Demonstration of CP2 skyrmions in three-band superconductors by self-consistent solutions of a Bogoliubov–de Gennes model

Topological defects, such as magnetic-flux-carrying quantum vortices, determine the magnetic response of superconductors and hence are of fundamental importance. Here, we show that stable $\mathbb{C}{P}²$ skyrmions exist in three-band $s+is$ superconductors as fully self-consistent solutions to a microscopic Bogoliubov--de Gennes model. This allows us to calculate microscopically the magnetic signatures of $\mathbb{C}{P}²$ skyrmions and their footprint in the local density of states.