state-of-the-art first-principles calculations of intrinsic angle-resolved photoemission spectra from Si valence bands.

Quasi-particle energies and optical excitations of wurtzite BeO and its nanosheet

The electronic and optical properties of BeO in wurtzite bulk and sheet structures are investigated by using ab-initio density functional theory calculations combined with many-body perturbation formalism. The electronic properties were analyzed at three levels of the many-body GW approach (G0W0, GW0 and GW) constructed over a Generalized Gradient Approximation functional. Our results show that GW approach does not change the sort of direct or indirect band gap in bulk or sheet systems of BeO. The best result for the insulating gap of the bulk system was obtained at the GW0 level. The optical properties and excitonic effects of these materials are investigated using the Bethe-Salpeter equation (BSE) approach. Comparison with experiment shows that the optical properties of the bulk system cannot be explained by independent-particle transitions but they are strongly dominated by excitonic effects. The binding energies of the first exciton for the bulk and sheet structures are 0.5 and 1.5 eV in E||x, respectively. The quantum confinement of BeO sheet significantly enhances the electron-hole interaction and finally leads to a larger binding energy. We show that the spectrum for both bulk and sheet systems is dominated by strongly bound Frenkel excitons.

Self-consistent Green's function embedding for advanced electronic structure methods based on a dynamical mean-field concept

We present an embedding scheme for periodic systems that facilitates the treatment of the physically important part (here the unit cell) with advanced electronic-structure methods, that are computationally too expensive for periodic systems. The rest of the periodic system is treated with computationally less demanding approaches, e.g., Kohn-Sham density-functional theory, in a self- consistent manner. Our scheme is based on the concept of dynamical mean-field theory (DMFT) formulated in terms of Green functions. In contrast to the original DMFT formulation for correlated model Hamiltonians, we here consider the unit cell as local embedded cluster in a first-principles way, that includes all electronic degrees of freedom. Our real-space dynamical mean-field embedding (RDMFE) scheme features two nested Dyson equations, one for the embedded cluster and another for the periodic surrounding. The total energy is computed from the resulting Green functions. The performance of our scheme is demonstrated by treating the embedded region with hybrid functionals and many-body perturbation theory in the GW approach for simple bulk systems. The total energy and the density of states converge rapidly with respect to the computational parameters and approach their bulk limit with increasing cluster (i.e., unit cell) size.

Electronic excitations in solution-processed oligothiophene small-molecules for organic solar cells.

First principles calculations based on density functional theory and many body perturbation theory have been employed to study the optical absorption properties of a newly synthesized oligo-thiophene molecule, with a quaterthiophene central unit, that has been designed for solution-processed bulk-heterojunction solar cells. To this aim we have employed the GW approach to obtain quasiparticle energies as a pre-requisite to solve the Bethe-Salpeter equation for the excitonic Hamiltonian. We show that the experimental absorption spectrum can be explained only by taking into account the inter-molecular transitions among the π-stacked poly-conjugated molecules that are typically obtained in solid-state organic samples.

Understanding the optical properties of ZnO1−xSx and ZnO1−xSex alloys

ZnO1−xYx with chalcogen element Y exhibits intriguing optoelectronic properties as the alloying strongly impacts the band-gap energy Eg(x). In this work, we analyze and compare the electronic structures and the dielectric responses of Zn(O,S) and Zn(O,Se) alloys by means of the density functional theory and the partially self-consistent GW approach. We model the crystalline stability from the total energies, and the results indicate that Zn(O,S) is more stable as alloy than Zn(O,Se). We demonstrate also that ion relaxation strongly affects total energies, and that the band-gap bowing depends primarily on local relaxation of the bonds. Moreover, we show that the composition dependent band-gap needs to be analyzed by the band anti-crossing model for small alloying concentration, while the alloying band-bowing model is accurate for strong alloying. We find that the Se-based alloys have a stronger change in the band-gap energy (for instance, ΔEg(0.50) = Eg(ZnO) – Eg(x = 0.50) ≈ 2.2 eV) compared with that of the S-based alloy (ΔEg(0.50) = 1.2 eV), mainly due to a stronger relaxation of the Zn–anion bonds that affects the electronic structure near the band edges. The optical properties of the alloys are discussed in terms of the complex dielectric function ε(ω) = ε1(ω) + iε2(ω) and the absorption coefficient α(ω). While the large band-gap bowing directly impacts the low-energy absorption spectra, the high-frequency dielectric constant ε∞ is correlated to the intensity of the dielectric response at energies above 4 eV. Therefore, the dielectric constant is only weakly affected by the non-linear band-gap variation. Despite strong structural relaxation, the high absorption coefficients of the alloys demonstrate that the alloys have well-behaved optoelectronic properties.

Many-body effects and excitonic features in 2D biphenylene carbon.

The remarkable excitonic effects in low dimensional materials in connection to large binding energies of excitons are of great importance for research and technological applications such as in solar energy and quantum information processing as well as for fundamental investigations. In this study, the unique electronic and excitonic properties of the two dimensional carbon network biphenylene carbon were investigated with GW approach and the Bethe-Salpeter equation accounting for electron correlation effects and electron-hole interactions, respectively. Biphenylene carbon exhibits characteristic features including bright and dark excitons populating the optical gap of 0.52 eV and exciton binding energies of 530 meV as well as a technologically relevant intrinsic band gap of 1.05 eV. Biphenylene carbon's excitonic features, possibly tuned, suggest possible applications in the field of solar energy and quantum information technology in the future.

Studying the electronic and phononic structure of penta-graphane

In this paper, we theoretically consider a two dimensional nanomaterial which is a form of hydrogenated penta-graphene; we call it penta-graphane. This structure is obtained by adding hydrogen atoms to the sp2 bonded carbon atoms of penta-graphene. We investigate the thermodynamic and mechanical stability of penta-graphane. We also study the electronic and phononic structure of penta-graphane. Firstly, we use density functional theory with the revised Perdew–Burke–Ernzerhof approximation to compute the band structure. Then one–shot GW (G0W0) approach for estimating accurate band gap is applied. The indirect band gap of penta-graphane is 5.78 eV, which is close to the band gap of diamond. Therefore, this new structure is a good electrical insulator. We also investigate the structural stability of penta-graphane by computing the phonon structure. Finally, we calculate its specific heat capacity from the phonon density of states. Penta-graphane has a high specific heat capacity, and can potentially be used for storing and transferring energy.

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.

QSGW+DMFT: an electronic structure scheme for the iron pnictides and beyond

While in strongly correlated materials one often focuses on local electronic correlations, the influence of non-local exchange and correlation effects beyond band-theory can be pertinent in systems with more extended orbitals. Thus in many compounds an adequate theoretical description requires the joint treatment of local and non-local self-energies. Here, I will argue that this is the case for the iron pnictide and chalcogenide superconductors. As an approach to tackle their electronic structure, I will detail the implementation of the recently proposed scheme that combines the quasi-particle self-consistent GW approach with dynamical mean-field theory: QSGW+DMFT. I will showcase the possibilities of QSGW+DMFT with an application on BaFe2As2. Further, I will discuss the empirical finding that in pnictides dynamical and non-local correlation effects separate within the quasi-particle band-width.

Atomically Precise Graphene Nanoribbon Heterojunctions for Excitonic Solar Cells

By mixing pure precursor monomers and nitrogen-doped equivalents, atomically sharp wiggle-edged heterojunctions can be obtained via the combined action of Ullmann coupling followed by cyclodehydrogenation [Cai et al., Nat. Nanotechnol. 2014, 9, 896]. We used first-principles density functional theory and the many-body GW approach to establish the role of doping (boron and nitrogen) in a variety of graphene nanowiggles displaying a range of band gaps. The substitution of C atoms located at the edges of the structures does not significantly affect the magnitude of the band gaps, but leads to their relative upshift or downshift depending on the dopant. This shift is found to vary quasi-linearly as the concentration of dopant increases. Consequently, tunable type-II staggered band alignments are formed in graphene nanowiggle heterojunctions. We predict that these type-II heterojunctions can provide ultrathin solar cells with power conversion efficiencies up to 22.0%.

Spectral properties of Dirac electron system

We present the extension of our previous G0W0 approach to the two-dimensional system of massless Dirac electrons interacting via the long-range Coulomb interaction. We determine the one-particle spectral function taking into account only a partially filled linear band above the Dirac point. The electron self-energy is calculated, paying particular attention to the contribution coming from the collective plasmon mode through the dynamically screened Coulomb electron–electron interaction. The obtained results show a dispersing feature in the spectral function and a low energy quasi-particle with the renormalized spectral weight. We expect the results obtained to be qualitatively in agreement with spectral properties of monolayer of MoS2 which has the large direct band gap between the valence and conduction bands. We also discuss the influence of the underlying substrate on the obtained results.

Linearized self-consistent GW approach satisfying the Ward identity

We propose a linearized self-consistent GW approach satisfying the Ward identity. The vertex function derived from the Ward-Takahashi identity in the limit of $\mathbit{q}=0$ and $\ensuremath{\omega}\ensuremath{-}{\ensuremath{\omega}}^{\ensuremath{'}}=0$ is included in the self-energy and the polarization function as a consequence of the linearization of the quasiparticle equation. Due to the energy dependence of the self-energy, the Hamiltonian is a non-Hermitian operator and quasiparticle states are nonorthonormal and linearly dependent. However, the linearized quasiparticle states recover orthonormality and fulfill the completeness condition. This approach is very efficient, and the resulting quasiparticle energies are greatly improved compared to the nonlinearized self-consistent GW approach, although its computational cost is not much increased. We show the results for atoms and dimers of Li and Na compared with other approaches. We also propose convenient ways to calculate the Luttinger-Ward functional $\ensuremath{\Phi}$ based on a plasmon-pole model and calculate the total energy for the ground state. As a result, we conclude that the linearization improves overall behaviors in the self-consistent GW approach.

Organic/Inorganic Hybrid Materials: Challenges for ab Initio Methodology

CONSPECTUS: Organic/inorganic hybrid structures are most exciting since one can expect new properties that are absent in either of their building blocks. They open new perspectives toward the design and tailoring of materials with desired features and functions. Prerequisite for real progress is, however, the in-depth understanding of what happens on the atomic and electronic scale. In this respect, hybrid materials pose a challenge for electronic-structure theory. Methods that proved useful for describing one side may not be applicable for the other one, and they are likely to fail for the interfaces. In this Account, we address the question to what extent we can quantitatively describe hybrid materials and where we even miss a qualitative description. We note that we are dealing with extended systems and thus adopt a solid-state approach. Therefore, density-functional theory (DFT) and many-body perturbation theory (MBPT), the GW approach for charged and the Bethe-Salpeter equation for neutral excitations, are our methods of choice. We give a brief summary of the used methodology, focusing on those aspects where problems can be expected when materials of different character meet at an interface. These issues are then taken up when discussing hybrid materials. We argue when and why, for example, standard DFT may fall short when it comes to the electronic structure of organic/metal interfaces or where the framework of MBPT can or must take over. Selected examples of organic/inorganic interfaces, structural properties, electronic bands, optical excitation spectra, and charge-transport properties as obtained from DFT and MBPT highlight which properties can be reliably computed for such materials. The crucial role of van der Waals forces is shown for sexiphenyl films, where the subtle interplay between intermolecular and molecule-substrate interactions is decisive for growth and morphologies. With a PTCDA monolayer on metal surfaces we discuss the performance of DFT in terms of interfacial electronic structure. We face the problem of a so far hidden variable, namely, electron-vibrational coupling, regarding level alignment at interfaces between organic and inorganic semiconductors. Poly(para-phenylene) adsorbed on graphene and encapsulated in carbon nanotubes represent case studies to demonstrate the impact of polarization effects and exciton delocalization in optoelectronic excitations, respectively. Polaron-induced band narrowing and its consequences for charge transport in organic crystals is exemplified for the HOMO bandwidth in naphthalene crystals. On the basis of these prototypical systems, we discuss what is missing to reach predictive power on a quantitative level for organic/inorganic hybrid materials and, thus, open a perspective toward the computational discovery of new materials for optoelectronic applications.

Probing excitonic dark states in single-layer tungsten disulphide.

Transition metal dichalcogenide (TMDC) monolayers have recently emerged as an important class of two-dimensional semiconductors with potential for electronic and optoelectronic devices. Unlike semi-metallic graphene, layered TMDCs have a sizeable bandgap. More interestingly, when thinned down to a monolayer, TMDCs transform from indirect-bandgap to direct-bandgap semiconductors, exhibiting a number of intriguing optical phenomena such as valley-selective circular dichroism, doping-dependent charged excitons and strong photocurrent responses. However, the fundamental mechanism underlying such a strong light-matter interaction is still under intensive investigation. First-principles calculations have predicted a quasiparticle bandgap much larger than the measured optical gap, and an optical response dominated by excitonic effects. In particular, a recent study based on a GW plus Bethe-Salpeter equation (GW-BSE) approach, which employed many-body Green's-function methodology to address electron-electron and electron-hole interactions, theoretically predicted a diversity of strongly bound excitons. Here we report experimental evidence of a series of excitonic dark states in single-layer WS2 using two-photon excitation spectroscopy. In combination with GW-BSE theory, we prove that the excitons are of Wannier type, meaning that each exciton wavefunction extends over multiple unit cells, but with extraordinarily large binding energy (∼0.7electronvolts), leading to a quasiparticle bandgap of 2.7electronvolts. These strongly bound exciton states are observed to be stable even at room temperature. We reveal an exciton series that deviates substantially from hydrogen models, with a novel energy dependence on the orbital angular momentum. These excitonic energy levels are experimentally found to be robust against environmental perturbations. The discovery of excitonic dark states and exceptionally large binding energy not only sheds light on the importance of many-electron effects in this two-dimensional gapped system, but also holds potential for the device application of TMDC monolayers and their heterostructures in computing, communication and bio-sensing.

Systematic investigation on topological properties of layered GaS and GaSe under strain

The topological properties of layered β-GaS and ε-GaSe under strain are systematically investigated by ab initio calculations with the electronic exchange-correlation interactions treated beyond the generalized gradient approximation (GGA). Based on the GW method and the Tran-Blaha modified Becke-Johnson potential approach, we find that while ε-GaSe can be strain-engineered to become a topological insulator, β-GaS remains a trivial one even under strong strain, which is different from the prediction based on GGA. The reliability of the fixed volume assumption rooted in nearly all the previous calculations is discussed. By comparing to strain calculations with optimized inter-layer distance, we find that the fixed volume assumption is qualitatively valid for β-GaS and ε-GaSe, but there are quantitative differences between the results from the fixed volume treatment and those from more realistic treatments. This work indicates that it is risky to use theoretical approaches like GGA that suffer from the band gap problem to address physical properties, including, in particular, the topological nature of band structures, for which the band gap plays a crucial role. In the latter case, careful calibration against more reliable methods like the GW approach is strongly recommended.

Modeling materials and processes in hybrid/organic photovoltaics: from dye-sensitized to perovskite solar cells.

CONSPECTUS: Over the last 2 decades, researchers have invested enormous research effort into hybrid/organic photovoltaics, leading to the recent launch of the first commercial products that use this technology. Dye-sensitized solar cells (DSCs) have shown clear advantages over competing technologies. The top certified efficiency of DSCs exceeds 11%, and the laboratory-cell efficiency is greater than 13%. In 2012, the first reports of high efficiency solid-state DSCs based on organohalide lead perovskites completely revolutionized the field. These materials are used as light absorbers in DSCs and as light-harvesting materials and electron conductors in meso-superstructured and flat heterojunction solar cells and show certified efficiencies that exceed 17%. To effectively compete with conventional photovoltaics, emerging technologies such as DSCs need to achieve higher efficiency and stability, while maintaining low production costs. Many of the advances in the DSC field have relied on the computational design and screening of new materials, with researchers examining material characteristics that can improve device performance or stability. Suitable modeling strategies allow researchers to observe the otherwise inaccessible but crucial heterointerfaces that control the operation of DSCs, offering the opportunity to develop new and more efficient materials and optimize processes. In this Account, we present a unified view of recent computational modeling research examining DSCs, illustrating how the principles and simulation tools used for these systems can also be adapted to study the emerging field of perovskite solar cells. Researchers have widely applied first-principles modeling to the DSC field and, more recently, to perovskite-based solar cells. DFT/TDDFT methods provide the basic framework to describe most of the desired materials and interfacial properties, and Car-Parrinello molecular dynamics allow researchers the further ability to sample local minima and dynamical fluctuations at finite temperatures. However, conventional DFT/TDDFT has some limitations, which can be overcome in part by tailored solutions or using many body perturbation theory within the GW approach, which is however more computationally intensive. Relativistic effects, such as spin-orbit coupling, are also included in simulations since they are fundamental for addressing systems that contain heavy atoms. We illustrate the performance of the proposed simulation toolbox along with the fundamental modeling strategies using selected examples of relevant isolated device constituents, including dye and perovskite absorbers, metal-oxide surfaces and nanoparticles, and hole transporters. We critically assess the accuracy of various computational approaches against the related experimental data. We analyze the representative interfaces that control the operational mechanism of the devices, including dye-sensitized TiO2/hole transporter and organohalide lead perovskite/TiO2, and the results reveal fundamental aspects of the device's operational mechanism. Although the modeling of DSCs is relatively mature, the recent "perovskite storm" has presented new problems and new modeling challenges, such as understanding exciton formation and dissociation at interfaces and carrier recombination in these materials.

Outer-valence Electron Spectra of Prototypical Aromatic Heterocycles from an Optimally Tuned Range-Separated Hybrid Functional.

Density functional theory with optimally tuned range-separated hybrid (OT-RSH) functionals has been recently suggested [Refaely-Abramson et al. Phys. Rev. Lett.2012, 109, 226405] as a nonempirical approach to predict the outer-valence electronic structure of molecules with the same accuracy as many-body perturbation theory. Here, we provide a quantitative evaluation of the OT-RSH approach by examining its performance in predicting the outer-valence electron spectra of several prototypical gas-phase molecules, from aromatic rings (benzene, pyridine, and pyrimidine) to more complex organic systems (terpyrimidinethiol and copper phthalocyanine). For a range up to several electronvolts away from the frontier orbital energies, we find that the outer-valence electronic structure obtained from the OT-RSH method agrees very well (typically within ∼0.1–0.2 eV) with both experimental photoemission and theoretical many-body perturbation theory data in the GW approximation. In particular, we find that with new strategies for an optimal choice of the short-range fraction of Fock exchange, the OT-RSH approach offers a balanced description of localized and delocalized states. We discuss in detail the sole exception found—a high-symmetry orbital, particular to small aromatic rings, which is relatively deep inside the valence state manifold. Overall, the OT-RSH method is an accurate DFT-based method for outer-valence electronic structure prediction for such systems and is of essentially the same level of accuracy as contemporary GW approaches, at a reduced computational cost.

HARTREE–FOCK SOLUTIONS OF 2D INTERACTING TIGHT-BINDING ELECTRONS: MOTT PROPERTIES AND ROOM TEMPERATURE SUPERCONDUCTIVITY INDICATIONS

Former results for a tight-binding (TB) model of CuO planes in La 2 CuO 4 are reinterpreted here to underline their wider implications. It is noted that physical systems being appropriately described by the TB model can exhibit the main strongly correlated electron system (SCES) properties, when they are solved in the HF approximation, by also allowing crystal symmetry breaking effects and noncollinear spin orientations of the HF orbitals. It is argued how a simple 2D square lattice system of Coulomb interacting electrons can exhibit insulator gaps and pseudogap states, and quantum phase transitions as illustrated by the mentioned former works. A discussion is also presented here indicating the possibility of attaining room temperature superconductivity, by means of a surface coating with water molecules of cleaved planes of graphite, being orthogonal to its c-axis. The possibility that 2D arrays of quantum dots can give rise to the same effect is also proposed to consideration. The analysis also furnishes theoretical insight to solve the Mott–Slater debate, at least for the La 2 CuO 4 and TMO band structures. The idea is to apply a properly noncollinear GW scheme to the electronic structure calculation of these materials. The fact is that the GW approach can be viewed as a HF procedure in which the screening polarization is also determined. This directly indicates the possibility of predicting the assumed dielectric constant in the previous works. Thus, the results seem to identify that the main correlation properties in these materials are determined by screening. Finally, the conclusions also seem to be of help for the description of the experimental observations of metal-insulator transitions and Mott properties in atoms trapped in planar photonic lattices.

A Comparison Between Hybrid Functional, GW Approach and the Bethe Salpether Equation: Optical Properties of High Pressure Phases of TiO<SUB>2</SUB>

Titanium dioxide has good corrosion resistance in aqueous solutions and is a good candidate for photoelectrodes. The limitation of the anatase phase of TiO2 is its large band gap. High pressure pha ...