Intrinsic Josephson-like interference currentsin overlapping relativistic vortices

We present a covariant field-theoretic description of interacting vortices in a relativistic superconducting condensate beyond the London approximation. Focusing on the regime where vortex cores overlap within a uniform symmetry-broken background, we show that coherent interference between vortex amplitudes generates intrinsic, phase-dependent oscillatory charge and supercurrent densities inside a simply connected condensate. Evaluating the conserved Noether current of scalar electrodynamics reveals AC supercurrents at the beat frequency set by the relative temporal phases of the vortices. This response is analogous to the AC Josephson effect, but arises without any physical junction or weak link. Instead, the region of vortex overlap functions as a distributed coupling domain embedded in a coherent condensate background. Our results extend Ginzburg–Landau intuition into the relativistic regime and identify overlapping vortices as intrinsic microscopic sources of narrowband electromagnetic response in Dirac superconducting platforms.