Vortex-skyrmions and fractional vortices as signatures of chiral d-wave superconductivity

Chiral superconductors belong to the class of integer quantum hall states, spontaneously breaking time-reversal symmetry and hosting topologically protected edge modes. These edge modes are associated with a Chern number and chiral edge currents. In particular, chiral d-wave superconductivity was recently proposed in many different materials, but characteristic experimental fingerprints have been largely lacking due to vanishing edge currents in many scenarios. We propose two different approaches to experimentally verify chiral superconductivity, based on enhancing the currents by mesoscopic finite-size effects, and signatures of unique topological vortex defects. Specifically, we find that vortex-skyrmions (coreless vortices) are prone to form in such systems, consisting of a closed chiral domain wall decorated with fractional vortices. We show how these vortex-skyrmions break axial and rotation symmetries in only one direction of external flux, such that a direct signature of the Chern number and superconducting pairing symmetry emerges in the local density of states and total magnetic moment.