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

TL;DR

This paper numerically investigates the emergence of one-dimensional surface and edge states in various geometries of topological insulators, revealing conditions for massless and massive modes in Bi2Se3 structures.

Contribution

It provides a detailed numerical analysis of surface and edge states in different geometries of topological insulators, highlighting the conditions for massless and massive modes.

Findings

Massless Dirac fermions appear at edges of thin ribbons.

Thick rods and slabs with surface steps host massive localized modes.

Absence of 1D states near edges of large rods and surface steps.

Abstract

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 modes are massive and their origin 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.