Interface metallic states between a topological insulator and a ferromagnetic insulator

We study electronic structures at an interface between a topological insulator and a ferromagnetic insulator by using a three-dimensional two-band model. In usual ferromagnetic insulators, the exchange potential is much larger than the bulk gap size in the topological insulators and electronic structures are asymmetric with respect to the Fermi level. In such situation, we show that unusual metallic states appear under the magnetic moment pointing the perpendicular direction to the junction plane, which cannot be described by the two-dimensional effective model around the Dirac point. When the magnetic moment is in the parallel direction to the plane, the number of Dirac cones becomes even integers. The conclusions obtained in analytical calculations are confirmed by numerical simulations on tight-binding lattice.