Reproducible inelastic tunneling in Nb/${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_{8+\mathit{x}}$ point-contact junctions

We discuss the reproducible dependence of tunneling conductance on voltage in Nb/${\mathrm{Bi}}_2$ ${\mathrm{Sr}}_2$ ${\mathrm{CaCu}}_2$ ${\mathrm{O}}_{8+\mathit{x}}$ (single-crystal) point-contact junctions. The large and symmetric deviations from the background conductance observed at voltages greater than the gap are interpreted in the framework of inelastic electron tunneling at the surface of the high-temperature superconductor. The peaks of the odd second derivative of the tunneling current (${\mathit{d}}^2$I/${\mathit{dV}}^2$ ${)}_{\mathrm{odd}}$, shifted of the sum of Nb and ${\mathrm{Bi}}_2$ ${\mathrm{Sr}}_2$ ${\mathrm{CaCu}}_2$ ${\mathrm{O}}_{8+\mathit{x}}$ energy gaps, show a good correspondence with the peaks of the generalized phonon density of states G(ω) determined from neutron-scattering data. The amplitude of the relative deviations of the conductance from the background is explained, as a first approximation, by means of inelastic tunneling at the surface of ${\mathrm{Bi}}_2$ ${\mathrm{Sr}}_2$ ${\mathrm{CaCu}}_2$ ${\mathrm{O}}_{8+\mathit{x}}$ assuming a large electron-phonon coupling strength λ for selected phonon modes and, simultaneously, a small potential barrier U and a small thickness δ of the region where the inelastic process occurs.