Pairing Glue in High Tc Cuprates from Tunneling Spectroscopy

Break junction tunneling spectroscopy data in Bi2212 over a wide range of doping are fit using a d-wave Eliashberg model. Self consistency is achieved as the electron-boson spectral function, $\alpha ^{2}$F($\omega )$, that fits the tunneling conductance dip feature also leads to the correct superconducting gap. The anomalous negative dI/dV observed in break junctions on optimal doped Bi2212 is also reproduced in the analysis. The diagonal and off-diagonal self energies, $\Sigma (\omega )$ and $\phi (\omega )$, respectively are generated in the analysis and they show trends with doping which are in agreement with numerical simulations of the Hubbard model. The peak in $\alpha ^{2}$F($\omega )$ is consistent with the resonance mode in the spin fluctuation spectrum. Tunneling data of other cuprates are also discussed.