Quantum ESPRESSO is an integrated suite of open-source computer codes for quantum simulations of materials using state-of-the-art electronic-structure techniques, based on density-functional theory, density-functional perturbation theory, and many-body perturbation theory, within the plane-wave pseudopotential and projector-augmented-wave approaches Quantum ESPRESSO owes its popularity to the wide variety of properties and processes it allows to simulate, to its performance on an increasingly broad array of hardware architectures, and to a community of researchers that rely on its capabilities as a core open-source development platform to implement their ideas In this paper we describe recent extensions and improvements, covering new methodologies and property calculators, improved parallelization, code modularization, and extended interoperability both within the distribution and with external software

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Advanced capabilities for materials modelling with Quantum ESPRESSO.

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

This article reviews the physics of high-temperature superconductors from the point of view of the doping of a Mott insulator. The basic electronic structure of cuprates is reviewed, emphasizing the physics of strong correlation and establishing the model of a doped Mott insulator as a starting point. A variety of experiments are discussed, focusing on the region of the phase diagram close to the Mott insulator (the underdoped region) where the behavior is most anomalous. The normal state in this region exhibits pseudogap phenomenon. In contrast, the quasiparticles in the superconducting state are well defined and behave according to theory. This review introduces Anderson's idea of the resonating valence bond and argues that it gives a qualitative account of the data. The importance of phase fluctuations is discussed, leading to a theory of the transition temperature, which is driven by phase fluctuations and the thermal excitation of quasiparticles. However, an argument is made that phase fluctuations can only explain pseudogap phenomenology over a limited temperature range, and some additional physics is needed to explain the onset of singlet formation at very high temperatures. A description of the numerical method of the projected wave function is presented, which turns out to be a very useful technique for implementing the strong correlation constraint and leads to a number of predictions which are in agreement with experiments. The remainder of the paper deals with an analytic treatment of the $t\text{\ensuremath{-}}J$ model, with the goal of putting the resonating valence bond idea on a more formal footing. The slave boson is introduced to enforce the constraint againt double occupation and it is shown that the implementation of this local constraint leads naturally to gauge theories. This review follows the historical order by first examining the U(1) formulation of the gauge theory. Some inadequacies of this formulation for underdoping are discussed, leading to the SU(2) formulation. Here follows a rather thorough discussion of the role of gauge theory in describing the spin-liquid phase of the undoped Mott insulator. The difference between the high-energy gauge group in the formulation of the problem versus the low-energy gauge group, which is an emergent phenomenon, is emphasized. Several possible routes to deconfinement based on different emergent gauge groups are discussed, which leads to the physics of fractionalization and spin-charge separation. Next the extension of the SU(2) formulation to nonzero doping is described with a focus on a part of the mean-field phase diagram called the staggered flux liquid phase. It will be shown that inclusion of the gauge fluctuation provides a reasonable description of the pseudogap phase. It is emphasized that $d$-wave superconductivity can be considered as evolving from a stable U(1) spin liquid. These ideas are applied to the high-${T}_{c}$ cuprates, and their implications for the vortex structure and the phase diagram are discussed. A possible test of the topological structure of the pseudogap phase is described.

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Doping a Mott insulator: Physics of high-temperature superconductivity

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

We have performed a comprehensive first-principles investigation of native point defects in ZnO based on density functional theory within the local density approximation (LDA) as well as the $\mathrm{LDA}+U$ approach for overcoming the band-gap problem. Oxygen deficiency, manifested in the form of oxygen vacancies and zinc interstitials, has long been invoked as the source of the commonly observed unintentional $n$-type conductivity in ZnO. However, contrary to the conventional wisdom, we find that native point defects are very unlikely to be the cause of unintentional $n$-type conductivity. Oxygen vacancies, which have most often been cited as the cause of unintentional doping, are deep rather than shallow donors and have high formation energies in $n$-type ZnO (and are therefore unlikely to form). Zinc interstitials are shallow donors, but they also have high formation energies in $n$-type ZnO and are fast diffusers with migration barriers as low as $0.57\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$; they are therefore unlikely to be stable. Zinc antisites are also shallow donors but their high formation energies (even in Zn-rich conditions) render them unlikely to be stable under equilibrium conditions. We have, however, identified a different low-energy atomic configuration for zinc antisites that may play a role under nonequilibrium conditions such as irradiation. Zinc vacancies are deep acceptors and probably related to the frequently observed green luminescence; they act as compensating centers in $n$-type ZnO. Oxygen interstitials have high formation energies; they can occur as electrically neutral split interstitials in semi-insulating and $p$-type materials or as deep acceptors at octahedral interstitial sites in $n$-type ZnO. Oxygen antisites have very high formation energies and are unlikely to exist in measurable concentrations under equilibrium conditions. Based on our results for migration energy barriers, we calculate activation energies for self-diffusion and estimate defect-annealing temperatures. Our results provide a guide to more refined experimental studies of point defects in ZnO and their influence on the control of $p$-type doping.

Native point defects in ZnO

Evidence is presented that within the density-functional theory orbital polarization has to be treated on an equal footing with spin polarization and charge density for strongly interacting electron systems. Using a basis-set independent generalization of the LDA+U functional, we show that electronic orbital ordering is a necessary condition to obtain the correct crystal structure and parameters of the exchange interaction for the Mott-Hubbard insulator ${\mathrm{KCuF}}_{3}$.

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Density-functional theory and strong interactions: Orbital ordering in Mott-Hubbard insulators

We describe the LDA bandstructure of YBa_2Cu_3O_7 in the 2 eV range from the Fermi energy using orbital projections and compare with YBa_2Cu_4O_8. Then, the high-energy and chain-related degrees of freedom are integrated out and we arrive at two, nearest-neighbor, orthogonal, two-center, 8-band Hamiltonians, the even and odd bands of the bi-layer. Of the 8 orbitals, Cu{x2-y2}, O2x, O3y, and Cus have \sigma character and Cu{xz}, Cu{yz} O2z, and O3z have \pi character. The roles of the Cu_s orbital, which has some Cu{3z2-1} character, and the four \pi orbitals are as follows: Cu_s provides 2nd- and 3rd-nearest-neighbor (t' and t') intra-plane hopping, as well as hopping between planes (t_{perp}). The \pi -orbitals are responsible for bifurcation of the saddle-points for dimpled planes. The 4-\sigma-band Hamiltonian is generic for flat CuO_2 planes and we use it for analytical studies. The reduction of the \sigma-Hamiltonian to 3- and 1-band Hamiltonians is explicitly discussed and we point out that, in addition to the hoppings commonly included in many-body calculations, the 3-band Hamiltonian should include hopping between all 2nd-nearest-neighbor oxygens and that the 1-band Hamiltonian should include 3rd-nearest-neighbor hoppings. We calculate the single-particle hopping between the planes of a bi-layer. We show that the inclusion of t' is crucial for understanding ARPES for the anti-ferromagnetic insulator Sr_2CuO_2Cl_2. Finally, we estimate the value of the inter-plane exchange constant for an un-doped bi-layer in mean-field theory using different single-particle Hamiltonians.

LDA energy bands, low-energy Hamiltonians, t', t'', t_{perp}(k), and J_{perp}

LDA energy bands, low-energy hamiltonians, t′, t″, t⊥ (k), and J⊥

We discuss the geometries of crystalline fcc ${\mathrm{C}}_{60}$ for three cases of directional order, the hypothetical undirectional structure with space group Fm3\ifmmode\bar\else\textasciimacron\fi{}, the bidirectional structure (P${4}_{2}$/mnm) which is the ordered version of the structure observed for alkali-metal-doped compounds at room temperature, and the quadridirectional, low-temperature structure (Pa3\ifmmode\bar\else\textasciimacron\fi{}) of pure ${\mathrm{C}}_{60}$. Analytical, parameter-free expressions for the ${\mathit{t}}_{1\mathit{u}}$ wave functions are derived and used to obtain analytical conduction-band Hamiltonians for all three structures. The interactions with other subbands are included in numerical tight-binding calculations with a basis of 60 radial carbon orbitals per molecule. Ab initio density-functional [local-density approximation (LDA)] calculations are performed for unidirectional fcc ${\mathrm{C}}_{60}$ and ${\mathrm{RbC}}_{60}$ for different lattice constants. We use the linear-muffin-tin-orbitals (LMTO) method in the atomic-spheres approximation with carefully chosen interstitial spheres. The LDA bands are compared with photoemission and inverse photoemission data for ${\mathrm{C}}_{60}$. For ${\mathrm{RbC}}_{60}$ we find that the alkali-metal atom is fully ionized and that the doped electron occupies the ${\mathit{t}}_{1\mathit{u}}$ band in a rigid-band-like fashion. Tight-binding theory explains why, and indicates that this holds generally for ${\mathit{A}}_{\mathit{n}\mathrm{\ensuremath{-}}\mathit{x}}$${\mathit{B}}_{\mathit{x}}$${\mathrm{C}}_{60}$ with n\ensuremath{\le}3.The LDA calculation shows that, for a given structure, the conduction band scales uniformly in energy when, because of doping, the lattice constant a is changed. The energy scale behaves like W\ensuremath{\propto}d(a)exp[-d(a)/0.58 \AA{}] where d is the shortest distance between atoms belonging to different molecules. Both the LDA-LMTO and the tight-binding conduction bands are well fitted by the ${\mathit{t}}_{1\mathit{u}}$ Hamiltonians. For a=14.1 \AA{} the density of states for a conduction-band occupation of three electrons is 15, 17, and 21 electrons/mol eV) for the unidirectional, bidirectional, and quadridirectional structures, respectively. The calculated Stoner exchange parameter is less than half the inverse density of states per spin and atom, but the Coulomb self-energy for a molecular orbital is presumably larger than the ${\mathit{t}}_{1\mathit{u}}$ bandwidths, which are 0.52 eV (uni), 0.64 eV (bi), and 0.44 eV (quadri) for a=14.1 \AA{}. The LDA value (0.58 \AA{}) for the decay of the intermolecular hopping was used together with experimental data for ${\mathit{T}}_{\mathit{c}}$ vs a for ${\mathrm{K}}_{3\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Rb}}_{\mathit{x}}$${\mathrm{C}}_{60}$ compounds in the McMillan formula. The assumptions that the Coulomb interaction ${\mathrm{\ensuremath{\mu}}}^{\mathrm{*}}$, the electron-phonon interaction ${\mathit{V}}_{\mathit{e}\mathrm{\ensuremath{-}}\mathrm{ph}}$, and the average phonon frequency \ensuremath{\omega} are all independent of a were found to be inconsistent.

Conduction-band structure of alkali-metal-doped C60.

We argue that extended saddle points observed at the Fermi level for optimally doped superconductors are essentially the bifurcated saddle points predicted by density-functional [local density approximation (LDA)] calculations. Such saddle points are caused by the dimple of the CuO[sub 2] planes and are enhanced by plane-plane hopping. Dimpling may provide a mechanism for pinning the Fermi level to the saddle points. Simple tight-binding Hamiltonians and an analytical expressions for the constant-energy contours are derived from the LDA bands of YBa[sub 2]Cu[sub 3]O[sub 7.] In addition to the O[sub 2] [ital x] O3 [ital y], and Cu [ital x][sup 2]-[ital y][sup 2] orbitals, we find that O2 [ital z] and O3 [ital z] are crucial and Cu [ital s], are crucial. The O [ital z] orbitals allow the [ital pd][sigma] antibond to tilt with the dimple.

A. I. Liechtenstein

Papers

Density-functional theory and strong interactions: Orbital ordering in Mott-Hubbard insulators

LDA energy bands, low-energy Hamiltonians, t', t'', t_{perp}(k), and J_{perp}

LDA energy bands, low-energy hamiltonians, t′, t″, t⊥ (k), and J⊥

Conduction-band structure of alkali-metal-doped C60.

Plane dimpling and saddle-point bifurcation in the band structures of optimally doped high-temperature superconductors: A tight-binding model.