The Impact of an Oxygen Dopant in an ideal Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ Crystal

Scanning tunneling microscopy studies have shown that local nanoscale pairing inhomogeneities are correlated with interstitial oxygen dopants in Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$. Combining electrostatic and cluster calculations, we examine the impact of a dopant on the local Madelung and charge transfer energies, magnetic exchange J , Zhang-Rice mobility, and interactions with the lattice. It is found that electrostatic modifications locally increases the charge transfer energy and slightly suppresses J. It is further shown that coupling to c-axis phonons is strongly modified near the dopant. The combined e?ects yield broadened spectral features, reduced charge gap energies, and a sizable local increase of J implying a strong local interplay between antiferromagnetism, polarons, and superconducting pairing.