Influence of inelastic effects on differential conductance of a high-Tcsuperconductor/metal junction

Both linear conductance and smeared gaplike structure were observed in differential characteristics measured on point contacts using a gold tip and ${\mathrm{Bi}}_2$ ${\mathrm{Sr}}_2$ ${\mathrm{CaCu}}_2$ ${\mathrm{O}}_{8+\mathit{y}}$ thin films as well as ${\mathrm{Bi}}_2$ ${\mathrm{Sr}}_2$ ${\mathrm{CaCu}}_2$ ${\mathrm{O}}_{8+\mathit{y}}$/${\mathrm{SrTiO}}_3$ bilayers with different thickness of ${\mathrm{SrTiO}}_3$. These features were described in terms of inelastic processes. For theoretical description the Blonder-Tinkham-Klapwijk theory extended by Kirtley’s model of the inelastic transport of quasiparticles through a normal metal–superconductor interface was used. In addition, we considered the shortening of quasiparticle lifetime τ due to the inelastic scattering in the superconductor near the interface. In agreement with theory a smeared gaplike structure as well as an increase or a decrease of conductance depending on the strength of the potential barrier corresponding to the ${\mathrm{SrTiO}}_3$ was obtained.