  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 $s+\rm{i} s$ superconductors as fully self-consistent solutions to a
microscopic Bogoluibov-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.

Superconductivity