The extended Hubbard model applied to phase diagram and the pressure effects in Bi2Sr2CaCu2O8+y superconductors

Abstract

We use the two dimensional extended Hubbard Hamiltonian with the position of the attractive potential as a variable parameter, within a BCS type approach, to study the interplay b e t ween the superconductor transition temperature Tc and hole content for high temperature superconductors.This method gives some insight on the range and intensity of the Cooper pair interaction. It suggests why di erent compounds have di erent v alues for their measured coherence lengths, and describes the experimental results of the superconducting phase diagram Tc n. The calculations may also be used to study the e ect of the applied pressure with the assumption that it increases the attractive potential which is accompanied by an increase in the superconductor gap. In this way we obtain a microscopic interpretation for the intrinsic term and a general expansion for Tc in terms of the pressure which reproduces well the experimental measurements on the Bi2Sr2CaCu2O8+y superconductors.

Hubbard-corrected DFT energy functionals: The LDA+U description of correlated systems

“…The interest on the extended Hubbard model has been revamped in the last decades by the discovery of high T c superconductors and the intense research activity focusing around them. Whether the inter-site coupling V has a determinant role in inducing superconductivity is, however, still matter of debate [158][159][160][161][162][163][164][165]. Several studies have also demonstrated that the relative strength of U and V controls many properties of the ground state of correlated materials as, for example, the occurrence of possible phase separations [166], the magnetic order [167,168], the onset of charge-density and spindensity-wave regimes [169].…”

Theory for high-Tcsuperconductors considering inhomogeneous charge distribution

“…In fact, the latest STM/S results yields grain boundaries of the order of 100-10 nanometers while the typical coherent lengths are of the order of angstroms. Thus, this approach, with appropriate choice of experimental or calculated parameters, was used before to derive the T c (ρ) curves [36][37][38] for some HTSC families, since T c was, as in normal superconductors, taken as the onset of vanishing gap and ρ was taken as ρ . A two dimension extended Hubbard Hamiltonian in a square lattice has been used to model the quasi-bidimensionality of the carriers motion through the CuO 2 planes [36][37][38]40 and is given by…”

Extended DFT +U+Vmethod with on-site and inter-site electronic interactions

“…The 'resonating valence bond' model [15] predicts a superconducting state (at least within mean-field theory) for a doped Mott insulator with only on-site couplings [16]. However, several numerical studies suggest that the inter-site interaction indeed plays an important role [17,18] and superconductivity is predicted in a regime with repulsive on-site (U > 0) and attractive intersite (V < 0) couplings [19][20][21][22]. Several studies have also demonstrated that in the 'normal' (non-superconducting) state of superconductors and, in general, in correlated materials, the relative strength of U and V controls many properties of the ground state as, for example, the occurrence of possible phase separations [23], the magnetic order [24,25], the onset of charge-density and spin-density-wave regimes [26].…”