Thermoelectric AC Josephson effect

A temperature gradient ${\Delta}T$ across a Josephson junction induces a thermoelectric current. We predict the AC Josephson effect is activated when this current surpasses the junction's critical current. Our investigation of this phenomenon employs the time-dependent Ginzburg-Landau theory framework in proximity to the critical temperature. Our results indicate that the frequency of the AC current is approximately given by ${\pi} S {\Delta} T / (2 {\Phi}_0)$, where $S$ represents the Seebeck coefficient and ${\Phi}_0$ the magnetic flux quantum and we estimate the frequency be on the range of GHz for Sn up to a THz for larger $S$ and $T_c$ materials. Furthermore, we propose two distinct experimental configurations to observe this effect.