A $d$-wave, Eliashberg analysis of break-junction and STM tunneling spectra on ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ (Bi2212) reveals that the spectral dip feature is directly linked to strong electronic coupling to a narrow boson spectrum, evidenced by a large peak in ${\alpha }^{2}F(\omega )$. The tunneling dip feature remains robust in the overdoped regime of Bi2212 with bulk $T_c$ values of 56 K–62 K. This is contrary to recent optical conductivity measurements of the self-energy that suggest the narrow boson spectrum disappears in overdoped Bi2212 and therefore cannot be essential for the pairing mechanism. The discrepancy is resolved by considering the way each technique probes the electron self-energy, in particular, the unique sensitivity of tunneling to the off-diagonal or pairing part of the self-energy.

• Received 26 June 2005
• Corrected 25 May 2007

DOI:https://doi.org/10.1103/PhysRevLett.96.017004