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A microscopic theory is presented for the observed electronic disorder insuperconducting Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$. The essential phenomenologyis shown to be consistent with the existence of two types of interstitialoxygen dopants: those serving primarily as charge reserviors and those close tothe apical plane contributing both carriers and electrostatic potential to theCuO$_2$ plane. The nonlinear screening of the latter produces nanoscalevariations in the doped hole concentration, leading to electronicinhomogeneity. Based on an unrestricted Gutzwiller approximation of theextended t-$J$ model, we provide a consistent explanation of the correlationbetween the observed dopant location and the pairing gap and its spatialevolutions. We show that the oxygen dopants are the primary cause of both thepairing gap disorder and the quasiparticle interference pattern.Comment: Revised version to appear in Phys. Rev. Lett. A microscopic origin of  two types of dopant oxygens is discussed. 4 pages, 3 figures, revtex4 fil

physical review letters

Correlating Off-Stoichiometric Doping and Nanoscale Electronic Inhomogeneity in the High-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>T</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:math>Superconductor<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>Bi</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>Sr</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>CaCu</mml:mi><mml:mn>2</mml:mn></mml:msub><mml…

Correlating Off-Stoichiometric Doping and Nanoscale Electronic Inhomogeneity in the High-TcSuperconductorBi2Sr2CaCu2