Exchange and correlation effects in electronic excitations of Cu(2)O

All-Electron many-body approach to resonant inelastic x-ray scattering

We present a formalism for the resonant inelastic x-ray scattering (RIXS) cross section. The resulting compact expression in terms of polarizability matrix elements, particularly lends itself to the implementation in...

Accuracy trade-off between one-electron and excitonic spectra of cuprous halides in first-principles calculations

Because of the sophisticated error cancellation in the density functional theory (DFT)-based calculations, a theoretically more accurate input would not guarantee a better output. In this work, our first-principles GW plus Bethe-Salpeter equation calculations using pseudopotentials show that cuprous halides (CuCl and CuBr) are such extreme cases for which a better one-electron band is not accompanied with a better exciton binding energy. Moreover, we find that the exchange interaction of Cu core electrons plays a crucial role in their ground-state electronic properties, especially in the energy gap and macroscopic dielectric constant. Our work provides new insights into the understanding of the electronic structure of cuprous halides from the DFT perspective.

Exclusive Substitutional Nitrogen Doping on Graphene Decoupled from an Insulating Substrate

The on-surface synthesis of atomically flat N-doped graphene on oxidized copper is presented. Besides circumventing the almost standard use of metallic substrates for growth, this method allows producing graphene with ∼2.0 at % N in a substitutional configuration directly decoupled from the substrate. Angle-resolved photoemission shows a linear energy-momentum dispersion where the Dirac point lies at the Fermi level. Additionally, the N functional centers can be selectively tailored in sp² substitutional configuration by making use of a purpose-made molecular precursor: dicyanopyrazophenanthroline (C₁₆H₆N₆).

Practical GW scheme for electronic structure of 3d-transition-metal monoxide anions: ScO-, TiO-, CuO-, and ZnO. J Chem Phys 2019;151:134305. [PMID: 31594362 DOI: 10.1063/1.5118671]

The GW approximation to many-body perturbation theory is a reliable tool for describing charged electronic excitations, and it has been successfully applied to a wide range of extended systems for several decades using a plane-wave basis. However, the GW approximation has been used to test limited spectral properties of a limited set of finite systems (e.g., frontier orbital energies of closed-shell sp molecules) only for about a decade using a local-orbital basis. Here, we calculate the quasiparticle spectra of closed- and open-shell molecular anions with partially and completely filled 3d shells (shallow and deep 3d states, respectively), ScO^-, TiO^-, CuO^-, and ZnO^-, using various levels of GW theory, and compare them to experiments to evaluate the performance of the GW approximation on the electronic structure of small molecules containing 3d transition metals. We find that the G-only eigenvalue self-consistent GW scheme with W fixed to the PBE level (G_nW₀@PBE), which gives the best compromise between accuracy and efficiency for solids, also gives good results for both localized (d) and delocalized (sp) states of 3d-transition-metal oxide molecules. The success of G_nW₀@PBE in predicting electronic excitations in these systems reasonably well is likely due to the fortuitous cancellation effect between the overscreening of the Coulomb interaction by PBE and the underscreening by the neglect of vertex corrections. Together with the absence of the self-consistent field convergence error (e.g., spin contamination in open-shell systems) and the GW multisolution issue, the G_nW₀@PBE scheme gives the possibility to predict the electronic structure of complex real systems (e.g., molecule-solid and sp-d hybrid systems) accurately and efficiently.

The GW Compendium: A Practical Guide to Theoretical Photoemission Spectroscopy

The GW approximation in electronic structure theory has become a widespread tool for predicting electronic excitations in chemical compounds and materials. In the realm of theoretical spectroscopy, the GW method provides access to charged excitations as measured in direct or inverse photoemission spectroscopy. The number of GW calculations in the past two decades has exploded with increased computing power and modern codes. The success of GW can be attributed to many factors: favorable scaling with respect to system size, a formal interpretation for charged excitation energies, the importance of dynamical screening in real systems, and its practical combination with other theories. In this review, we provide an overview of these formal and practical considerations. We expand, in detail, on the choices presented to the scientist performing GW calculations for the first time. We also give an introduction to the many-body theory behind GW, a review of modern applications like molecules and surfaces, and a perspective on methods which go beyond conventional GW calculations. This review addresses chemists, physicists and material scientists with an interest in theoretical spectroscopy. It is intended for newcomers to GW calculations but can also serve as an alternative perspective for experts and an up-to-date source of computational techniques.

Anisotropic Plasmonic CuS Nanocrystals as a Natural Electronic Material with Hyperbolic Optical Dispersion

Copper sulfide nanocrystals have recently been studied due to their metal-like behavior and strong plasmonic response, which make them an attractive material for nanophotonic applications in the near-infrared spectral range; however, the nature of the plasmonic response remains unclear. We have performed a combined experimental and theoretical study of the optical properties of copper sulfide colloidal nanocrystals and show that bulk CuS resembles a heavily doped p-type semiconductor with a very anisotropic energy band structure. As a consequence, CuS nanoparticles possess key properties of relevance to nanophotonics applications: they exhibit anisotropic plasmonic behavior in the infrared and support optical modes with hyperbolic dispersion in the 670-1050 nm spectral range. We also predict that the ohmic loss is low compared to conventional plasmonic materials such as noble metals in the NIR. The plasmonic resonances can be tuned by controlling the size and shape of the nanocrystals, providing a playground for future nanophotonic applications in the near-infrared.

Electron Localization Function and Compton Profiles of Cu2O

The nature of bonding in the cubic cuprous oxide is studied by means of the theoretical tools, namely, the electron localization function and Compton profiles. The isotropic Compton profiles together with the anisotropies in the directional Compton profiles are presented. Taking free-atom Compton profiles, the charge-transfer model is also applied. The first-principles calculations based on the GGA are performed, and the self-interaction correction is incorporated, adopting the GGA+U approach. Both types of calculations are performed deploying the linearized augmented plane-wave (LAPW) method. The effect of self-interaction correction on the electron localization function, Compton profiles, and anisotropies is discussed. The electron localization function reveals ionic behavior in the (110) plane and covalent nature in the Cu-O bond intersecting plane. The GGA+U exhibits more covalent nature. The two LAPW calculations of the Compton profiles show better agreement with the available experimental data than the free-atom profiles. Among all of the calculations undertaken, the GGA+U shows the best agreement with the experiment. The GGA+U calculation shows more anisotropic behavior in directional Compton profiles.

Towards efficient time-resolved X-ray absorption studies of electron dynamics at photocatalytic interfaces

We present a picosecond time-resolved X-ray absorption spectroscopy (tr-XAS) setup designed for synchrotron-based studies of interfacial photochemical dynamics. The apparatus combines a high power, variable repetition rate picosecond laser system with a time-resolved X-ray fluorescence yield detection technique. Time-tagging of the detected fluorescence signals enables the parallel acquisition of X-ray absorption spectra at a variety of pump-probe delays employing the well-defined time structure of the X-ray pulse trains. The viability of the setup is demonstrated by resolving dynamic changes in the fine structure near the O1s X-ray absorption edge of cuprous oxide (Cu₂O) after photo-excitation with a 355 nm laser pulse. Two distinct responses are detected. A pronounced, quasi-static, reversible change of the Cu₂O O1s X-ray absorption spectrum by up to ∼30% compared to its static line shape corresponds to a redshift of the absorption edge by ∼1 eV. This value is small compared to the 2.2 eV band gap of Cu₂O but in agreement with previously published results. The lifetime of this effect exceeds the laser pulse-to-pulse period of 8 μs, resulting in a quasi-static spectral change that persists as long as the sample is exposed to the laser light, and completely vanishes once the laser is blocked. Additionally, a short-lived response corresponding to a laser-induced shift of the main absorption line by ∼2 eV to lower energies appears within <200 ps and decays with a characteristic timescale of 43 ± 5 ns. Both the picosecond rise and nanosecond decay of this X-ray response are simultaneously captured by making use of a time-tagging approach - highlighting the prospects of the experimental setup for efficient probing of the electronic and structural dynamics in photocatalytic systems on multiple timescales.

Accuracy of dielectric-dependent hybrid functionals in the prediction of optoelectronic properties of metal oxide semiconductors: a comprehensive comparison with many-body GW and experiments

Understanding the electronic structure of metal oxide semiconductors is crucial to their numerous technological applications, such as photoelectrochemical water splitting and solar cells. The needed experimental and theoretical knowledge goes beyond that of pristine bulk crystals, and must include the effects of surfaces and interfaces, as well as those due to the presence of intrinsic defects (e.g. oxygen vacancies), or dopants for band engineering. In this review, we present an account of the recent efforts in predicting and understanding the optoelectronic properties of oxides using ab initio theoretical methods. In particular, we discuss the performance of recently developed dielectric-dependent hybrid functionals, providing a comparison against the results of many-body GW calculations, including G ₀ W ₀ as well as more refined approaches, such as quasiparticle self-consistent GW. We summarize results in the recent literature for the band gap, the band level alignment at surfaces, and optical transition energies in defective oxides, including wide gap oxide semiconductors and transition metal oxides. Correlated transition metal oxides are also discussed. For each method, we describe successes and drawbacks, emphasizing the challenges faced by the development of improved theoretical approaches. The theoretical section is preceded by a critical overview of the main experimental techniques needed to characterize the optoelectronic properties of semiconductors, including absorption and reflection spectroscopy, photoemission, and scanning tunneling spectroscopy (STS).

Justifying quasiparticle self-consistent schemes via gradient optimization in Baym-Kadanoff theory

The question of which non-interacting Green's function 'best' describes an interacting many-body electronic system is both of fundamental interest as well as of practical importance in describing electronic properties of materials in a realistic manner. Here, we study this question within the framework of Baym-Kadanoff theory, an approach where one locates the stationary point of a total energy functional of the one-particle Green's function in order to find the total ground-state energy as well as all one-particle properties such as the density matrix, chemical potential, or the quasiparticle energy spectrum and quasiparticle wave functions. For the case of the Klein functional, our basic finding is that minimizing the length of the gradient of the total energy functional over non-interacting Green's functions yields a set of self-consistent equations for quasiparticles that is identical to those of the quasiparticle self-consistent GW (QSGW) (van Schilfgaarde et al 2006 Phys. Rev. Lett. 96 226402-4) approach, thereby providing an a priori justification for such an approach to electronic structure calculations. In fact, this result is general, applies to any self-energy operator, and is not restricted to any particular approximation, e.g., the GW approximation for the self-energy. The approach also shows that, when working in the basis of quasiparticle states, solving the diagonal part of the self-consistent Dyson equation is of primary importance while the off-diagonals are of secondary importance, a common observation in the electronic structure literature of self-energy calculations. Finally, numerical tests and analytical arguments show that when the Dyson equation produces multiple quasiparticle solutions corresponding to a single non-interacting state, minimizing the length of the gradient translates into choosing the solution with largest quasiparticle weight.

Anomalous thickness-dependent optical energy gap of ALD-grown ultra-thin CuO films

Usually an inverse square relation between the optical energy gap and the size of crystallites is observed for semiconducting materials due to the strong quantum localization effect. Coulomb attraction that may lead to a proportional dependence is often ignored or considered less important to the optical energy gap when the crystallite size or the thickness of a thin film changes. Here we report a proportional dependence between the optical energy gap and the thickness of ALD-grown CuO thin films due to a strong Coulomb attraction. The ultrathin films deposited in the thickness range of 9-81 nm show a p-type semiconducting behavior when analyzed by Seebeck coefficient and electrical resistivity measurements. The indirect optical energy gap nature of the films is verified from UV-vis spectrophotometric measurements. A progressive increase in the indirect optical energy gap from 1.06 to 1.24 eV is observed with the increase in the thickness of the films. The data are analyzed in the presence of Coulomb attractions using the Brus model. The optical energy gap when plotted against the cubic root of the thickness of the films shows a linear dependence.

Semiconducting transition metal oxides

Open shell transition metal oxides are usually described as Mott or charge transfer insulators, which are often viewed as being disparate from semiconductors. Based on the premise that the presence of a correlated gap and semiconductivity are not mutually exclusive, this work reviews electronic structure calculations on the binary 3d oxides, so to distill trends and design principles for semiconducting transition metal oxides. This class of materials possesses the potential for discovery, design, and development of novel functional semiconducting compounds, e.g. for energy applications. In order to place the 3d orbitals and the sp bands into an integrated picture, band structure calculations should treat both contributions on the same footing and, at the same time, account fully for electron correlation in the 3d shell. Fundamentally, this is a rather daunting task for electronic structure calculations, but quasi-particle energy calculations in GW approximation offer a viable approach for band structure predictions in these materials. Compared to conventional semiconductors, the inherent multivalent nature of transition metal cations is more likely to cause undesirable localization of electron or hole carriers. Therefore, a quantitative prediction of the carrier self-trapping energy is essential for the assessing the semiconducting properties and to determine whether the transport mechanism is a band-like large-polaron conduction or a small-polaron hopping conduction. An overview is given for the binary 3d oxides on how the hybridization between the 3d crystal field symmetries with the O-p orbitals of the ligands affects the effective masses and the likelihood of electron and hole self-trapping, identifying those situations where small masses and band-like conduction are more likely to be expected. The review concludes with an illustration of the implications of the increased electronic complexity of transition metal cations on the defect physics and doping, using as an example the diversity of possible atomic and magnetic configurations of the O vacancy in TiO(2), and the high levels of hole doping in Co(2)ZnO(4) due to a self-doping mechanism that originates from the multivalence of Co.

A new look at oxide formation at the copper/electrolyte interface by in situ spectroscopies

The oxide layer passivating copper consists mainly of a complex, defect-rich oxide on the basis of copper mixed oxide, Cu₄O₃.

Insights and challenges of applying the GW method to transition metal oxides

The ab initio GW method is considered as the most accurate approach for calculating the band gaps of semiconductors and insulators. Yet its application to transition metal oxides (TMOs) has been hindered by the failure of traditional approximations developed for conventional semiconductors. In this work, we examine the effects of these approximations on the values of band gaps for ZnO, Cu2O, and TiO2. In particular, we explore the origin of the differences between the two widely used plasmon-pole models. Based on the comparison of our results with the experimental data and previously published calculations, we discuss which approximations are suitable for TMOs and why.

Strong renormalization of the electronic band gap due to lattice polarization in the GW formalism

The self-consistent GW band gaps are known to be significantly overestimated. We show that this overestimation is, to a large extent, due to the neglect of the contribution of the lattice polarization to the screening of the electron-electron interaction. To solve this problem, we derive within the GW formalism a generalized plasmon-pole model that accounts for lattice polarization. The resulting GW self-energy is used to calculate the band structures of a set of binary semiconductors and insulators. The lattice contribution always decreases the band gap. The shrinkage increases with the size of the longitudinal-transverse optical splitting and it can represent more than 15% of the band gap in highly polar compounds, reducing the band-gap percentage error by a factor of 3.

On the accuracy of the non-self-consistent calculation of the electronic structure of solids with hybrid functionals

A simple approximation within the framework of the hybrid methods for the calculation of the electronic structure of solids is presented. By considering only the diagonal elements of the matrix of the perturbation operator (Hartree-Fock exchange minus semilocal exchange) calculated in the basis of the semilocal orbitals, the computational time is drastically reduced, while keeping very well in most studied cases the accuracy of the results obtained with hybrid functionals when applied without any approximations.

Cu₂O behavior under pressure: an ab initio study

We have performed density-functional theory calculations for three crystallographic phases (cuprite, CdI(2), and CdCl(2)) of the cuprous oxide by using both the local-density approximation (LDA) and the Perdew-Burke-Ernzerhof generalized-gradient approximation. The latter gives a very good description of the properties of the cuprite phase at room temperature. In particular, the bulk modulus and the elastic constants at zero pressure are in excellent agreement with experiment. At 10 GPa (7 in LDA calculations), the transition from the cuprite to the CdI(2) phase occurs, and the latter remains the phase having the smallest Gibbs energy up to the maximum pressure we have considered (20 GPa). We have also determined the elastic constants of Cu(2)O in the cuprite phase for various applied pressures. The results indicate that this structure becomes unstable with respect to trigonal deformations before the transition to the CdI(2) phase. On the other hand, no indication of instability with respect to tetragonal deformations has been found. This kind of instability would occur at pressures greater than the phase transition pressure.

Advanced Computational Design of Intermediate-Band Photovoltaic Material V-substituted MgIn2S4

An intermediate-band material based on thiospinel semiconductor MgIn2S4is presented. This material is proposed as high efficiency photovoltaic material for intermediate-band solar cells. We analyze V substitution for In in the parent compound MgIn2S4and the formation of the V d-states intermediate band. For the proper characterization of the width and position of this band inside the band gap, the standardone-shotGW method within the plasmon-pole approximation is applied. The electronic properties thus obtained are discussed and compared to those studied with Density Functional Theory (DFT), and the advantages and the limitations of the two methods are discussed. In addition, DFT electronic-charge density analysis is shown.

Effects of electronic and lattice polarization on the band structure of delafossite transparent conductive oxides

We use hybrid functionals and restricted self-consistent GW, state-of-the-art theoretical approaches for quasiparticle band structures, to study the electronic states of delafossite Cu(Al,In)O2, the first p-type and bipolar transparent conductive oxides. We show that a self-consistent GW approximation gives remarkably wider band gaps than all the other approaches used so far. Accounting for polaronic effects in the GW scheme we recover a very nice agreement with experiments. Furthermore, the modifications with respect to the Kohn-Sham bands are strongly k dependent, which makes questionable the common practice of using a scissor operator. Finally, our results support the view that the low energy structures found in optical experiments, and initially attributed to an indirect transition, are due to intrinsic defects in the samples.

Strong interplay between structure and electronic properties in CuIn(S,Se){2}: a first-principles study

We present a first-principles study of the electronic properties of CuIn(S,Se){2} (CIS) using state-of-the-art self-consistent GW and hybrid functionals. The calculated band gap depends strongly on the anion displacement u, an internal structural parameter that measures lattice distortion. This contrasts with the observed stability of the band gap of CIS solar panels under operating conditions, where a relatively large dispersion of values for u occurs. We solve this apparent paradox considering the coupled effect on the band gap of copper vacancies and lattice distortions. The correct treatment of d electrons in these materials requires going beyond density functional theory, and GW self-consistency is critical to evaluate the quasiparticle gap and the valence band maximum.

Localized and itinerant states in lanthanide oxides united by GW @ LDA+U

Many-body perturbation theory in the GW approach is applied to lanthanide oxides, using the local-density approximation plus a Hubbard U correction (LDA+U) as the starting point. Good agreement between the G0W0 density of states and experimental spectra is observed for CeO2 and Ce2O3. Unlike the LDA+U method G0W0 exhibits only a weak dependence on U in a physically meaningful range of U values. For the whole lanthanide sesquioxide (Ln2O3) series G0W0 @ LDA+U reproduces the main features found for the optical experimental band gaps. The relative positions of the occupied and unoccupied f states predicted by G0W0 confirm the experimental conjecture derived from phenomenological arguments.

Electronic band structure of Cu(2)O by spin density functional theory

The band structure of Cu(2)O is calculated using density functional theory in the generalized gradient approximation. By taking spin-orbit coupling into account the split between the Γ(7)(+) and the Γ(8)(+) valence band states is obtained as 128 meV. The highest valence band shows a noticeable nonparabolicity close to the Γ point. This is important for the quantitative description of excitons in this material, which is considered to be the best candidate for the confirmation that Bose-Einstein condensation also occurs in excitonic systems.

Understanding correlations in vanadium dioxide from first principles

Vanadium dioxide is a prototype material for the discussion of correlation effects in solids. First-principles density-functional theory does not describe the metal-insulator transition, whereas strongly correlated models reproduce the main features. Here we present a parameter-free GW calculation of VO2 and show that the correlation effects in the band structure of both the metallic and the insulating phases are correctly reproduced, provided that quasiparticle energies and wave functions are calculated self-consistently. Our calculations explain the satellite in the photoemission spectrum of the metal as due to a plasmon resonance in the energy-loss function and show that this feature disappears in the insulator.

Ab initio method for calculating electron-phonon scattering times in semiconductors: application to GaAs and GaP

We propose a fully ab initio approach to calculate electron-phonon scattering times for excited electrons interacting with short-wavelength (intervalley) phonons in semiconductors. Our approach is based on density functional perturbation theory and on the direct integration of electronic scattering probabilities over all possible final states with no ad hoc assumptions. We apply it to the deexcitation of hot electrons in GaAs, and calculate the lifetime of the direct exciton in GaP, both in excellent agreement with experiments. Matrix elements of the electron-phonon coupling, and their dependence on the wave vector of the final state and on the phonon modes, are shown to be crucial ingredients of the evaluation of electron-phonon scattering times.