Numerical analysis of surface and edge states in slabs, stripes, rods and surface steps of topological insulators

By numerically solving the effective continuous model of a topological insulator with parameters corresponding to the band structure of the topological insulator Bi₂Se₃, we analyze possible appearance of one-dimensional states in various geometries. Massless Dirac fermions are found at the edges of thin ribbons with surface oriented not only along the van der Waals gap but also in the perpendicular direction. Thick rods and slabs with surface steps host massive modes localized on surface faces. We argue that the the origin of the massive modes is due to the difference in the Dirac point energy of adjacent faces. The absence of one-dimensional states near edges of a large rectangular rod and surface steps is demonstrated.