  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.
