On the Electron Pairing Mechanism of Copper-Oxide High Temperature Superconductivity

The elementary CuO2 plane sustaining cuprate high-temperature superconductivity occurs typically at the base of a periodic array of edge-sharing CuO5 pyramids (Fig 1a). Virtual transitions of electrons between adjacent planar Cu and O atoms, occurring at a rate $t/{\hbar}$ and across the charge-transfer energy gap E, generate 'superexchange' spin-spin interactions of energy $J\approx4t^4/E^3$ in an antiferromagnetic correlated-insulator state1. Hole doping the CuO2 plane disrupts this magnetic order while perhaps retaining superexchange interactions, thus motivating a hypothesis of spin-singlet electron-pair formation at energy scale J as the mechanism of high-temperature superconductivity. Although the response of the superconductor's electron-pair wavefunction $\Psi\equiv $ to alterations in E should provide a direct test of such hypotheses, measurements have proven impracticable. Focus has turned instead to the distance ${\delta}$ between each Cu atom and the O atom at the apex of its CuO5 pyramid. Varying ${\delta}$ should alter the Coulomb potential at the planar Cu and O atoms, modifying E and thus J, and thereby controlling ${\Psi}$ in a predictable manner. Here we implement atomic-scale imaging of E and ${\Psi}$, both as a function of the periodic modulation in ${\delta}$ that occurs naturally in $Bi_2Sr_2CaCu_2O_{8+x}$. We demonstrate that the responses of E and ${\Psi}$ to varying ${\delta}$, and crucially those of ${\Psi}$ to the varying E, conform to theoretical predictions. These data provide direct atomic-scale verification that charge-transfer superexchange is key to the electron-pairing mechanism in the hole-doped cuprate superconductor ${Bi_2Sr_2CaCu_2O_{8+x}}$.