A Theory for High-$T_c$ Superconductors Considering Inhomogeneous Charge Distribution

Abstract

We propose a general theory for the critical $T_c$ and pseudogap $T^{\ast }$ temperature dependence on the doping concentration for high-$T_c$ oxides, taking into account the charge inhomogeneities in the $Cu{O}_2$ 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, $T^{\ast }$, which is the maximum of all $T_c(r)$. Below $T^{\ast }$, 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.

7 pages, 5 eps figures, corrected typos

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