The generalization of the Local Density Approximation (LDA) method for the systems with strong Coulomb correlations is presented which gives a correct description of the Mott insulators. The LDA+U method is based on the model hamiltonian approach and allows to take into account the non-sphericity of the Coulomb and exchange interactions. parameters. Orbital-dependent LDA+U potential gives correct orbital polarization and corresponding Jahn-Teller distortion. To calculate the spectra of the strongly correlated systems the impurity Anderson model should be solved with a many-electron trial wave function. All parameters of the many-electron hamiltonian are taken from LDA+U calculations. The method was applied to NiO and has shown good agreement with experimental photoemission spectra and with the oxygen Kα X-ray emission spectrum.

https://iopscience.iop.org/article/10.1088/0953-8984/9/4/002/pdf

First-principles calculations of the electronic structure and spectra of strongly correlated systems: the LDA+ U method

The last decade witnessed significant progress in angle-resolved photoemission spectroscopy (ARPES) and its applications. Today, ARPES experiments with 2-meV energy resolution and $0.2\ifmmode^\circ\else\textdegree\fi{}$ angular resolution are a reality even for photoemission on solids. These technological advances and the improved sample quality have enabled ARPES to emerge as a leading tool in the investigation of the high-${T}_{c}$ superconductors. This paper reviews the most recent ARPES results on the cuprate superconductors and their insulating parent and sister compounds, with the purpose of providing an updated summary of the extensive literature. The low-energy excitations are discussed with emphasis on some of the most relevant issues, such as the Fermi surface and remnant Fermi surface, the superconducting gap, the pseudogap and $d$-wave-like dispersion, evidence of electronic inhomogeneity and nanoscale phase separation, the emergence of coherent quasiparticles through the superconducting transition, and many-body effects in the one-particle spectral function due to the interaction of the charge with magnetic and/or lattice degrees of freedom. Given the dynamic nature of the field, we chose to focus mainly on reviewing the experimental data, as on the experimental side a general consensus has been reached, whereas interpretations and related theoretical models can vary significantly. The first part of the paper introduces photoemission spectroscopy in the context of strongly interacting systems, along with an update on the state-of-the-art instrumentation. The second part provides an overview of the scientific issues relevant to the investigation of the low-energy electronic structure by ARPES. The rest of the paper is devoted to the experimental results from the cuprates, and the discussion is organized along conceptual lines: normal-state electronic structure, interlayer interaction, superconducting gap, coherent superconducting peak, pseudogap, electron self-energy, and collective modes. Within each topic, ARPES data from the various copper oxides are presented.

https://arxiv.org/pdf/cond-mat/0208504.pdf

Angle-resolved photoemission studies of the cuprate superconductors

During the past decade, computer simulations based on a quantum-mechanical description of the interactions between electrons and between electrons and atomic nuclei have developed an increasingly important impact on solid-state physics and chemistry and on materials science—promoting not only a deeper understanding, but also the possibility to contribute significantly to materials design for future technologies. This development is based on two important columns: (i) The improved description of electronic many-body effects within density-functional theory (DFT) and the upcoming post-DFT methods. (ii) The implementation of the new functionals and many-body techniques within highly efficient, stable, and versatile computer codes, which allow to exploit the potential of modern computer architectures. In this review, I discuss the implementation of various DFT functionals [local-density approximation (LDA), generalized gradient approximation (GGA), meta-GGA, hybrid functional mixing DFT, and exact (Hartree-Fock) exchange] and post-DFT approaches [DFT + U for strong electronic correlations in narrow bands, many-body perturbation theory (GW) for quasiparticle spectra, dynamical correlation effects via the adiabatic-connection fluctuation-dissipation theorem (AC-FDT)] in the Vienna ab initio simulation package VASP. VASP is a plane-wave all-electron code using the projector-augmented wave method to describe the electron-core interaction. The code uses fast iterative techniques for the diagonalization of the DFT Hamiltonian and allows to perform total-energy calculations and structural optimizations for systems with thousands of atoms and ab initio molecular dynamics simulations for ensembles with a few hundred atoms extending over several tens of ps. Applications in many different areas (structure and phase stability, mechanical and dynamical properties, liquids, glasses and quasicrystals, magnetism and magnetic nanostructures, semiconductors and insulators, surfaces, interfaces and thin films, chemical reactions, and catalysis) are reviewed. © 2008 Wiley Periodicals, Inc. J Comput Chem, 2008

Ab-initio simulations of materials using VASP: Density-functional theory and beyond.

Hybrid Fock exchange/density functional theory functionals have shown to be very successful in describing a wide range of molecular properties. For periodic systems, however, the long-range nature of the Fock exchange interaction and the resultant large computational requirements present a major drawback. This is especially true for metallic systems, which require a dense Brillouin zone sampling. Recently, a new hybrid functional [HSE03, J. Heyd, G. E. Scuseria, and M. Ernzerhof, J. Chem. Phys. 118, 8207 (2003)] that addresses this problem within the context of methods that evaluate the Fock exchange in real space was introduced. We discuss the advantages the HSE03 functional brings to methods that rely on a reciprocal space description of the Fock exchange interaction, e.g., all methods that use plane wave basis sets. Furthermore, we present a detailed comparison of the performance of the HSE03 and PBE0 functionals for a set of archetypical solid state systems by calculating lattice parameters, bulk moduli, heats of formation, and band gaps. The results indicate that the hybrid functionals indeed often improve the description of these properties, but in several cases the results are not yet on par with standard gradient corrected functionals. This concerns in particular metallic systems for which the bandwidth and exchange splitting are seriously overestimated.

Screened hybrid density functionals applied to solids

Electronic structure calculations have become an indispensable tool in many areas of materials science and quantum chemistry. Even though the Kohn-Sham formulation of the density-functional theory (DFT) simplifies the many-body problem significantly, one is still confronted with several numerical challenges. In this article we present the projector augmented-wave (PAW) method as implemented in the GPAW program package (https://wiki.fysik.dtu.dk/gpaw) using a uniform real-space grid representation of the electronic wavefunctions. Compared to more traditional plane wave or localized basis set approaches, real-space grids offer several advantages, most notably good computational scalability and systematic convergence properties. However, as a unique feature GPAW also facilitates a localized atomic-orbital basis set in addition to the grid. The efficient atomic basis set is complementary to the more accurate grid, and the possibility to seamlessly switch between the two representations provides great flexibility. While DFT allows one to study ground state properties, time-dependent density-functional theory (TDDFT) provides access to the excited states. We have implemented the two common formulations of TDDFT, namely the linear-response and the time propagation schemes. Electron transport calculations under finite-bias conditions can be performed with GPAW using non-equilibrium Green functions and the localized basis set. In addition to the basic features of the real-space PAW method, we also describe the implementation of selected exchange-correlation functionals, parallelization schemes, Delta SCF-method, x-ray absorption spectra, and maximally localized Wannier orbitals.

https://iopscience.iop.org/article/10.1088/0953-8984/22/25/253202/pdf

Electronic structure calculations with GPAW: a real-space implementation of the projector augmented-wave method

Electronic structure and properties of YBa2Cu3O7-δ, a low dimensional, low density of states superconductor

Results of a highly precise local density determination of the electronic structure (energy bands, densities of states, Fermi surface and charge densities) of the new high-Tc superconductor Bi2Sr2CaCu2O8 are presented. The calculations employed the full-potential linearized augmented plane wave (FLAPW) method and the subcell structure parameters given by the work of Hazen et al. and Sunshine et al. As in the case of the other Cu-O superconductors, we find a relatively simple band structure at EF and strongly anisotropic highly 2D properties. The Sr and Ca atoms are highly ionic, with the Ca2+ ions serving to insulate the Cu-O planes. The Bi-O planes contribute substantially to N(EF), the density of states at EF, and to the transport properties whereas neither the Sr or Ca do. The N(EF) contribution from the Cu-O planes (∼1.0 states/eV-Cu atom) is lower (per Cu atom) than that found previously for the La-Sr-Cu-O and Y-Ba-Cu-O superconductors. The highly 2D Fermi surface shows regions of strong Cu-O and Bi-O hybridization from which highly anisotropic superconducting energy gaps are predicted. Here, too, an electron-phonon calculation of Tc (using the crude rigid ion approximation) is found to be inadequate. As in the case of YBa2Cu3O7-δ, strongly localized states at EF (arising from Bi-O and Cu-O) may be responsible for charge transfer excitations (excitons) which cause the high Tc.

Electronic structure and properties of Bi2Sr2CaCu2O8, the third high-Tc superconductor

Bonds, bands, charge transfer excitations and superconductivity of YBa2Cu3O7-δ

Results of highly precise local density energy band studies of the new electron doped superconductor, Nd 2− x Ce x CuO 4 , are presented which demonstrate the close similarity to the other hole doped superconductors (the important role of the strongly two-dimensional Cu-O antibonding dpσ band, a somewhat lower density of states at the Fermi energy and a highly 2D Fermi surface). This adds additional evidence to support the Fermi liquid description of the normal metallic state of the high T c superconductors.

Electronic structure of Nd-Ce-Cu-O, a Fermi liquid superconductor

We present a scheme for calculating the (spin-unrestricted) Hartree-Fock (HF) band structure of periodic solids that uses the accurate linearized-augmented-plane-wave basis set. In contrast with linear-combination-of-atomic-orbitals-like schemes, the convergence of the variational HF results can be easily monitored, and the cumbersome evaluation of multicenter integrals is avoided. Potentials and charge densities are evaluated without any shape approximation, and the singularity due to the long-range nature of the Coulomb potential is handled in reciprocal space. All the elements of the Periodic Table can be equally treated, and the relativistic effects for heavy elements are included as in the standard local-density-approximation case. The method is tested on silicon and diamond, where recent HF calculations are available for comparison. The diagonal Coulomb-hole-plus-screened-exchange approximation can also be implemented with little additional computational effort.

S. Massidda

Papers

Electronic structure and properties of YBa2Cu3O7-δ, a low dimensional, low density of states superconductor

Electronic structure and properties of Bi2Sr2CaCu2O8, the third high-Tc superconductor

Bonds, bands, charge transfer excitations and superconductivity of YBa2Cu3O7-δ

Electronic structure of Nd-Ce-Cu-O, a Fermi liquid superconductor

Hartree-Fock LAPW approach to the electronic properties of periodic systems