Eliashberg Analysis of Tunneling Experiments: Support for the Pairing Glue Hypothesis in Cuprate Superconductors

Evidence for the validity of the pairing glue interpretation of high temperature superconductivity is presented using a modified Eliashberg analysis of experimental superconductor-insulator-superconductor (SIS) tunneling data in ${\mathrm{B}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_8$ (Bi2212) over a wide range of doping. This is accomplished by extracting detailed information on the diagonal and anomalous contributions to the quasiparticle self-energy. In particular, a comparison of the imaginary part of the anomalous self-energy $\mathrm{Im}\Phi (\omega )$ and the pairing glue spectral function ${\alpha }^{2}F(\omega )$ used in the model is consistent with Hubbard model simulations in the literature. In addition, the real part of the diagonal self-energy for optimal doped Bi2212 bears a strong resemblance to that obtained from photoemission experiments.

Figure 1

Comparison of normalized SIS break junction tunneling conductance (black curves) and $d$-wave Eliashberg fits for four junctions with $\Delta =10.5\mathrm{meV}$ (OD51), 17.5 meV (OD62), 31 meV (OD92), and 38 meV (OPT95). The $(c_Z,c_{\Delta })$ values used for the light gray (green) curves, for example, are $(0.14,0.9)$, $(0.15,0.78)$, $(0.2,0.8)$, and $(0.2,0.83)$, and the directional tunneling ($a,b$) values used are $(0.08,1.8)$, $(0.28,0.7)$, $(0.28,0.7)$, and $(0.2,0.87)$, respectively. Upper inset: Experimental optimal doped superconducting and normal state normalization curve (see text). Lower inset: An enlargement of the small feature on the main conductance peak for the case of $\Delta =31\mathrm{meV}$ (OD92).

Figure 2

$\mathrm{Im}\Phi (\omega )$ extracted from the fits of the junctions of Fig. 1 [light gray (green) curves]. Inset: The ${\Omega }_M$ values used for the light gray (green) curves of Fig. 1 are indicated by the light gray (green) dots, and those for the dark gray (red) curves of Fig. 1 by the dark gray (red) dots. The solid line denotes the INS derived $5.4k_B{T}_c$ scaling relation.

Figure 3

The $\mathrm{Re}\Sigma (\omega )$ extracted from the four fits shown in Fig. 1 [light gray (green) curves]. The curves are plotted as a function of negative frequency for ease of comparison with the self-energy extracted from ARPES (black crosses, Ref. 26). Inset: The four ${\alpha }^{2}F(\omega )$ spectra used in the light gray (green) curve fits in Fig. 1.