Phase diagram and dependence of the critical temperature T_c on the pressure for Tl_{0.5}Pb_{0.5}Sr_2Ca_{1-x}Y_xCu_2)_7

Using a mean-field BCS-like approach on the bidimensional extended Hubbard Hamiltonian we calculate the superconducting transition temperature Tc as a function of the hole content nh, for the d-wave and extended-s wave gap symmetries. To describe the pressure effect on Tc we assume it induces a change in the magnitude V of the attractive superconductor potential. This assumption yields an explanation for the intrinsic term, and together with the well known change in nh, we set the critical temperature as Tc=Tc(nh(P),V(P)). With this we obtain a general expansion of Tc in terms of the pressure P and the hole content nh. We apply this expansion to the Tl_{0.5}Pb_{0.5}Sr_2Ca_{1-x}Y_xCu_2)_7 system

Phase Separation and the Dual Nature of the Electronic Structure in Cuprates

The dual nature of the electronic structure of stripes in $La_{2-x}Sr_xCuO_4$ was characterized by experimental observations, mainly by ARPES, of nodal spectral weight together with the straight segments near antinodal regions. We present here an attempt to understand this dual behavior in terms of the competition of order and disorder, by applying the phase separation theory of Cahn-Hilliard (CH) to the high pseudogap temperature, which is very large in the far underdoping region and vanishs near the doping level p=0.2. The spinodal phase separation predictions together with the Bogoliubov-deGennes (BdG) superconducting theory provides several interesting insights. For instance, we find that the disorder enhances the local superconducting gap which scales with the leading edge shift and that, upon doping, the size of the hole-rich stripes increases, yielding to the system their metallic properties.Comment: revised version, 4 pages and 3 fig

Theoretical high-TcT_c d-wave superconducting gap in an inhomogeneous medium

We perform theoretical calculations to obtain a distribution of local d-wave superconducting gaps $\Delta_0({r})$ for a high temperature superconducting (HTSC) series in a disordered superconductor with an average doping level $$. To reproduce the inhomogeneous medium a nonmagnetic random potential $V^{imp}$, within a Bogoliubov-de Gennes (BdG) formalism, is considered. First the phase diagram $\Delta_0 x$ for the LSCO HTSC series, with V^{imp}=0, is obtained. Then, we perform calculations considering a fixed value of the disorder strength $V^{imp}$ and obtain a distribution of local superconducting gaps $\Delta_0({r})$, and local density of charge carriers $\rho({r})$. It is shown that the underdoped compounds are more inhomogeneous than the overdoped ones, which is in accordance with experimental findings. Also, the spatial variation of $\Delta_0({r})$ indicates that as increases, the system becomes more homogeneous.Comment: 6 pages and 6 fig

Heavy fermion d-wave superconductivity: a X-boson approach

From an extension of the periodic Anderson model (PAM) in the $U=\infty$ limit taking into account the effect of a nearest neighbor attractive interaction between $f$-electrons, we compare the obtained superconducting phase diagram of a two dimensional d-wave superconductor with the results obtained for an isotropic s-wave superconductor employing the X-boson method.Comment: Submitted to the Proceeding of the ICM 2003-Rome. Requires elsart3.cl

Crossover behavior for complex order parameter in high-Tc superconductors

A number of recent experiments have suggested the presence of either real or complex components in the gap symmetry of high-$T_c$ superconductors (HTSC). In this paper we introduce a novel approach to study the competition of such complex order parameter mixtures by varying the position of the two-body attractive potential in a two dimensional extended Hubbard Hamiltonian. We show that this procedure explain a number of experimental results and on the theoretical side, it may be related with certain HTSC microscopic models like the spin fluctuation theory. Following current trends we concentrate on the study of $d_{x^2-y^2}$ order parameter with a component of the type $d_{xy}$ or a s-wave like $s_{x^2+y^2}$ and $s_{xy}$ symmetry. We show that the position of the optimal s-component peak changes with the position parameter $b$ while the d-component occurs always in the optimally region around hole content $\rho \approx 0.39$.Comment: 6 pages in RevTex, 5 figs. in epsi, accepted in the Physica

A Theory for High-TcT_c Superconductors Considering Inhomogeneous Charge Distribution

We propose a general theory for the critical $T_c$ and pseudogap $T^*$ temperature dependence on the doping concentration for high-$T_c$ oxides, taking into account the charge inhomogeneities in the $CuO_2$ planes. The well measured experimental inhomogeneous charge density in a given compound is assumed to produce a spatial distribution of local $\rho(r)$. These differences in the local charge concentration is assumed to yield insulator and metallic regions, possibly in a stripe morphology. In the metallic region, the inhomogeneous charge density yields also spatial distributions of superconducting critical temperatures $T_c(r)$ and zero temperature gap $\Delta_0(r)$. For a given sample, the measured onset of vanishing gap temperature is identified as the pseudogap temperature, that is, $T^*$, which is the maximum of all $T_c(r)$. Below $T^*$, due to the distribution of $T_c(r)$'s, there are some superconducting regions surrounded by insulator or metallic medium. The transition to a superconducting state corresponds to the percolation threshold among the superconducting regions with different $T_c(r)$'s. To model the charge inhomogeneities we use a double branched Poisson-Gaussian distribution. To make definite calculations and compare with the experimental results, we derive phase diagrams for the BSCO, LSCO and YBCO families, with a mean field theory for superconductivity using an extended Hubbard Hamiltonian. We show also that this novel approach provides new insights on several experimental features of high-$T_c$ oxides.Comment: 7 pages, 5 eps figures, corrected typo

Numerical Study of the Cahn-Hilliard Equation in One, Two and Three Dimensions

The Cahn-Hilliard equation is related with a number of interesting physical phenomena like the spinodal decomposition, phase separation and phase ordering dynamics. On the other hand this equation is very stiff an the difficulty to solve it numerically increases with the dimensionality and therefore, there are several published numerical studies in one dimension (1D), dealing with different approaches, and much fewer in two dimensions (2D). In three dimensions (3D) there are very few publications, usually concentrate in some specific result without the details of the used numerical scheme. We present here a stable and fast conservative finite difference scheme to solve the Cahn-Hilliard with two improvements: a splitting potential into a implicit and explicit in time part and a the use of free boundary conditions. We show that gradient stability is achieved in one, two and three dimensions with large time marching steps than normal methods.Comment: 20 pages with 12 figs. Accepted in the Physica

Theory of the Diamagnetism Above the Critical Temperature for Cuprates

Recently experiments on high critical temperature superconductors has shown that the doping levels and the superconducting gap are usually not uniform properties but strongly dependent on their positions inside a given sample. Local superconducting regions develop at the pseudogap temperature ($T^*$) and upon cooling, grow continuously. As one of the consequences a large diamagnetic signal above the critical temperature ($T_c$) has been measured by different groups. Here we apply a critical-state model for the magnetic response to the local superconducting domains between $T^*$ and $T_c$ and show that the resulting diamagnetic signal is in agreement with the experimental results.Comment: published versio

BCS Model in Tsallis' Statistical Framework

We show that there is an effect of nonextensivity acting upon the BCS model for superconductors in the ground state that motivates its study in the Tsallis' statistical framework. We show that the weak-coupling limit superconductors are well described by $q \sim 1$, where q is a real parameter which characterizes the degree of nonextensivity of the Tsallis' entropy. Nevertheless, small deviations with respect to q = 1 provide better agreement when compared with experimental results. To illustrate this point, making use of an approximated Fermi function, we show that measurements of the specific heat, ultrasonic attenuation and tunneling experiments for tin (Sn) are better described with q = 0.99.Comment: 13 pages, amssym