Modeling Excess Current in Josephson I-V Characteristics

The current-voltage characteristics ($I$-$V$) of some metal-barrier Josephson junctions include a current component that does not exhibit the DC, or AC Josephson effects. This current is referred to as the excess current, $I_\chi$. Moreover, while $I_\chi$ is negligible around the transition temperature $T_C$, it increases and can exceed 50\% of the total current as temperature is decreased. Normally, $I_\chi$ is omitted from Josephson $I$-$V$ models and this leads to a large overestimate of the product of Josephson critical current, $I_C$, and normal-state resistance, $R_N$ (i.e., $I_CR_N$). We have developed an extended $I$-$V$ model based on the Stewart-McCumber and Ambegaokar-Halperin models that includes $I_\chi$. Using our model, we fit experimental $I$-$V$ data for planar Y-Ba-Cu-O junctions over a range of temperatures. From these fits we obtain values for $I_\chi$, $I_C$ and $R_N$, as well as noise temperature. Our values agree well with experimental measurements. $I_C$ is suppressed using a magnetic field. Further, our $I_C$ exhibits an asymptotic temperature dependence like that expected for a superconducting energy gap well below $T_C$. Our model is an improvement over existing models as it reliably estimates $I_C R_N$.