Surface State Magnetization and Chiral Edge States on Topological Insulators

We study the interaction between a ferromagnetically ordered medium and the surface states of a topological insulator with a general surface termination. This interaction is strongly crystal face dependent and can generate chiral states along edges between crystal facets even for a uniform magnetization. While magnetization parallel to quintuple layers shifts the momentum of Dirac point, perpendicular magnetization lifts the Kramers degeneracy at any Dirac points except on the side face where the spectrum remains gapless and the Hall conductivity switches sign. Chiral states can be found at any edge that reverses the projection of surface normal to the stacking direction of quintuple layers. Magnetization also weakly hybridizes non cleavage surfaces.