Evidence for two-particle normal-state tunneling in ${\mathrm{Ba}}_{1\mathrm{-}\mathit{x}}$${\mathrm{K}}_{\mathit{x}}$${\mathrm{BiO}}_3$ native-barrier tunnel junctions

The asymmetric background conductance linear in bias voltage usually observed in ${\mathrm{Ba}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{K}}_{\mathit{x}}$ ${\mathrm{BiO}}_3$ superconductor-insulator-normal (SIN) tunnel junctions is associated with a zero-bias conductance linear in temperature above the superconducting transition. The ratio of the temperature coefficient and the voltage coefficient provides insight into the mechanism causing the linear background conductance. We present a simple model involving tunneling through two-particle states (negative-U, bipolaron) in the barrier that explains the linear background, the asymmetry, and the linear temperature dependence of the conductance. Measurements of native-barrier ${\mathrm{Ba}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{K}}_{\mathit{x}}$ ${\mathrm{BiO}}_3$ tunnel junctions are in quantitative agreement with the model.