Dirac Electrons on a Sharply Edged Surface of Topological Insulators

Abstract

An unpaired gapless Dirac electron emergent at the surface of a strong topological insulator (STI) is protected by the bulk-surface correspondence and believed to be immune to backward scattering. It is less obvious, however, and yet to be verified explicitly whether such a gapless Dirac state is smoothly extended over the entire surface when the surface is composed of more than a single facet with different orientations in contact with one another at sharp corner edges (typically forming a steplike structure). In the realistic situation that we consider, the anisotropy of the sample leads to different group velocities in each of such facets. Here, we propose that much insight on this issue can be obtained by studying the electronic states on a hyperbolic surface of an STI. By explicitly constructing the surface effective Hamiltonian, we demonstrate that no backward scattering takes place at a concave $90^{\circ }$ step edge. A strong renormalization of the velocity in the close vicinity of the step edge is also suggested.

4 pages, 2 figures, to be published in J. Phys. Soc. Jpn

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• Topological Insulators
• Topological Insulators in Three Dimensions
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• Topological invariants of time-reversal-invariant band structures
• Model Hamiltonian for Topological Insulators
• Effective continuous model for surface states and thin films of three dimensional topological insulators
• Transmission of topological surface states through surface barriers
• Velocity-modulation control of electron-wave propagation in graphene
• Gapless interface states between topological insulators with opposite Dirac velocities
• The effect of a velocity barrier on the ballistic transport of Dirac fermions
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• Spin Berry phase in anisotropic topological insulators

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• Edge states of a three-dimensional topological insulator
• Topological surface states scattering in Antimony
• Unified description of Dirac electrons on a curved surface of topological insulators
• Ab-initio transport across Bismuth Selenide surface barriers
• Performance of Topological Insulator Interconnects
• Experimental search for one-dimensional edge states at surface steps of the topological insulator Bi${}_2$Se${}_3$: Distinguishing between effects and artifacts
• Protection of the surface states in topological insulators: Berry phase perspective
• Transport and STM studies of hyperbolic surface states of topological insulators
• Manipulating quantum channels in weak topological insulator nanoarchitectures