R.M. Méndez-Moreno

The self-consistent ground state of the two-dimensional electron gas

The self-consistent Hartree-Fock approximation and the deformable jellium model are used to describe the ground state of the two-dimensional electron gas. Improved precision in the calculations allows us to confirm the existence of a stable corrugated state at finite densities. This is strongly corroborated by an extrapolation of our results to the low-density region. A positive bulk modulus is obtained in this region. A comparison with experimental data for the melting point and our model calculation is made and agreement is found within a factor of 2.

Magnetic character of the two-dimensional electron gas

Abstract The energies of the paramagnetic and ferromagnetic states of the two-dimensional electron gas are evaluated and compared in order to determine the magnetic character of the ground state. The calculations are made with the self-consistent Hartree–Fock approximation and the deformable jellium model. Several transition points between different magnetic phases are obtained. At very high densities of r s ≈2 a first transition is obtained from a paramagnetic fluid to a ferromagnetic one. At r st1 ≈4.8 a symmetry and magnetic transition is obtained from a ferromagnetic fluid to a paramagnetic localized state with a periodic density centered on a hexagonal lattice. A ferromagnetic localized state is predicted at lower densities. The results are compared with those reported for the system with square symmetry.

A Multiband Model for LaO1-xFxFeAs

Based on electronic structure calculations using WIEN2k code for the iron oxypnictide LaO1-xFxFeAs a multi-band model is proposed. Within the BCS framework a generalized Fermi surface with overlapping bands is introduced. s-wave pairing symmetry and different doping values are considered. This model is used to describe some properties of iron-based oxypnictide superconductors as function of the coupling parameter as well as other relevant parameters of the model. In order to get numerical results the experimental data of LaO1-xFxFeAs with several doping concentrations provide the input of this work.

Three-dimensional electron gas with localization along one, two, and three directions

Abstract A powerful non-perturbative technique, which allows a direct evaluation of the ground state properties of an interacting electron gas in three dimensions, has been developed. In a unified approach, the low-, intermediate-, and high-density regions are considered. This technique is applied to three-dimensional (3D) systems with periodic electron density along one and two directions. The electronic and magnetic states of these systems are theoretically studied on the basis of the deformable jellium model, within a self-consistent Hartree–Fock approach. To determine the magnetic character of the 3D electron gas ground state, the paramagnetic and ferromagnetic energies are calculated and compared at low, intermediate, and high densities. As r s increases, several symmetry and/or magnetic transitions occur, in each system. The electronic and magnetic states obtained are compared with other theoretical results reported in the literature with different models. In addition to planar and linear periodic electron densities, cubic electron densities are considered in order to look for symmetry transitions among these systems.

Properties of the two-dimensional electron gas

Abstract Ground state properties of the two-dimensional electron gas are studied in the deformable jellium model. The calculations are made within the self-consistent Hartree–Fock approximation. The phase transition from plane wave solutions to the corrugated state (Wigner like transition) is analysed for two different crystallographic symmetries. A comparison of the results in the cases studied is presented. The behaviour of the energy curve is studied for a wide range of densities. Our calculations of the melting point are within an order of magnitude of experimental data.

PAIRING THEORY AND DIRAC SUPERSYMMETRY

Abstract A pairing theory is obtained within a Dirac supersymmetric framework. Admixtures of triplet and singlet pairing systems are shown to posses Dirac supersymmetry for a two component (heavy) fermion. Application of this framework to layered materials as the cuprate superconductors could lead to a better understanding of the high T c . Realizations of components are discussed.

Quasi-normal occupancy for high-Tc superconductor cuprates

Abstract A model with quasi-normal occupancy is applied to several typical high-Tc superconductors obtaining tighter-bound Cooper fermion pairs. Within this model a small energy gap of the order of the Debye energy near the Fermi surface is proposed. An important physical requirement of the model is that the anomaly in the occupancy occurs simultaneously to the pair formation. The role of the variation of the ratio R = 2Δ 0 κT c in the range 2 – 10 is studied. The phonon barrier can be overcomed and then obtain a good description of high-Tc superconductor cuprates in all the range of values for R suggested by experimental results.

Crystalline Structures in the Deformable Jellium

The electron gas in the deformable jellium is studied with different crystallographic symmetries. The single particle state function can be written in terms of expansions which give charge density centered around different specific three-dimensional lattices as the cubic lattices or the tetragonal ones. Symmetries in less than three dimensions have also been proposed, one can propose an expansion with charge density centered around a square lattice and homogenous density in the orthogonal direction, or expansions with periodic charge density in only one direction and homogenous density in the orthogonal plane. A brief review of the ground state properties with some of these symmetries is presented in this work. A comparison of the results in the cases studied is presented.

Relativistic Equations in External Fields

A general method to find exact non-relativistic equivalent problems for a large class of potential-interactions in Dirac-like Hamiltonians is presented. The included interactions are the supersymmetric ones and “large” projected non-supersymmetric interactions. The identification of the corresponding Lorentz structure for the Dirac equation in 3 + 1, 4 + 1 and 2 + 1 space-time dimensions is performed. A general outline of previous relevant works is presented.