Thermoelectric AC Josephson effect

A temperature gradient $\mathrm{\Delta }T$ 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 $\pi S\mathrm{\Delta }T\mathrm{/}(2{\mathrm{\Phi }}_0)$, where $S$ represents the Seebeck coefficient and ${\mathrm{\Phi }}_0$ 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.