Group theory of Wannier functions providing the basis for a deeper understanding of magnetism and superconductivity

The paper presents the group theory of best localized and symmetry-adapted Wannier functions in a crystal of any given space group G or magnetic group M. Provided that the calculated band structure of the considered material is given and that the symmetry of the Bloch functions at all the points of symmetry in the Brillouin zone is known, the paper details whether or not the Bloch functions of particular energy bands can be unitarily transformed into best localized Wannier functions symmetry-adapted to the space group G, to the magnetic group M, or to a subgroup of G or M. In this context, the paper considers usual as well as spin-dependent Wannier functions, the latter representing the most general definition of Wannier functions. The presented group theory is a review of the theory published by one of the authors in several former papers and is independent of any physical model of magnetism or superconductivity. However, it is suggested to interpret the special symmetry of the best localized Wannier functions in the framework of a nonadiabatic extension of the Heisenberg model, the nonadiabatic Heisenberg model. On the basis of the symmetry of the Wannier functions, this model of strongly correlated localized electrons makes clear predictions whether or not the system can possess superconducting or magnetic eigenstates

K-space magnetism as the origin of superconductivity

The nonadiabatic Heisenberg model presents a nonadiabatic mechanism generating Cooper pairs in narrow, roughly half-filled "superconducting bands" of special symmetry. Here we show that this mechanism may be understood as the outcome of a special spin structure in the reciprocal space, hereinafter referred to as k-space magnetism. The presented picture permits a vivid depiction of this new mechanism highlighting the height similarity as well as the essential difference between the new nonadiabatic and the familiar Bardeen-Cooper-Schrieffer mechanism

Constraining forces causing the Meissner effect

As shown in former papers, the nonadiabatic Heisenberg model presents a novel mechanism of Cooper pair formation which is not the result of an attractive electron-electron interaction but can be described in terms of quantum mechanical constraining forces. This mechanism operates in narrow, roughly half-filled superconducting bands of special symmetry and is evidently responsible for the formation of Cooper pairs in all superconductors. Here we consider this new mechanism within an outer magnetic field. We show that in the magnetic field the constraining forces produce Cooper pairs of non-vanishing total momentum with the consequence that an electric current flows within the superconductor. This current satisfies the London equations and, consequently, leads to the Meissner effect. This theoretical result is confirmed by the experimental observation that all superconductors, whether conventional or unconventional, exhibit the Meissner effect

Nonadiabatic Atomic-like State Stabilizing Antiferromagnetism and Mott Insulation in MnO

In this paper I report evidence that the antiferromagnetic and insulating ground state of MnO is caused by a nonadiabatic atomic-like motion as it is evidently the case in NiO. In addition, I show that the experimental findings of Goodwin et al. [Phys. Rev. Lett. (2006), 96,~047209] corroborate my suggestion that the rhombohedral-like distortion in antiferromagnetic MnO as well as in antiferromagnetic NiO is an inner distortion of the monoclinic base-centered Bravais lattice of the antiferromagnetic phases.Comment: arXiv admin note: text overlap with arXiv:1911.0819

Variational Principle of Bogoliubov and Generalized Mean Fields in Many-Particle Interacting Systems

The approach to the theory of many-particle interacting systems from a unified standpoint, based on the variational principle for free energy is reviewed. A systematic discussion is given of the approximate free energies of complex statistical systems. The analysis is centered around the variational principle of N. N. Bogoliubov for free energy in the context of its applications to various problems of statistical mechanics and condensed matter physics. The review presents a terse discussion of selected works carried out over the past few decades on the theory of many-particle interacting systems in terms of the variational inequalities. It is the purpose of this paper to discuss some of the general principles which form the mathematical background to this approach, and to establish a connection of the variational technique with other methods, such as the method of the mean (or self-consistent) field in the many-body problem, in which the effect of all the other particles on any given particle is approximated by a single averaged effect, thus reducing a many-body problem to a single-body problem. The method is illustrated by applying it to various systems of many-particle interacting systems, such as Ising and Heisenberg models, superconducting and superfluid systems, strongly correlated systems, etc. It seems likely that these technical advances in the many-body problem will be useful in suggesting new methods for treating and understanding many-particle interacting systems. This work proposes a new, general and pedagogical presentation, intended both for those who are interested in basic aspects, and for those who are interested in concrete applications.Comment: 60 pages, Refs.25

Spectral properties of transition metal pnictides and chalcogenides: angle-resolved photoemission spectroscopy and dynamical mean field theory

Electronic Coulomb correlations lead to characteristic signatures in the spectroscopy of transition metal pnictides and chalcogenides: quasi-particle renormalizations, lifetime effects or incoherent badly metallic behavior above relatively low coherence temperatures are measures of many-body effects due to local Hubbard and Hund's couplings. We review and compare the results of angle-resolved photoemission spectroscopy experiments (ARPES) and of combined density functional dynamical mean field theory (DFT+DMFT) calculations. We emphasize the doping-dependence of the quasi-particle mass renormalization and coherence properties