Origin of Hysteresis in a Proximity Josephson Junction

We investigate hysteresis in the transport properties of superconductor–normal-metal–superconductor (S-N-S) junctions at low temperatures by measuring directly the electron temperature in the normal metal. Our results demonstrate unambiguously that the hysteresis results from an increase of the normal-metal electron temperature once the junction switches to the resistive state. In our geometry, the electron temperature increase is governed by the thermal resistance of the superconducting electrodes of the junction.

Figure 1

Top panel: Micrograph of sample 2 containing a S-N-S junction of $1.5\mu \mathrm{m}$ length with a sketch of the measurement circuit. Two tunnel probes (top of the image) are connected to the normal metal embedded between two superconducting banks (on the left and right sides of the image). The overlap of the superconducting banks (dark gray) with the normal-metal layer (light gray) is visible. During the measurement, the S-I-N-I-S junction is biased at a fixed current $I_{\mathrm{SINIS}}$ and the voltage drop $V_{\mathrm{SINIS}}$ is monitored. Bottom left panel: Temperature dependence of the voltage $V_{\mathrm{SINIS}}$ of the same sample with a current bias $I_{\mathrm{SINIS}}=6\mathrm{pA}$ (no current is flowing through the S-N-S junction). Bottom right panel: A close-up of the sample image.

Figure 2

Current-voltage characteristic of the sample 1 S-N-S junction (bottom panel) shown on the same current scale with the S-I-N-I-S thermometer voltage response (top panel) measured simultaneously at a 50 mK cryostat temperature. In the top panel, the right vertical axis gives the corresponding electron temperature.

Figure 3

Temperature dependence of the $R_n{I}_c$ product, where $I_c$ is the measured critical current, for samples 1–3 (open symbols). The fits are displayed as solid lines. For sample 3, the theoretical prediction using $\alpha =0.5$ and $E_{\mathrm{Th}}=1.12\mu \mathrm{eV}$ (close to the expected value) is shown as a dotted line. The $R_n{I}_r$ product including the retrapping current $I_r$ at a bath temperature of 50 mK is plotted for each sample versus the electron temperature just before retrapping (solid squares, indicated by arrows).

Figure 4

Injected Joule power $I_{\mathrm{SNS}}{V}_{\mathrm{SNS}}$ in the S-N-S junction as a function of the inverse of the measured electronic temperature $T_e$. The cryostat temperature is 50 mK. The expected behavior due to the electron-phonon coupling is plotted as dotted lines. The dash-dotted line is the power calculated using Eq. (2) and $\Delta =200\mu \mathrm{eV}$. The numbers refer to the samples.