Skyrmion-induced bound states on the surface of 3D Topological Insulators

The interaction between the surface of a 3D topological insulator and a skyrmion / anti-skyrmion structure is studied in order to investigate the possibility of electron confinement due to skyrmion presence. Both hedgehog (N\'eel) and vortex (Bloch) skyrmions are considered. For the hedgehog skyrmion the in-plane components cannot be disregarded and their interaction with the surface state of the TI has to be taken into account. A semi-classical description of the skyrmion chiral angle is obtained using the variational principle. It is shown that both the hedgehog and the vortex skyrmion can induce bound states on the surface of the TI. However, the number and the properties of these states depend strongly on the skyrmion type and on the skyrmion topological number $N_{Sk}$. The probability densities of the bound electrons are also derived where it is shown that they are localized within the skyrmion region.