For pt.II see ibid., vol.7, p.1009 (1978). The s and d contributions to the pressure and bulk modulus across the series and as a function of volume are presented using Pettifor's partial pressure expression and the results of part I of this series on the behaviour of the energy bands. It is shown that whereas Friedel's d bond contribution is primarily responsible for the cohesive energy, the s electrons are crucial for providing the repulsive pressure to counter the attractive d contribution at the equilibrium atomic volume. Moreover, because of ion core orthogonality constraints, the s electrons determine the bulk modulus away from the noble metal end of the series. The hybridisation contribution is included by assuming it to be proportional to the d resonant width. The cohesive energy is predicted to better than about 10%, the equilibrium atomic volume to 25%, and the bulk modulus (excluding Pd and Ag) to better than 20% across the 4d series. The importance of the neglected second-order contributions such as three-centre integrals is demonstrated.

https://iopscience.iop.org/article/10.1088/0305-4608/8/2/008/pdf

Theory of energy bands and related properties of 4d transition metals. III. s and d contributions to the equation of state

The use of self-consistent band calculations to understand the electronic structure of solids is reviewed. The formal basis for the approach is first examined to emphasise that not all band calculations are applications of the same theory. Similarly the critical points, both fundamental and mundane, of the self-consistency process are examined. Again, the central theme is the idea that perhaps some aspects of the self-consistent calculation are not completely established. On the other hand, band structure technique, while still developing, has been rather well explored. Thus one can examine it from the general point of view of seeing what the various techniques imply about the nature of the band structure problem. Finally, some applications of self-consistent band structure calculations are examined.

http://iopscience.iop.org/article/10.1088/0034-4885/44/2/002/pdf

Self-consistent energy band calculations

Two-dimensional materials research has recently advanced to free-standing, atomically thin metallic nanostructures. To facilitate further progress, the authors construct a periodic table for the properties of 2D elemental metals using density functional theory. The theoretical values for cohesive energies, bond lengths, and elastic moduli of 45 metals correlate linearly with the corresponding properties of the familiar bulk metals. The presentation of these correlations and their causes provides for profound insights into material research that would help design new 2D nanosize heterostructures with optical, catalytic, and nanoelectronic applications.

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Atlas for the properties of elemental two-dimensional metals

Structural and electronic properties of linear chain compounds and their molecular analogies

The development of methods of quantum statistical mechanics is considered in light of their applications to quantum solid-state theory. We discuss fundamental problems of the physics of magnetic materials and the methods of the quantum theory of magnetism, including the method of two-time temperature Green’s functions, which is widely used in various physical problems of many-particle systems with interaction. Quantum cooperative effects and quasi-particle dynamics in the basic microscopic models of quantum theory of magnetism: the Heisenberg model, the Hubbard model, the Anderson Model, and the spinfermion model are considered in the framework of novel self-consistent-field approximation. We present a comparative analysis of these models; in particular, we compare their applicability for description of complex magnetic materials. The concepts of broken symmetry, quantum protectorate, and quasi-averages are analyzed in the context of quantum theory of magnetism and theory of superconductivity. The notion of broken symmetry is presented within the nonequilibrium statistical operator approach developed by D.N. Zubarev. In the framework of the latter approach we discuss the derivation of kinetic equations for a system in a thermal bath. Finally, the results of investigation of the dynamic behavior of a particle in an environment, taking into account dissipative effects, are presented.

/pdf/statistical-mechanics-and-the-physics-of-many-particle-model-3v7g2lkk9p.pdf

Statistical Mechanics and the Physics of Many-Particle Model Systems

The Hamiltonian for a completely degenerate d-band including intra-atomic Coulomb and exchange interactions is derived and studied using the alloy analogy method. Green's function, the magnetic susceptibility and a criterion for the appearance of ferromagnetism are obtained by this method. The dependence of the magnetization on the exchange constant and on the number of electrons per atom is calculated for strong Coulomb correlation and for the uncorrelated case. It is shown that Coulomb correlation of any strength leads to a decrease of the exchange interaction constant needed to produce ferromagnetism and additionally to a change in the shapes of the magnetic dependences for (and only for) weakly ferromagnetic metals.



[Russian Text Ignored.]

CPA Treatment of the Hubbard Model with Intra-Atomic Exchange Interaction

The energy of cohesion in transition metals is calculated on the basis of Hubbard Hamiltonian with exchange interaction. The Coulomb correlation term is treated in the statistical (0,1) approximation. The calculations are performed in the limits of weak and strong Coulomb correlations in both paramagnetic and ferromagnetic states using the CPA technique. It is shown that the decrease in energy of cohesion near half-filled 3d bands in the first transition series is due to the strong Coulomb correlations resulting in 3d band splitting. Such a decrease is not observed in other transition metal series, where these correlations seem to be smaller in comparison to the bandwidth.

https://iopscience.iop.org/article/10.1088/0305-4608/7/7/013/pdf

Energy of cohesion in transition metals

This book is devoted to the mathematical description of interesting phenomena which occur in solids, such as ferromagnetism, antiferromagnetism and superconductivity. Superconductivity and its interaction with ferro and antiferromagnetism is of special importance since over the last 15 years the temperature of superconductivity existence has been raised from 15-20 K to 100 K, which will allow in the near future numerous practical applications of this phenomenon. Although the book is written in a rather rigorous mathematical language it is made easy to read by detailed derivation for those having only an undergraduate background in physics. Key Features: - new field of research - common formalism for superconductivity and magnetism - easy and simple models - easy reading which includes all derivations - good for graduate students and young researchers * A new field of research * Common formalism for superconductivity and magnetism * Easy reading and simple models, which includes all derivations

Models of Itinerant Ordering in Crystals: An Introduction

The Hamiltonian for a completely degenerate d-band including intra-atomic Coulomb and exchange interactions is studied using the two-sublattice alloy analogy method. The density of states and the criterion for the appearance of antiferromagnetism are calculated by this method. At the transition from paramagnetism to antiferromagnetism the energy gap appears. The interaction constant required to produce antiferromagnetism tends to zero at the maxima of the state density function.



[Russian Text Ignored].

CPA treatment of the extended Hubbard model

We study non-equilibrium electron transport through a quantum dot coupled to metallic leads. We use an alternative equation of motion approach in which we calculate the retarded Green function of the impurity by differentiating Green functions over both time variables. Such an approach allows us to obtain the resonance Kondo state in the particle-hole symmetric case and in the asymmetric cases. We apply this technique for calculating the density of the states of quantum dot and the differential conductance as a function of bias voltage. The differential conductance dependence on temperature and on Coulomb interaction is also calculated.

J. Mizia

Papers

CPA Treatment of the Hubbard Model with Intra-Atomic Exchange Interaction

Energy of cohesion in transition metals

Models of Itinerant Ordering in Crystals: An Introduction

CPA treatment of the extended Hubbard model

Alternative equation of motion approach applied to transport through a Quantum Dot