Orbital vortices in s-wave spin-singlet superconductors in zero magnetic field

The breaking of time-reversal and point-group spatial symmetries can have a profound impact on superconductivity. One of the most extraordinary effects, due to the application of a magnetic field, is represented by the Abrikosov vortices with charged supercurrents circulating around their cores. Whether a similar phenomenon can be obtained by exploiting spatial symmetry breaking, e.g., through electric fields or mechanical strain, is a fundamentally relevant but not yet fully settled problem. Here, we show that in two-dimensional spin-singlet superconductors with an unusually low degree of spatial symmetry content, vortices with supercurrents carrying angular momentum around the core can form and be energetically stable. The vortex has zero net magnetic flux since it is made up of counterpropagating Cooper pairs with opposite orbital moments. By solving self-consistently the Bogoliubov-de Gennes equations in real space, we demonstrate that the orbital vortex is stable and we unveil the spatial distribution of the superconducting order parameter around its core. The resulting amplitude has a characteristic pattern with a pronounced angular anisotropy that deviates from the profile of conventional magnetic vortices. These hallmarks guide predictions for the experimental detection.