Surface states scattering from a step defect in topological insulator Bi_{2}Te_{3}

Abstract

We study theoretically by a quantum-mechanical approach the general scattering problem of a straight step defect on the surface of topological insulator ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ with strong warping effect. At high energy where the warping effect is large, an incident electron on a step defect running along $\Gamma -\mathrm{M}$ direction may exhibit perfect transmission whereas on a defect running along $\Gamma -\mathrm{K}$ direction has a finite probability to be reflected and may even exhibit resonant total reflection. Transmission properties in the latter case are also very sensitive to whether there is particle-hole symmetry. The predicted Friedel oscillations and the power-law decaying behavior of the local density of states (LDOS) near the defect are in good agreement with recent scanning tunneling microscope experiments on ${\mathrm{Bi}}_2{\mathrm{Te}}_3$. The high-energy LDOS of the surface states is also found to show the multi-periodic Friedel oscillations, caused by competing characteristic scattering processes.

11 pages,7 figures

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• Anisotropic Fabry-Pérot resonant states confined within nano-steps on the topological insulator surface
• Bound states and controllable currents on Topological Insulator surfaces with extended magnetic defects
• Surface state transport in double-gated and magnetized topological insulators with hexagonal warping effects
• Numerical analysis of surface and edge states in slabs, stripes, rods and surface steps of topological insulators
• Experimental Observation of Bound States of 2D Dirac Electrons at Surface Steps of the Topological Insulator Bi${}_2$Se${}_3$
• Spin-polarized scanning tunneling microscopy measurement scheme for determining the quantum geometric tensor
• Local density of state oscillations in laterally heterostructured topological insulator-semiconductor systems
• Proposed Detection of Time Reversal Symmetry in Topological Surface States