Topological insulators are new states of quantum matter which cannot be adiabatically connected to conventional insulators and semiconductors. They are characterized by a full insulating gap in the bulk and gapless edge or surface states which are protected by time-reversal symmetry. These topological materials have been theoretically predicted and experimentally observed in a variety of systems, including HgTe quantum wells, BiSb alloys, and Bi2Te3 and Bi2Se3 crystals. Theoretical models, materials properties, and experimental results on two-dimensional and three-dimensional topological insulators are reviewed, and both the topological band theory and the topological field theory are discussed. Topological superconductors have a full pairing gap in the bulk and gapless surface states consisting of Majorana fermions. The theory of topological superconductors is reviewed, in close analogy to the theory of topological insulators.

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Topological insulators and superconductors

This article reviews the current status of lattice-dynamical calculations in crystals, using density-functional perturbation theory, with emphasis on the plane-wave pseudopotential method. Several specialized topics are treated, including the implementation for metals, the calculation of the response to macroscopic electric fields and their relevance to long-wavelength vibrations in polar materials, the response to strain deformations, and higher-order responses. The success of this methodology is demonstrated with a number of applications existing in the literature.

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Phonons and related crystal properties from density-functional perturbation theory

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.

Weyl and Dirac semimetals are three-dimensional phases of matter with gapless electronic excitations that are protected by topology and symmetry. As three-dimensional analogs of graphene, they have generated much recent interest. Deep connections exist with particle physics models of relativistic chiral fermions, and, despite their gaplessness, to solid-state topological and Chern insulators. Their characteristic electronic properties lead to protected surface states and novel responses to applied electric and magnetic fields. The theoretical foundations of these phases, their proposed realizations in solid-state systems, and recent experiments on candidate materials as well as their relation to other states of matter are reviewed.

Weyl and Dirac semimetals in three-dimensional solids

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

Many metals, semiconductors, and insulators are well described by the "standard model" of solid state physics. In this picture the excitations are band electrons, and their dispersion can be computed quantitatively in perturbation theory starting from the density functional theory using the GW method [1]. When this standard model fails, we talk about strongly correlated electron systems. The presence of strong correlations is debated with each new material discovery, as for example in the context of the iron pnictide superconductors. On the experimental side, controversies arose because optical experiments revealed signicant mass renormalizations [2{4] while Xray absorption, core level spectroscopies and resonant inelastic Xray scattering indicated the absence of satellite peaks [5, 6], which are standard ngerprints of strong correlations. Photoemission studies indicate that the overall bandwidth is narrowed by a factor of two [7, 8] but substantially larger mass renormalizations are present near the Fermi level [9]. Similar controversies arose within the rst principles approaches to the treatment of correlations with some theoretical studies supporting the notion of weak correlations [10{14], while others advocate a more correlated picture [15{18]. To make progress on this issues one needs to develop fully ab initio tools for addressing the problem of determining the strength of correlations and test their predictions against experiments. In this letter we introduce a new rst principles methodology for evaluating the strength of the correlations based on the self-consistent GW method. This approach has been shown to predict accurate total energy [19, 20], and we expect to obtain reliable estimates for the interaction strength since this quantity can be thought as a second derivative of the total energy with respect to the occupation of the correlated orbitals. We test successfully the method on the well studied example of a correlated material NiO, and then we apply it to a prototypical iron pnictide BaFe2As2. We nd that the correlations in iron pnictides are strong, as pointed out in Refs. [15{18] but unlike earlier studies our ab-initio method accounts for the absence of well dened Hubbard bands in the spectral functions. Our results are thus in excellent agreement with experiment and reconcile the results of apparently conicting spectroscopies. We start with the one-particle electron Green’s function in the solid,G, which is measurable in photoemission experiments. We split it into G 1 = G 0 1 + , where G 0 describes the non-interacting system of electrons, and is the frequency dependent self-energy. Both G and are matrices in r;r 0 . The electrons interact among themselves via the Coulomb interactionVc(r;r 0 ) = 1 jr r0j , however, the mobile electrons screen it and is therefore useful to reformulate the problem in terms of a screened Coulomb interaction W dened

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Self consistent GW determination of the interaction strength: application to the iron arsenide superconductors

Understanding exotic, non-s-wave-like states of Cooper pairs is important and may lead to new superconductors with higher critical temperatures and novel properties. Their existence is known to be possible but has always been thought to be associated with non-traditional mechanisms of superconductivity where electronic correlations play an important role. Here we use a first principles linear response calculation to show that in doped Bi2Se3 an unconventional p-wave-like state can be favoured via a conventional phonon-mediated mechanism, as driven by an unusual, almost singular behaviour of the electron-phonon interaction at long wavelengths. This may provide a new platform for our understanding of superconductivity phenomena in doped band insulators.

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Turning a band insulator into an exotic superconductor

A self-consistent implementation of Hedin's GW perturbation theory is introduced. This finite-temperature method uses Hartree-Fock wave functions obtained with full potential linear augmented plane-wave method to represent Green's function. With our approach we are able to calculate total energy as a function of the lattice parameter. Ground-state properties calculated for Na, Al, and Si compare well with experimental data.

Ground-state properties of simple elements from GW calculations

The discovery of superconductivity in Nd${}_{1\ensuremath{-}x}$Sr${}_{x}$NiO${}_{2}$ has resulted in a flurry of experimental and theoretical work to understand the nature of nickelate superconductivity as compared to that of the cuprates and pnictides. Here, the authors use a combination of LDA+U and linear-response methods to study the magnetic exchange interactions in Nd${}_{1\ensuremath{-}x}$Sr${}_{x}$NiO${}_{2}$. The analysis reveals an underlying Mott insulating state comprised of Ni-3${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$/Ni-3${d}_{{z}^{2}\ensuremath{-}{r}^{2}}$ orbitals with either an $S$=0 or $S$=1 two-hole ground state depending on the precise value of intra-atomic Hund's coupling.

Exchange interactions and sensitivity of the Ni two-hole spin state to Hund's coupling in doped NdNiO 2

Accurate high-energy electron diffraction measurements of structure factors of NiO have been carried out to investigate how strong correlations in the Ni $3d$ shell affect electron charge density in the interior area of nickel ions and whether the ab initio approaches to the electronic structure of strongly correlated metal oxides are in accord with experimental observations. The generalized gradient approximation and the local spin density approximation corrected by the Hubbard U term are found to provide the closest match to experimental measurements. The comparison of calculated and observed electron charge densities shows that correlations in the Ni $3d$ shell suppress covalent bonding between the oxygen and nickel sublattices.

https://arxiv.org/pdf/cond-mat/9906331.pdf

Correlation effects in the ground-state charge density of Mott insulating NiO: A comparison of ab initio calculations and high-energy electron diffraction measurements

Sergey Y. Savrasov

Papers

Self consistent GW determination of the interaction strength: application to the iron arsenide superconductors

Turning a band insulator into an exotic superconductor

Ground-state properties of simple elements from GW calculations

Exchange interactions and sensitivity of the Ni two-hole spin state to Hund's coupling in doped NdNiO 2

Correlation effects in the ground-state charge density of Mott insulating NiO: A comparison of ab initio calculations and high-energy electron diffraction measurements