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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 wellmeasured experimental inhomogeneous charge density in a given compound isassumed to produce a spatial distribution of local $\rho(r)$. These differencesin the local charge concentration is assumed to yield insulator and metallicregions, possibly in a stripe morphology. In the metallic region, theinhomogeneous charge density yields also spatial distributions ofsuperconducting critical temperatures $T_c(r)$ and zero temperature gap$\Delta_0(r)$. For a given sample, the measured onset of vanishing gaptemperature is identified as the pseudogap temperature, that is, $T^*$, whichis 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 ormetallic medium. The transition to a superconducting state corresponds to thepercolation threshold among the superconducting regions with different$T_c(r)$'s. To model the charge inhomogeneities we use a double branchedPoisson-Gaussian distribution. To make definite calculations and compare withthe experimental results, we derive phase diagrams for the BSCO, LSCO and YBCOfamilies, with a mean field theory for superconductivity using an extendedHubbard Hamiltonian. We show also that this novel approach provides newinsights on several experimental features of high-$T_c$ oxides.Comment: 7 pages, 5 eps figures, corrected typo

physical review. b, condensed matter

Theory for high-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>superconductors considering inhomogeneous charge distribution

Theory for high-Tcsuperconductors considering inhomogeneous charge distribution