Tunneling spectra of high-temperature superconductors

The frequency dependence of the tunneling spectrum ${\alpha }^{2}F\left(\omega \right)$ is analyzed in terms of electron pairing induced by exchange of acoustic plasmons in addition to the usual phonon-exchange mechanism. Analytic expressions are obtained for the electron self-energy, the tunneling function ${\alpha }^{2}F$, and the electron pairing coupling $\lambda$ which determines the superconducting properties. The resulting theory is applied to recent tunneling data of ${\mathrm{Nb}}_3$Sn in order to examine the anomalous discrepancies with the phonon density of states found by neutron scattering experiments. The results demonstrate how the high-temperature ($T_c\sim 20°$K) superconducting properties of $A-15\mathrm{}$ compounds are enhanced by acoustic-plasmon contributions, and thus they reconcile these high transition temperatures with the relatively small values of the phonon part of $\lambda$ estimated from several independent experiments.