Josephson anomalous vortices

We show that vortices with circulating current, related with odd-frequency triplet pairing, appear in Josephson junctions where the barrier is a weak ferromagnet with strong spin-orbit coupling. By symmetry analysis we show that there is an additional term—a rotary invariant—in the superconducting free energy which allows for magnetoelectric effects even when the previously considered Lifshitz invariant vanishes. Using a microscopic model based on a modified Usadel equation incorporating those effects, we show that the size, shape, and position of these vortices can be controlled by manipulating Rashba spin-orbit coupling in the weak link, via gates, and we suggest that these vortices could be detected via scanning magnetometry techniques. We also show that the transverse triplet components of the pairing amplitudes can form a texture.