GW Band Structure Research Articles

GPAW: An open Python package for electronic structure calculations.

We review the GPAW open-source Python package for electronic structure calculations. GPAW is based on the projector-augmented wave method and can solve the self-consistent density functional theory (DFT) equations using three different wave-function representations, namely real-space grids, plane waves, and numerical atomic orbitals. The three representations are complementary and mutually independent and can be connected by transformations via the real-space grid. This multi-basis feature renders GPAW highly versatile and unique among similar codes. By virtue of its modular structure, the GPAW code constitutes an ideal platform for the implementation of new features and methodologies. Moreover, it is well integrated with the Atomic Simulation Environment (ASE), providing a flexible and dynamic user interface. In addition to ground-state DFT calculations, GPAW supports many-body GW band structures, optical excitations from the Bethe-Salpeter Equation, variational calculations of excited states in molecules and solids via direct optimization, and real-time propagation of the Kohn-Sham equations within time-dependent DFT. A range of more advanced methods to describe magnetic excitations and non-collinear magnetism in solids are also now available. In addition, GPAW can calculate non-linear optical tensors of solids, charged crystal point defects, and much more. Recently, support for graphics processing unit (GPU) acceleration has been achieved with minor modifications to the GPAW code thanks to the CuPy library. We end the review with an outlook, describing some future plans for GPAW.

Electronic band structures and optical properties of 2D XOF (X = Ga or In) oxyfluoride monolayers using density functional theory and GW approximation

The class of two-dimensional oxyfluoride monolayers is currently considered one of the most attractive nanomaterials for enhancing design and pushing the limits of different cutting-edge technologies. Two-dimensional semiconductor materials are the most promising systems for various applications in optoelectronic devices because they have a unique optical properties. We continue in this way by investigating the GW band structures and optical properties of unique 2D XOF (X = Ga or In) oxyfluoride monolayers, involving absorption, conductivity, refractive index, and dielectric function. We find no imaginary frequencies in the computed phonon spectra, indicating that these systems are dynamically stable. Furthermore, GaOF and InOF stay stable for temperatures T ≤ 840 K. The band gap of GaOF obtained with the single shot (G0W0) is larger than the band gap energy Eg of InOF. Where the direct band gap energies of GaOF and InOF are 6.1 eV and 4.8 eV, respectively. Our GW(PBE) numerical simulations demonstrate that the GaOF monolayer moves transparent once the frequency of the incoming light exceeds the plasma frequency (35.00 eV). Furthermore, InOF switches transparently once the incident light frequency exceeds the plasma frequency ∼ 35.00 eV. Interestingly, we obtain that these 2D sheets have a strong absorption coefficient in the range of ∼ 3.00–60.00 eV. They are emerging as a potential for the building blocks of the nano-size and ultra-thin optoelectronics of the future since they productively emit and absorb light.

Representing individual electronic states for machine learning GW band structures of 2D materials

Choosing optimal representation methods of atomic and electronic structures is essential when machine learning properties of materials. We address the problem of representing quantum states of electrons in a solid for the purpose of machine leaning state-specific electronic properties. Specifically, we construct a fingerprint based on energy decomposed operator matrix elements (ENDOME) and radially decomposed projected density of states (RAD-PDOS), which are both obtainable from a standard density functional theory (DFT) calculation. Using such fingerprints we train a gradient boosting model on a set of 46k G0W0 quasiparticle energies. The resulting model predicts the self-energy correction of states in materials not seen by the model with a mean absolute error of 0.14 eV. By including the material’s calculated dielectric constant in the fingerprint the error can be further reduced by 30%, which we find is due to an enhanced ability to learn the correlation/screening part of the self-energy. Our work paves the way for accurate estimates of quasiparticle band structures at the cost of a standard DFT calculation.

Quasiparticle band structures of bulk and few-layer PdSe2 from first-principles GW calculations

We performed first-principles density functional theory (DFT) and GW calculations to investigate electronic structures of bulk and few-layer PdSe2. We obtained the quasiparticle band structure of bulk PdSe2, and the obtained energy gap agrees excellently with the reported experimental value. For monolayer and bilayer PdSe2, we obtained quasiparticle band structures with respect to the vacuum level. We analyzed DFT and GW band structures in detail, finding k-space positions of valence band maxima and conduction band minima, effective masses, the quasiparticle density of states, work functions, ionization potentials, electron affinities, and k-space shapes of electron and hole pockets. These results provide a foundation for development of basic studies and device applications.

Towards fully automated GW band structure calculations: What we can learn from 60.000 self-energy evaluations

We analyze a data set comprising 370 GW band structures of two-dimensional (2D) materials covering 14 different crystal structures and 52 chemical elements. The band structures contain a total of 61716 quasiparticle (QP) energies obtained from plane-wave-based one-shot G0W0@PBE calculations with full frequency integration. We investigate the distribution of key quantities, like the QP self-energy corrections and QP weights, and explore their dependence on chemical composition and magnetic state. The linear QP approximation is identified as a significant error source and we propose schemes for controlling and drastically reducing this error at low computational cost. We analyze the reliability of the 1/N basis set extrapolation and find that is well-founded with a narrow distribution of coefficients of determination (r2) peaked very close to 1. Finally, we explore the accuracy of the scissors operator approximation and conclude that its validity is very limited. Our work represents a step towards the development of automatized workflows for high-throughput G0W0 band structure calculations for solids.

Comparison of GW band structure to semiempirical approach for an FeSe monolayer

We present the ${G}_{0}{W}_{0}$ band structure, core levels, and deformation potential of monolayer FeSe in the paramagnetic phase based on a starting mean field of the Kohn-Sham density functional theory (DFT) with the Perdew, Burke, and Ernzerhof functional. We find the GW correction increases the bandwidth of the states forming the $M$ pocket near the Fermi energy, while leaving the $\mathrm{\ensuremath{\Gamma}}$ pocket roughly unchanged. We then compare the ${G}_{0}{W}_{0}$ quasiparticle band energies with the band structure from a simple empirical $+\mathrm{A}$ approach, which was recently proposed to capture the renormalization of the electron-phonon interaction going beyond DFT in FeSe, when used as a starting point in density functional perturbation theory. We show that this empirical correction succeeds in approximating the GW nonlocal and dynamical self-energy in monolayer FeSe and reproduces the GW band structure near the Fermi surface, the core energy levels, and the deformation potential (electron-phonon coupling).

GeC/GaN vdW Heterojunctions: A Promising Photocatalyst for Overall Water Splitting and Solar Energy Conversion.

Two-dimensional van der Waals (vdW) heterojunctions have been regarded as promising candidates for photocatalytic water splitting and solar energy conversion. Here, we propose a two-dimensional GeC/GaN vdW heterostructure, where the GaN monolayer and the GeC monolayer are stacked. The binding energy, phonon spectrum, and elastic constants demonstrate this material's high dynamic and mechanical stability. Most notably, the GW band structure, GW + Bethe-Salpeter equation (BSE) optical absorption spectrum, and the band alignment of the density functional theory (DFT) scheme and empirical formula reveal that the GeC/GaN vdW heterostructures have a dramatically high optical absorption coefficient (∼105 cm-1) in the visible region and a suitable band edge with sufficiently large kinetic overpotentials of the hydrogen evolution reaction (ΔEc ≥ 1.945 eV) and the oxygen evolution reaction (ΔEv ≥ 1.244 eV). Photogenerated electrons and holes aggregate on the GeC monolayer and GaN monolayer surfaces, respectively, which could make this heterojunction a promising candidate for photocatalytic water splitting and solar energy conversion.

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.

Interband absorption edge in the topological insulators Bi2(Te1−xSex)3

We have investigated the optical properties of thin films of topological insulators Bi$_{2}$Te$_{3}$, Bi$_{2}$Se$_{3}$ and their alloys Bi$_2$(Te$_{1-x}$Se$_x$)$_3$ on BaF$_{2}$ substrates by a combination of infrared ellipsometry and reflectivity in the energy range from 0.06 to 6.5 eV. For the onset of interband absorption in Bi$_2$Se$_3$, after the correction for the Burstein-Moss effect, we find the value of direct bandgap of $215\pm10$ meV at 10 K. Our data supports the picture that Bi$_2$Se$_3$ has a direct band gap located at the $\Gamma$ point in the Brillouin zone and that the valence band reaches up to the Dirac point and has the shape of a downward oriented paraboloid, i.e. without a camel-back structure. In Bi$_2$Te$_3$, the onset of strong direct interband absorption at 10 K is at a similar energy of about 200 meV, with a weaker additional feature at about 170 meV. Our data support the recent GW band structure calculations suggesting that the direct interband transition does not occur at the $\Gamma$ point but near the Z-F line of the Brillouin zone. In the Bi$_2$(Te$_{1-x}$Se$_x$)$_3$ alloy, the energy of the onset of direct interband transitions exhibits a maximum near $x=0.3$ (i.e. the composition of Bi$_2$Te$_2$Se), suggesting that the crossover of the direct interband transitions between the two points in the Brillouin zone occurs close to this composition.

Quasiparticle band structure and optical properties of theα12Si-Ge superstructure from first principles

The quasi-particle band structure and dielectric function for the so-called magic sequence SiGe$_2$Si$_2$Ge$_2$SiGe$_{12}$ (or $\alpha_{12}$) structure [PRL 108, 027401 (2012)] are calculated by many-body perturbation theory (MBPT) within an ab-initio framework. On top of density functional calculations within the local density approximation (LDA) leading to a fundamental band gap of 0.23 eV, we have computed the quasi-particle band structure within the G$_0$W$_0$ approach opening the gap to 0.61 eV. Moreover, we have calculated the optical properties by solving the Bethe-Salpeter equation (BSE) for the electron-hole two-particle correlation function. When comparing the imaginary part of the dielectric function obtained at various levels of approximation, \emph{i.e.} the independent particle approximation (or random phase approximation) based on (i) the LDA or (ii) GW band structures, and (iii) the BSE including local field effects and electron-hole correlations, we observe that the important first transition is better explained with taking into account excitonic effects. Moreover, the onset transition originating from the direct transition of the magic sequence structure is also investigated.

Quasiparticle band structure of rocksalt-CdO determined using maximally localized Wannier functions

CdO in the rocksalt structure is an indirect band gap semiconductor. Thus, in order to determine its band gap one needs to calculate the complete band structure. However, in practice, the exact evaluation of the quasiparticle band structure for the large number of k-points which constitute the different symmetry lines in the Brillouin zone can be an extremely demanding task compared to the standard density functional theory (DFT) calculation. In this paper we report the full quasiparticle band structure of CdO using a plane-wave pseudopotential approach. In order to reduce the computational effort and time, we make use of maximally localized Wannier functions (MLWFs). The MLWFs offer a highly accurate method for interpolation of the DFT or GW band structure from a coarse k-point mesh in the irreducible Brillouin zone, resulting in a much reduced computational effort. The present paper discusses the technical details of the scheme along with the results obtained for the quasiparticle band gap and the electron effective mass.

Possible magnetic behavior in oxygen-deficientβ-PtO2

We studied the electronic properties of beta-platinum dioxide ({\beta}-PtO2), a catalytic material, based on density functional theory. Using the GGA+U method which reproduces the GW band structures and the experimental structural parameters, we found that the creation of an oxygen vacancy will induce local magnetic moment on the neighboring Pt and O atoms. The magnetism originates not only from the unpaired electrons that occupy the vacancy induced gap state, but also from the itinerant valence electrons. Because of antiferromagnetic (AF) coupling and the localized nature of gap states, the total magnetic moment is zero for charge-neutral state (V_o^0) and is ~ 1 \mu B for singly-charged states (V_o^\mu). Calculation of grand potential shows that, the three charge states (V_o^0, V_o^\pm) are of the same stability within a small region, and the negatively charged state (V_o^-) is energetically favored within a wide range of the band gap. On this basis we discussed the implication on catalytic behavior.

Accurate pseudopotential description of the GW bandstructure of ZnO

We present the GW band structure of ZnO in its wurtzite (WZ), zincblende (ZB) and rocksalt (RS) phases at the Γ point, calculated within the GW approximation. We have used a Zn 20+ pseudopotential which is essential for the adequate treatment of the exchange interaction in the self-energy. The accuracy of the pseudopotential used is also discussed. The effect of the p – d hybridization on the GW corrections to the band gap is correlated by comparing the ZB and RS phase.

Maximally localized Wannier functions for GW quasiparticles

We review the formalisms of the self-consistent GW approximation to many-body perturbation theory and of the generation of optimally localized Wannier functions from groups of energy bands. We show that the quasiparticle Bloch wave functions from such GW calculations can be used within this Wannier framework. These Wannier functions can be used to interpolate the many-body band structure from the coarse mesh of Brillouin-zone points on which it is known from the initial calculation to the usual symmetry lines, and we demonstrate that this procedure is accurate and efficient for the self-consistent GW band structure. The resemblance of these Wannier functions to the bond orbitals discussed in the chemical community led us to expect differences between density-functional and many-body functions that could be qualitatively interpreted. However, the differences proved to be minimal in the cases studied. Detailed results are presented for ${\text{SrTiO}}_{3}$ and solid argon.

Model GW band structure ofInAsandGaAsin the wurtzite phase

We report quasiparticle calculations of the newly observed wurtzite polymorph of $\mathrm{InAs}$ and $\mathrm{GaAs}$. The calculations are performed in the GW approximation (based on a model dielectric function) using plane waves and pseudopotentials. For comparison we also report the study of the zinc-blende phase within the same approximations. In the $\mathrm{InAs}$ compound the $\mathrm{In}\phantom{\rule{0.3em}{0ex}}4d$ electrons play a very important role: whether they are frozen in the core or not leads either to a correct or a wrong band ordering (negative gap) within the local-density appproximation (LDA). We have calculated the GW band structure in both cases. In the first approach, we have estimated the correction to the pd repulsion calculated within the LDA and included this effect in the calculation of the GW corrections to the LDA spectrum. In the second case, we circumvent the negative gap problem by first using the screened exchange approximation and then calculating the GW corrections starting from the so obtained eigenvalues and eigenfunctions. This approach, that can be thought of as a step towards self-consistency, leads to a more realistic band structure and was also used for $\mathrm{GaAs}$. For both $\mathrm{InAs}$ and $\mathrm{GaAs}$ in the wurtzite phase we predict an increase of the quasiparticle gap with respect to the zinc-blende polytype.