Bound states induced by a ferromagnetic delta-layer inserted into a three-dimensional topological insulator

We report on theoretical study of the bound electron states induced by a ferromagnetic delta-layer embedded into a narrow-band-gap semiconductor of the Bi$_2$Se$_3$-type which is a three-dimensional topological insulator with large spin-orbit coupling. We make use of an effective Hamiltonian taking into account the inverted band structure of the semiconductor host at the $\Gamma $ point and describe the properties of the in-gap bound states: energy spectrum, characteristic length and spin polarization. We highlight a role of these states for a magnetic proximity effect in digital magnetic heterostructures based on the Bi$_2$Se$_3$-type semiconductors.