Effect of thermal noise on current-voltage characteristics of Josephson junctions

Abstract

Measurements are reported of the current-voltage ($I-V$) characteristics of externally shunted oxide-barrier tunnel junctions at temperatures $T$ and critical currents $I_c$ such that the Josephson coupling energy $\left(\frac{\hslash }{2e}\right)I_c$ is comparable to the thermal energy $kT$. The measurements are in complete quantitative agreement with the theory of Ambegaokar and Halperin in the limit that the dimensionless parameter ${\beta }_c=\left(\frac{2e}{\hslash }\right)\left(\frac{I_{c}C}{{\sigma }^2}\right)\ll 1$, where $C$ is the capacitance and $\sigma$ the total conductance of the shunted junction. Measurements for larger values of ${\beta }_c$ are in qualitative agreement with the theory of Kurkijärvi and Ambegaokar. In addition, the Ambegaokar-Halperin theory is generalized to include the $cos\varphi$ pair-quasiparticle interference term. It is concluded that a measurement of the $cos\varphi$ term using only the $I-V$ characteristic will be difficult.