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Θ Φ : Solid state package allowing Bardeen-Cooper-Schrieffer and magnetic superstructure electronic states
Abstract
We propose the ΘΦ package which addresses two of the most important extensions of the essentially single-particle mean-field paradigm of the computational solid state physics: the admission of the Bardeen–Cooper–Schrieffer electronic ground state and allowance of the magnetically ordered states with an arbitrary superstructure (pitch) wave vector. Both features are implemented in the context of multi-band systems which paves the way to an interplay with the solid state quantum physics packages eventually providing access to the first-principles estimates of the relevant matrix elements of the model Hamiltonians derived from the standard DFT calculations. Several examples showing the workability of the proposed code are given.
... Thus, we recently undertook some developments with a goal to heel the outlined deficiencies in the existing software which resulted in the package ΘΦ. 15,16 In previous works we implemented, respectively, (i) the BCS states and the magnetic phases with an arbitrary superstructure vectors 15 and (ii) the energy optimization with respect to the vector of magnetic superstructure 16 in the ΘΦ package. By the present paper we round up the development of ΘΦ by adding the option of having RVB state (for more detailed explanation of these see below) as a result of the solution of an electronic problem. ...
... Thus, we recently undertook some developments with a goal to heel the outlined deficiencies in the existing software which resulted in the package ΘΦ. 15,16 In previous works we implemented, respectively, (i) the BCS states and the magnetic phases with an arbitrary superstructure vectors 15 and (ii) the energy optimization with respect to the vector of magnetic superstructure 16 in the ΘΦ package. By the present paper we round up the development of ΘΦ by adding the option of having RVB state (for more detailed explanation of these see below) as a result of the solution of an electronic problem. ...
... Their explicit forms are available. 15 Central objects in any mean-field theory are the mean-field version of the Hamiltonianthe Fockian and the density matrix. In that or another form, they are present in all existing software. ...
The available solid-state electronic-structure codes are devoid of hot topics of physics: incommensurate magnetic, superconducting and spin-liquid electronic states/phases. The temperature dependence of the solutions of electronic problem is not accessible either. These gaps are closed by the proposed ΘΦ (ThetaPhi) package.
... On the other hand, recently, our program ΘΦ 10,11 , allows for ISS, superconductivity of arbitrary order and Resonating Valence Bond (RVB) states in multi-orbital electronic systems at finite temperature. In addition, ΘΦ is capable to import the hopping parameters from major ab-initio codes by means of wannier90 12 and lobster 13-15 programs, which makes it possible to perform practically ab-initio strongly correlated magnetic or superconducting calculations. ...
... Secondly, in this paper, we present a general framework for the spin quantization axis rotation in a general case when no assumptions are made on the spin dependence of the Hamiltonian's hopping matrix elements. This general framework extends the one already presented in the Ref. 11 and allows to treat the cases when the hopping is spin-dependent and contains the spin-flip terms, thus permitting simulations of systems with spin-orbit coupling and explicit break of timereversal symmetry. ...
... • The interaction terms like Coulomb repulsion and Heisenberg exchange, which are typically fourth rang tensors, have to be transformed according to the formulas given in Ref. 11, and this task is facilitated by the fact that the most important contributions to them are local i.e. do not extend outside of the unit cell. ...
Simulating the incommensurate spin density waves (ISDW) states is not a simple task within the standard \emph{ab-initio} methods. Moreover, in the context of new material discovery, there is a need for fast and reliable tool capable to scan and optimize the total energy as a function of the pitch vector, thus allowing to automatize the search for new materials. In this paper we show how the ISDW can be efficiently obtained within the recently released $\Theta\Phi$ program. We illustrate this on an example of the single orbital Hubbard model and of $\gamma$-Fe, where the ISDW emerge within the mean-field approximation and by using the twisted boundary conditions. We show the excellent agreement of the $\Theta\Phi$ with the previously published ones and discuss possible extensions. Finally, we generalize the previously given framework for spin quantization axis rotation to the most general case of spin-dependent hopping matrix elements.
... For the case of TM impurities, GoGreenGo calculates the density and GF matrices, perturbed due to the presence of a defect, from the band structure of an ideal, defect-free solid by solving the Dyson equation. Popov et al. [31] The band structure of a perfect crystal can also be pre-calculated using any available software of choice, including most commonly used VASP [58], ABINIT [65] or (ThetaPhi) [66][67][68]. More details on GoGreenGo software can be found in Refs. ...
Effective Hamiltonian of Crystal Field (EHCF) is a hybrid quantum chemical method originally developed for an accurate treatment of highly correlated d-shells in molecular complexes of transition metals. In the present work, we generalise the EHCF method to periodic systems containing transition metal atoms with isolated d-shells, either as a part of their crystal structure or as point defects. A general solution is achieved by expressing the effective resonance interactions of an isolated d-shell with the band structure of the crystal in terms of the Green's functions represented in the basis of local atomic orbitals. Such representation can be obtained for perfect crystals and for periodic systems containing atomic scale defects. Our test results for transition metal oxides (MnO, FeO, CoO, and NiO) and MgO periodic solid containing transition metal impurities demonstrate the ability of the EHCF method to accurately reproduce the spin multiplicity and spatial symmetry of the ground state. For the studied materials, these results are in a good agreement with experimentally observed d-d transitions in optical spectra. The proposed method is discussed in the context of modern solid state quantum chemistry and physics.
We present a software package GoGreenGo—an overlay aimed to model local perturbations of periodic systems due to either chemisorption or point defects. The electronic structure of an ideal crystal is obtained by worldwide‐distributed standard quantum physics/chemistry codes, and then processed by various tools performing projection to atomic orbital basis sets. Starting from this, the perturbation is addressed by GoGreenGo with use of the Green's functions formalism, which allows evaluating its effect on the electronic structure, density matrix, and energy of the system. In the present contribution, the main accent is made on processes of chemical nature, such as chemisorption or doping. We address a general theory and its computational implementation supported by a series of test calculations of the electronic structure perturbations for benchmark model solids: simple, face‐centered, and body‐centered cubium systems. In addition, more realistic problems of local perturbations in graphene lattice, such as lattice substitution, vacancy, and “on‐top” chemisorption, are considered. Point defects in crystals form a wide class of processes being of great importance in solid‐state chemistry. Only by considering surface chemistry one can propose a numerous examples ‐ from formation of isolated surface defects to single particle chemisorption and elementary reactions on catalysts' surfaces. Theoretical investigation of these processes, aiming to understand their mechanisms from the electronic structure perspective, presents one of many important branches of solid‐state chemistry deserving close attention. In this work we present a new software package GoGreenGo specifically designed to perform computationally effective quantum chemical calculations of local processes in solids and to provide results in “chemical” terms.
We present a standalone ΘΦ (ThetaPhi) package capable to read the results of ab initio DFT/PAW quantum‐chemical solid‐state calculations processed through various tools projecting them to the atomic basis states as an input and to perform on top of this an analysis of so derived electronic structure which includes (among other options) the possibility to obtain a superconducting (Bardeen‐Cooper‐Schrieffer, BCS), spin‐liquid (resonating valence bond, RVB) states/phases as solutions of the electronic structure problem along with the magnetically ordered phases with an arbitrary pitch (magnetic superstructure) vector. Remarkably, different solutions of electronic‐structure problems come out as temperature‐dependent (exemplified by various superconducting and spin‐liquid phases) which feature is as well implemented. All that is exemplified by model calculations on 1D chain, 2D square lattice as well as on more realistic superconducting doped graphene, magnetic phases of iron, and spin‐liquid and magnetically ordered states of a simplest nitrogen‐based copper pseudo‐oxide, CuNCN, resembling socalled metal‐oxide framework (MOF) phases by the atomic interlinkage. The available solid‐state electronic‐structure codes are devoid of hot topics of physics: incommensurate magnetic, superconducting, and spin‐liquid electronic states/phases. The temperature dependence of the solutions of electronic problem is not accessible either. These gaps are closed by the proposed ΘΦ package.
Simulating the incommensurate spin density waves (ISDW) states is not a simple task within the standard ab initio methods. Moreover, in the context of new material discovery, there is a need for fast and reliable tool capable to scan and optimize the total energy as a function of the pitch vector, thus allowing to automatize the search for new materials. In this paper we show how the ISDW can be efficiently obtained within the recently released ΘΦ program. We illustrate this on an example of the single orbital Hubbard model and of γ-Fe, where the ISDW emerge within the mean-field approximation and by using the twisted boundary conditions. We show the excellent agreement of the ΘΦ with the previously published ones and discuss possible extensions. Finally, we generalize the previously given framework for spin quantization axis rotation to the most general case of spin-dependent hopping matrix elements.
The understanding of strongly-correlated materials, and in particular unconventional superconductors, has puzzled physicists for decades. Such difficulties have stimulated new research paradigms, such as ultra-cold atom lattices for simulating quantum materials. Here we report on the realization of intrinsic unconventional superconductivity in a 2D superlattice created by stacking two graphene sheets with a small twist angle. For angles near $1.1^\circ$, the first `magic' angle, twisted bilayer graphene (TBG) exhibits ultra-flat bands near charge neutrality, which lead to correlated insulating states at half-filling. Upon electrostatic doping away from these correlated insulating states, we observe tunable zero-resistance states with a critical temperature $T_c$ up to 1.7 K. The temperature-density phase diagram shows similarities with that of the cuprates, including superconducting domes. Moreover, quantum oscillations indicate small Fermi surfaces near the correlated insulating phase, in analogy with under-doped cuprates. The relative high $T_c$, given such small Fermi surface (corresponding to a record-low 2D carrier density of $10^{11} \textrm{cm}^{-2}$ , renders TBG among the strongest coupling superconductors, in a regime close to the BCS-BEC crossover. These novel results establish TBG as the first purely carbon-based 2D superconductor and as a highly tunable platform to investigate strongly-correlated phenomena, which could lead to insights into the physics of high-$T_c$ superconductors and quantum spin liquids.
Van der Waals (vdW) heterostructures are an emergent class of metamaterials comprised of vertically stacked two-dimensional (2D) building blocks, which provide us with a vast tool set to engineer their properties on top of the already rich tunability of 2D materials. One of the knobs, the twist angle between different layers, plays a crucial role in the ultimate electronic properties of a vdW heterostructure and does not have a direct analog in other systems such as MBE-grown semiconductor heterostructures. For small twist angles, the moir\'e pattern produced by the lattice misorientation creates a long-range modulation. So far, the study of the effect of twist angles in vdW heterostructures has been mostly concentrated in graphene/hexagonal boron nitride (h-BN) twisted structures, which exhibit relatively weak interlayer interaction due to the presence of a large bandgap in h-BN. Here we show that when two graphene sheets are twisted by an angle close to the theoretically predicted 'magic angle', the resulting flat band structure near charge neutrality gives rise to a strongly-correlated electronic system. These flat bands exhibit half-filling insulating phases at zero magnetic field, which we show to be a Mott-like insulator arising from electrons localized in the moir\'e superlattice. These unique properties of magic-angle twisted bilayer graphene (TwBLG) open up a new playground for exotic many-body quantum phases in a 2D platform made of pure carbon and without magnetic field. The easy accessibility of the flat bands, the electrical tunability, and the bandwidth tunability though twist angle may pave the way towards more exotic correlated systems, such as unconventional superconductors or quantum spin liquids.
The computer program LOBSTER (Local Orbital Basis Suite Towards Electronic-Structure Reconstruction) enables chemical-bonding analysis based on periodic plane-wave (PAW) density-functional theory (DFT) output and is applicable to a wide range of first-principles simulations in solid-state and materials chemistry. LOBSTER incorporates analytic projection routines described previously in this very journal [J. Comput. Chem. 2013, 34, 2557] and offers improved functionality. It calculates, among others, atom-projected densities of states (pDOS), projected crystal orbital Hamilton population (pCOHP) curves, and the recently introduced bond-weighted distribution function (BWDF). The software is offered free-of-charge for non-commercial research. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.
Research on graphene has revealed remarkable phenomena arising in the honeycomb lattice. However, the quantum spin Hall effect predicted at the K point could not be observed in graphene and other honeycomb structures of light elements due to an insufficiently strong spin-orbit coupling. Here we show theoretically that 2D honeycomb lattices of HgTe can combine the effects of the honeycomb geometry and strong spin-orbit coupling. The conduction bands, experimentally accessible via doping, can be described by a tight-binding lattice model as in graphene, but including multi-orbital degrees of freedom and spin-orbit coupling. This results in very large topological gaps (up to 35 meV) and a flattened band detached from the others. Owing to this flat band and the sizable Coulomb interaction, honeycomb structures of HgTe constitute a promising platform for the observation of a fractional Chern insulator or a fractional quantum spin Hall phase.
Nanoparticle lattices and surfaces
The challenge of resolving the details of the surfaces or assemblies of colloidal semiconductor nanoparticles can be overcome if several characterization methods are used (see the Perspective by Boles and Talapin). Boneschanscher et al. examined honeycomb superlattices of lead selenide nanocrystals formed by the bonding of crystal faces using several methods, including high-resolution electron microscopy and tomography. The structure had octahedral symmetry with the nanocrystals distorted through “necking”: the expansion of the contact points between the nanocrystals. Zherebetskyy et al. used a combination of theoretical calculations and spectroscopic methods to study the surface layer of lead sulfide nanocrystals synthesized in water. In addition to the oleic acid groups that capped the nanocrystals, hydroxyl groups were present as well.
Science , this issue p. 1377 , p. 1380 ; see also p. 1340
A highly unconventional superconducting state with a spin-singlet
$d_{x^2-y^2}\pm id_{xy}$-wave, or chiral $d$-wave, symmetry has recently been
proposed to emerge from electron-electron interactions in doped graphene.
Especially graphene doped to the van Hove singularity at $1/4$ doping, where
the density of states diverges, has been argued to likely be a chiral $d$-wave
superconductor. In this review we summarize the currently mounting theoretical
evidence for the existence of a chiral $d$-wave superconducting state in
graphene, obtained with methods ranging from mean-field studies of effective
Hamiltonians to angle-resolved renormalization group calculations. We further
discuss multiple distinctive properties of the chiral $d$-wave superconducting
state in graphene, as well as its stability in the presence of disorder. We
also review means of enhancing the chiral $d$-wave state using
proximity-induced superconductivity. The appearance of chiral $d$-wave
superconductivity is intimately linked to the hexagonal crystal lattice and we
also offer a brief overview of other materials which have also been proposed to
be chiral $d$-wave superconductors.
We study theoretically two-dimensional single-crystalline sheets of semiconductors that form a honeycomb lattice with a period below 10 nm. These systems could combine the usual semiconductor properties with Dirac bands. Using atomistic tight-binding calculations, we show that both the atomic lattice and the overall geometry influence the band structure, revealing materials with unusual electronic properties. In rocksalt Pb chalcogenides, the expected Dirac-type features are clouded by a complex band structure. However, in the case of zinc-blende Cd-chalcogenide semiconductors, the honeycomb nanogeometry leads to rich band structures, including, in the conduction band, Dirac cones at two distinct energies and nontrivial flat bands and, in the valence band, topological edge states. These edge states are present in several electronic gaps opened in the valence band by the spin-orbit coupling and the quantum confinement in the honeycomb geometry. The lowest Dirac conduction band has S-orbital character and is equivalent to the π−π⋆ band of graphene but with renormalized couplings. The conduction bands higher in energy have no counterpart in graphene; they combine a Dirac cone and flat bands because of their P-orbital character. We show that the width of the Dirac bands varies between tens and hundreds of meV. These systems emerge as remarkable platforms for studying complex electronic phases starting from conventional semiconductors. Recent advancements in colloidal chemistry indicate that these materials can be synthesized from semiconductor nanocrystals
Manganese is an element with outstanding structural and magnetic properties. While most metallic elements adopt a simple crystal structure and order magnetically—if at all—in a simple ferromagnetic or antiferromagnetic configuration, the stable phase of manganese at ambient conditions, paramagnetic α-Mn, adopts a complex crystal structure with 58 atoms in the cubic cell. At a Néel temperature of TN=95K, a transition to a complex noncollinear antiferromagnetic phase takes place. The magnetic phase transition is coupled to a tetragonal distortion of the crystalline structure. In this paper we present an ab initio spin-density functional study of the structural and magnetic properties of α-Mn. It is shown that the strange properties of Mn arise from conflicting tendencies to simultaneously maximize according to Hund’s rule the magnetic spin moment and the bond strength, as expected for a half-filled d band. Short interatomic distances produced by strong bonding tend to quench magnetism. The crystal structure of α-Mn is essentially a consequence of these conflicting tendencies—it may be considered as a topologically close-packed intermetallic compound formed by strongly magnetic (MnI, MnII) and weakly magnetic (MnIII) or even nearly nonmagnetic (MnIV) atoms. The noncollinear magnetic structure is due to the fact that the MnIV atoms arranged on triangular faces of the coordination polyhedra are not entirely nonmagnetic—their frustrated antiferromagnetic coupling leads to the formation of a local spin structure reminiscent of the Néel structure of a frustrated triangular antiferromagnet. Consequently, also the other magnetic moments are rotated out of their collinear orientation. The calculated crystalline and magnetic structures are in good agreement with experiment. However, it is suggested that the magnetism leads to a splitting of the crystallographically inequivalent sites into a larger number of magnetic subgroups than deduced from the magnetic neutron diffraction data, but in accordance with NMR experiments. In a companion paper, the properties of the other polymorphs of Mn and their relative stability will be discussed.
We demonstrate how by taking better account of electron correlations in the 3d shell of metal ions in nickel oxide it is possible to improve the description of both electron energy loss spectra and parameters characterizing the structural stability of the material compared with local spin density functional theory.
We identify graphene as a system where chiral superconductivity can be
realized. Chiral superconductivity involves a pairing gap that winds in phase
around the Fermi surface, breaking time reversal symmetry. We consider a unique
situation arising in graphene at a specific level of doping, where the density
of states is singular, strongly enhancing the critical temperature T_c. At this
doping level, the Fermi surface is nested, allowing superconductivity to emerge
from repulsive electron-electron interactions. We show using a renormalization
group method that superconductivity dominates over all competing orders for any
choice of weak repulsive interactions. Superconductivity develops in a doubly
degenerate, spin singlet channel, and a mean field calculation indicates that
the superconductivity is of a chiral d+id type. We therefore predict that doped
graphene can provide experimental realization of spin-singlet chiral
superconductivity.
Properties of incommensurate spiral spin phases are calculated at the mean-field level for a single-band Hubbard Hamiltonian with variable hole density, by adapting both the Hartree-Fock decoupling and the Kotliar-Ruckenstein slave-boson approach to a regular twist of the spin quantization axes from site to site in a two-dimensional square lattice. The relative stability of the (1,1) and (1,0) spiral phases, the coexistence of the antiferromagnetic and the spiral phases over a finite range of hole density, and the stiffness of the spirals against fluctuations of their direction and pitch are discussed within the model Hamiltonian over a wide range of hole density and interaction strength.
We propose a form for the exchange-correlation potential in local-density band theory, appropriate for Mott insulators. The idea is to use the ``constrained-local-density-approximation'' Hubbard parameter U as the quantity relating the single-particle potentials to the magnetic- (and orbital-) order parameters. Our energy functional is that of the local-density approximation plus the mean-field approximation to the remaining part of the U term. We argue that such a method should make sense, if one accepts the Hubbard model and the success of constrained-local-density-approximation parameter calculations. Using this ab initio scheme, we find that all late-3d-transition-metal monoxides, as well as the parent compounds of the high-Tc compounds, are large-gap magnetic insulators of the charge-transfer type. Further, the method predicts that LiNiO2 is a low-spin ferromagnet and NiS a local-moment p-type metal. The present version of the scheme fails for the early-3d-transition-metal monoxides and for the late 3d transition metals.
In this work we reexamine the LDA+U method of Anisimov and coworkers in the framework of a plane-wave pseudopotential approach. A simplified rotational-invariant formulation is adopted. The calculation of the Hubbard U entering the expression of the functional is discussed and a linear response approach is proposed that is internally consistent with the chosen definition for the occupation matrix of the relevant localized orbitals. In this way we obtain a scheme whose functionality should not depend strongly on the particular implementation of the model in ab-initio calculations. We demonstrate the accuracy of the method, computing structural and electronic properties of a few systems including transition and rare-earth correlated metals, transition metal monoxides and iron-silicate. Comment: 18 pages, 18 figures, 3 tables
We investigate the possibility of inducing superconductivity in a graphite layer by electronic correlation effects. We use a phenomenological microscopic Hamiltonian which includes nearest neighbor hopping and an interaction term which explicitly favors nearest neighbor spin-singlets through the well-known resonance valence bond (RVB) character of planar organic molecules. Treating this Hamiltonian in mean-field theory, allowing for bond-dependent variation of the RVB order parameter, we show that both s- and d-wave superconducting states are possible. The d-wave solution belongs to a two-dimensional representation and breaks time reversal symmetry. At zero doping there exists a quantum critical point at the dimensionless coupling J/t = 1.91 and the s- and d-wave solutions are degenerate for low temperatures. At finite doping the d-wave solution has a significantly higher Tc than the s-wave solution. By using density functional theory we show that the doping induced from sulfur absorption on a graphite layer is enough to cause an electronically driven d-wave superconductivity at graphite-sulfur interfaces. We also discuss applying our results to the case of the intercalated graphites as well as the validity of a mean-field approach. Comment: 10 pages, 3 figures: minor revisions
This article reviews the basic theoretical aspects of graphene, a one atom thick allotrope of carbon, with unusual two-dimensional Dirac-like electronic excitations. The Dirac electrons can be controlled by application of external electric and magnetic fields, or by altering sample geometry and/or topology. We show that the Dirac electrons behave in unusual ways in tunneling, confinement, and integer quantum Hall effect. We discuss the electronic properties of graphene stacks and show that they vary with stacking order and number of layers. Edge (surface) states in graphene are strongly dependent on the edge termination (zigzag or armchair) and affect the physical properties of nanoribbons. We also discuss how different types of disorder modify the Dirac equation leading to unusual spectroscopic and transport properties. The effects of electron-electron and electron-phonon interactions in single layer and multilayer graphene are also presented.
Iron played an important role in the development of the industrial society and has not lost any of its significance since today. This book provides the foundations of understanding the physical nature of iron and its alloys. Basics and recent developments concerning its constitution and magnetism are presented as well as its thermal properties. The exceptional role of iron with its wide spectrum of most different technological and physical properties relies on its versatility, its polymorphism of its crystal structure and its magnetism. Therefore it is the aim of the book to link together the constitution and magnetism of iron.
In little more than 20 years, the number of applications of the density functional (DF) formalism in chemistry and materials science has grown in an astonishing fashion. The number of publications alone shows that DF calculations make up a huge success story, and many younger colleagues are surprised to learn that the widespread application of density functional methods, particularly in chemistry, began only after 1990. This is indeed unexpected, because the origins are usually traced to the papers of Hohenberg, Kohn, and Sham more than a quarter of a century earlier. The DF formalism, its applications, and prospects were reviewed for this journal in 1989. About the same time, the combination of DF calculations with molecular dynamics promised to provide an efficient way to study structures and reactions in molecules and extended systems. This paper reviews the development of density-related methods back to the early years of quantum mechanics and follows the breakthrough in their application after 1990. The two examples from biochemistry and materials science are among the many current applications that were simply far beyond expectations in 1990. The reasons why - 50 years after its modern formulation and after two decades of rapid expansion - some of the most cited practitioners in the field are concerned about its future are discussed.
State-of-the-art electronic-structure calculations based on the
local-density approximation (LDA) to the density functional fail to
reproduce the insulating antiferromagnetic ground state in the parent
compounds of the high-temperature oxide superconductors. Similar
problems have been observed earlier in classical transition-metal oxides
such as FeO, CoO, and NiO. In this work we present the method which
delivers the correct insulating antiferromagnet ground state in the
correlated oxides preserving other properties as well as the efficiency
of the standard LDA. The method embeds the relevant (for a given system
of electrons) part of the Hubbard Hamiltonian into the Kohn-Sham LDA
equation. The resulting Hamiltonian attempts to fix two intrinsic
problems of the LDA: the deficiency in forming localized (atomiclike)
moments and the lack of discontinuity of the effective one-particle
potential when going from occupied to unoccupied states. We present the
detailed study of La2CuO4 and LaCuO3.
In the case of La2CuO4 the energy gap and the
value of the localized magnetic moment in the stable insulating
antiferromagnetic solution are in good agreement with experiment. We
compare our results with standard local spin density approximation
calculation and multiband Hubbard model calculations, as well as with
results of spectroscopy: inverse photoemission, valence photoemission,
and x-ray absorption at the K edge of oxygen. In the case of
LaCuO3 such an extensive comparison is limited due to the
limited data available for this compound. We discuss, however, the
electric and magnetic properties and the insulator-metal-insulator
transitions upon increase of oxygen deficiency.
Key steps in the development of the microscopic understanding of superconductivity are discussed.
An intrinsic issue of the LDA + DMFT approach is the so called double counting of interaction terms. How to choose the double-counting potential in a manner that is both physically sound and consistent is unknown. We have conducted an extensive study of the charge-transfer system NiO in the LDA + DMFT framework using quantum Monte Carlo and exact diagonalization as impurity solvers. By explicitly treating the double-counting correction as an adjustable parameter we systematically investigated the effects of different choices for the double counting on the spectral function. Different methods for fixing the double counting can drive the result from Mott insulating to almost metallic. We propose a reasonable scheme for the determination of double-counting corrections for insulating systems.
Quantum-chemical computations of solids benefit enormously from numerically efficient plane-wave (PW) basis sets, and together with the projector augmented-wave (PAW) method, the latter have risen to one of the predominant standards in computational solid-state sciences. Despite their advantages, plane waves lack local information, which makes the interpretation of local densities-of-states (DOS) difficult and precludes the direct use of atom-resolved chemical bonding indicators such as the crystal orbital overlap population (COOP) and the crystal orbital Hamilton population (COHP) techniques. Recently, a number of methods have been proposed to overcome this fundamental issue, built around the concept of basis-set projection onto a local auxiliary basis. In this work, we propose a novel computational technique toward this goal by transferring the PW/PAW wavefunctions to a properly chosen local basis using analytically derived expressions. In particular, we describe a general approach to project both PW and PAW eigenstates onto given custom orbitals, which we then exemplify at the hand of contracted multiple-ζ Slater-type orbitals. The validity of the method presented here is illustrated by applications to chemical textbook examples-diamond, gallium arsenide, the transition-metal titanium-as well as nanoscale allotropes of carbon: a nanotube and the C60 fullerene. Remarkably, the analytical approach not only recovers the total and projected electronic DOS with a high degree of confidence, but it also yields a realistic chemical-bonding picture in the framework of the projected COHP method. Copyright © 2013 Wiley Periodicals, Inc.
The calculation of the 3d-intra-shell excitations in coordination compounds by means of the Effective Hamiltonian Crystal Field (EHCF) method is generalized to their polynuclear analogs to properly describe several open d-shells and their magnetic interactions. This challenge requires improving the precision of ca. 1000 cm(-1) to ca. 100 cm(-1) characteristic for the spin-reorientation energies. The method follows the successful EHCF paradigm, namely the concerted usage of McWeeny's group-function approximation and Löwdin's partitioning technique, for an effective description of the multi-center d-systems. The novel approach is implemented in the MagAîxTic package and validated against a series of binuclear complexes of Cr(III) featuring µ-oxygen super-exchange paths. The trends in the compound series in terms of exchange constants are correctly reproduced, despite differing details of composition and structure, and the numerical results agree by order of magnitude with available experimental data and other theoretical methods.
Our aim is to present further evidence supporting a recent suggestion by Anderson (1973) that the ground state of the triangular antiferromagnet is different from the conventional three-sublattice Néel state. The anisotropic Heisenberg model is investigated. Near the Ising limit a peculiar, possibly liquid-like state is found to be energetically more favourable than the Néel-state. It seems to be probable that this type of ground state prevails in the anisotropy region between the Ising model and the isotropic Heisenberg model. The implications for the applicability of the resonating valence bond picture to the S = ½ antiferromagnets are also discussed.
It is by now well established that in antiferromagnetic γ-Fe, stabilized in the form of precipitates in a Cu matrix or by epitaxial growth on an appropriate substrate, magnetic and/or crystalline symmetries are broken. Little is known, however, on the physical effects driving the symmetry reduction, and on the interplay of crystalline and magnetic symmetry breaking. We have used a recently developed unconstrained vector-field description of noncollinear magnetism, implemented in an ab initio spin-density-functional code, to search for the magnetic and crystalline structure of γ-Fe, stabilized by different types of constraints. We show that in near face-centered-cubic γ-Fe, stabilized by three-dimensional constraints, the magnetic ground state is a spin-spiral with propagation vector q⃗=2π/a×(0.2,0,1) at an equilibrium atomic volume of Ω=10.63Å3, very close to the propagation vector qexp=2π/a×(0.1,0,1), determined experimentally, but at considerably lower volume than the atomic volume of the γ-Fe precipitates in Cu on which the experiments were performed (Ω=11.44Å3). At these larger volumes our calculations predict an helical spin solution at q⃗=2π/a×(0,0,0.6) to be the ground state. Epitaxially stabilized γ-Fe is found to be unstable against both tetragonal distortion as well as monoclinic shear deformation, and the structural distortions suppress the formation of spin-spiral states, in agreement with experimental observations on Fe/Cu(100) films.
A theory of superconductivity is presented, based on the fact that the interaction between electrons resulting from virtual exchange of phonons is attractive when the energy difference between the electrons states involved is less than the phonon energy, ℏω. It is favorable to form a superconducting phase when this attractive interaction dominates the repulsive screened Coulomb interaction. The normal phase is described by the Bloch individual-particle model. The ground state of a superconductor, formed from a linear combination of normal state configurations in which electrons are virtually excited in pairs of opposite spin and momentum, is lower in energy than the normal state by amount proportional to an average (ℏω)2, consistent with the isotope effect. A mutually orthogonal set of excited states in one-to-one correspondence with those of the normal phase is obtained by specifying occupation of certain Bloch states and by using the rest to form a linear combination of virtual pair configurations. The theory yields a second-order phase transition and a Meissner effect in the form suggested by Pippard. Calculated values of specific heats and penetration depths and their temperature variation are in good agreement with experiment. There is an energy gap for individual-particle excitations which decreases from about 3.5kTc at T=0°K to zero at Tc. Tables of matrix elements of single-particle operators between the excited-state superconducting wave functions, useful for perturbation expansions and calculations of transition probabilities, are given.
The electronic structure of a graphite monolayer with electron count corresponding to the graphite intercalation compound (GIC), described by the extended Hubbard Hamiltonian, is studied in the unrestricted Hartree−Fock approximation. We also interpret the data on observed STM images of graphite intercalation compounds. The well-known (and puzzling) pattern of graphite STM images with only three of the six atoms of each carbon hexagon visible is tentatively explained by the formation of a charge density wave (CDW) state of the surface graphite monolayer, which is an intrinsic feature of its electronic structure, rather than invoking well-known attributions of the observed effect to structural differences between the sites and/or to interactions external to the monolayer. A tentative, purely electronic, explanation for the Moiré patterns is proposed as well.
On the basis of the electronic structure of a graphite monolayer, represented in the unrestricted Hartree-Fock approximation by an extended Hubbard Hamiltonian, we
interpret the data on observed scanning tunneling microscopy (STM) images of b ulk
graphite, graphite monolayers on Pt(111) and graphite intercalation compounds. The
well-known(and puzzling) pattern of graphite STM images, with only three of the six
atoms of each carbon hexagon visible, is tentatively explained by the intrinsic features
of the electronic structure of a graphite monolayer, without invoking well-known explanations attributing the observed effect to structural differences between the sites and
to interlayer interactions. In particular we construct a phase diagram for graphite in the
space defined by the magnitude of on-site and nearest-neighbor electron repulsions.
The conditions for insulating charge and spin density wave solutions are delineated.
A charge density wave state, which we estimate is reasonable for the graphite monolayer,
would give the 3-fold STM image. A spin density wave state, which we think somewhat less
likely, will also give unequal tunneling currents from A and B sites of graphite monolayer,
provided the STM tip carries a local magnetic moment.
Dyson's systematic approach to the reduction of the Heisenberg $S$-Matrix into a sum of "graph" terms can be simplified. A notation is introduced and an algebraic theorem is proved, which allow one to handle the reduction problem quite easily and in the same manner for any type of field.
Simple, yet predictive bonding models are essential achievements of chemistry. In the solid state, in particular, they often appear in the form of visual bonding indicators. Because the latter require the crystal orbitals to be constructed from local basis sets, the application of the most popular density-functional theory codes (namely, those based on plane waves and pseudopotentials) appears as being ill-fitted to retrieve the chemical bonding information. In this paper, we describe a way to re-extract Hamilton-weighted populations from plane-wave electronic-structure calculations to develop a tool analogous to the familiar crystal orbital Hamilton population (COHP) method. We derive the new technique, dubbed "projected COHP" (pCOHP), and demonstrate its viability using examples of covalent, ionic, and metallic crystals (diamond, GaAs, CsCl, and Na). For the first time, this chemical bonding information is directly extracted from the results of plane-wave calculations.
A method is described for the minimization of a function of n variables, which depends on the comparison of function values at the (n + 1) vertices of a general simplex, followed by the replacement of the vertex with the highest value by another point. The
simplex adapts itself to the local landscape, and contracts on to the final minimum. The method is shown to be effective and
computationally compact. A procedure is given for the estimation of the Hessian matrix in the neighbourhood of the minimum,
needed in statistical estimation problems.
By combining the Dirac equation of relativistic quantum mechanics with the Bogoliubov-de Gennes equation of superconductivity we investigate the electron-hole conversion at a normal-metal-superconductor interface in graphene. We find that the Andreev reflection of Dirac fermions has several unusual features: (1) the electron and hole occupy different valleys of the band structure; (2) at normal incidence the electron-hole conversion happens with unit efficiency in spite of the large mismatch in Fermi wavelengths at the two sides of the interface; and, most fundamentally: (3) away from normal incidence the reflection angle may be the same as the angle of incidence (retroreflection) or it may be inverted (specular reflection). Specular Andreev reflection dominates in weakly doped graphene, when the Fermi wavelength in the normal region is large compared to the superconducting coherence length.
The oxide superconductors, particularly those recently discovered that are based on La2CuO4, have a set of peculiarities that suggest a common, unique mechanism: they tend in every case to occur near a metal-insulator
transition into an odd-electron insulator with peculiar magnetic properties. This insulating phase is proposed to be the long-sought
"resonating-valence-bond" state or "quantum spin liquid" hypothesized in 1973. This insulating magnetic phase is favored by
low spin, low dimensionality, and magnetic frustration. The preexisting magnetic singlet pairs of the insulating state become
charged superconducting pairs when the insulator is doped sufficiently strongly. The mechanism for superconductivity is hence
predominantly electronic and magnetic, although weak phonon interactions may favor the state. Many unusual properties are
predicted, especially of the insulating state.
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