Josephson Currents Induced by the Witten Effect

We reveal the existence of a new type of topological Josephson effect involving type II superconductors and three-dimensional topological insulators as tunnel junctions. We predict that vortex lines induce a variant of the Witten effect that is the consequence of the axion electromagnetic response of the topological insulator: at the interface of the junction each flux quantum attains a fractional electrical charge of $e/4$. As a consequence, if an external magnetic field is applied perpendicular to the junction, the Witten effect induces an ac Josephson effect in the absence of any external voltage. We derive a number of further experimental consequences and propose potential setups where these quantized, flux induced Witten effects may be observed.