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

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