The Roth's two-pole approximation has been used by the present authors to investigate the role of d − p hybridization in the superconducting properties of an extended d−p Hubbard model. Superconductivity with singlet d x 2 −y 2 -wave pairing is treated by following Beenen and Edwards formalism. In this work, the Coulomb interaction, the temperature and the superconductivity have been considered in the calculation of some relevant correlation functions present in the Roth's band shift. The behavior of the order parameter associated with temperature, hybridization, Coulomb interaction and the Roth's band shift effects on superconductivity are studied. *

In this work the variational Roth's approach previously developed by the present authors to describe cuprate systems is extended to include the superconducting properties. We extend the Beenen and Edwards approach by including the d–p hybridization. The role of the d–p hybridization in modifying the values of superconducting order parameter is then studied in terms of the adopted values of the parameters defining the Hamiltonian of the system.

URu 2 Si 2 exhibits a second-order phase transition at 17.5 K. Initially it was thought that the transition was to a spin density wave phase, however, subsequent measurements do not support this assignment. Despite the unknown nature of the order parameter, many experimental results can be described in terms of the formation of a generic density wave. Here, we report calculations on an unusual phase of the underscreened Anderson lattice model, the so called spin-dependent inter-orbital density wave that has been proposed as describing the "hidden order" phase of URu 2 Si 2 . We determine the effects of an applied magnetic field. Since the order parameter describes an ordering in the x-y plane, the electronic properties of the system are anisotropic below the critical temperature T HO . We show that the magnetic susceptibility becomes anisotropic below T HO . Furthermore, for fields applied along a spontaneously chosen hard axis, T HO decreases towards zero and that the HO transition changes from second order to first order at a large value of the magnetic field. Also, we find that the system undergoes a cascade of field-induced Lifshitz transitions and also show how these properties originate from the dependence of the quasi-particle bands on the orientation of the applied field. The good qualitative agreement with experimental findings provides strong support for the proposed description of the HO phase as a spin-dependent inter-orbital density wave phase.

In this work, a two-dimensional one-band Hubbard model is investigated within a two-pole approximation. The model presents a non-local attractive potential U (U < 0) that allows the study of d-wave superconductivity and also includes hopping up to second-nearest-neighbors. The twopole scheme has been proposed to improve the Hubbard-I approximation. The analytical results show a more complex form for the gap ∆(T ), when compared to the one obtained in the latter approximation. Indeed, new anomalous correlation functions associated with the superconductivity are involved in the calculation of ∆(T ). Numerical results in a range of temperatures are presented.Moreover, the structure of the quasiparticle bands and the topology of the Fermi surface are studied in detail in the normal state. Connections with some experimental results are also included.

The competition among spin glass (SG), antiferromagnetism (AF) and local pairing superconductivity (PAIR) is studied in a two-sublattice fermionic Ising spin glass model with a local BCS pairing interaction in the presence of an applied magnetic transverse field Γ. In the present approach, spins in different sublattices interact with a Gaussian random coupling with an antiferromagnetic mean J0 and standard deviation J. The problem is formulated in the path integral formalism in which spin operators are represented by bilinear combinations of Grassmann variables. The saddle-point Grand Canonical potential is obtained within the static approximation and the replica symmetric ansatz. The results are analysed in phase diagrams in which the AF and the SG phases can occur for small g (g is the strength of the local superconductor coupling written in units of J), while the PAIR phase appears as unique solution for large g. However, there is a complex line transition separating the PAIR phase from the others. It is second order at high temperature that ends in a tricritical point. The quantum fluctuations affect deeply the transition lines and the tricritical point due to the presence of Γ. *