One-dimensional Topological Edge States of Bismuth Bilayers

Abstract

The hallmark of a time-reversal symmetry protected topologically insulating state of matter in two-dimensions (2D) is the existence of chiral edge modes propagating along the perimeter of the system. To date, evidence for such electronic modes has come from experiments on semiconducting heterostructures in the topological phase which showed approximately quantized values of the overall conductance as well as edge-dominated current flow. However, there have not been any spectroscopic measurements to demonstrate the one-dimensional (1D) nature of the edge modes. Among the first systems predicted to be a 2D topological insulator are bilayers of bismuth (Bi) and there have been recent experimental indications of possible topological boundary states at their edges. However, the experiments on such bilayers suffered from irregular structure of their edges or the coupling of the edge states to substrate's bulk states. Here we report scanning tunneling microscopy (STM) experiments which show that a subset of the predicted Bi-bilayers' edge states are decoupled from states of Bi substrate and provide direct spectroscopic evidence of their 1D nature. Moreover, by visualizing the quantum interference of edge mode quasi-particles in confined geometries, we demonstrate their remarkable coherent propagation along the edge with scattering properties that are consistent with strong suppression of backscattering as predicted for the propagating topological edge states.

15 pages, 5 figures, and supplementary material

References in corpus (17)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Topological Insulators with Inversion Symmetry
• Discovery (theoretical prediction and experimental observation) of a large-gap topological-insulator class with spin-polarized single-Dirac-cone on the surface
• Topological Field Theory of Time-Reversal Invariant Insulators
• First direct observation of Spin-textures in Topological Insulators : Spin-resolved ARPES as a probe of topological quantum spin Hall effect and Berry's phase
• Topological Surface States Protected From Backscattering by Chiral Spin Texture
• Nonlocal edge state transport in the quantum spin Hall state
• Surface States of the Topological Insulator Bi_{1-x}Sb_x
• Strong spin-orbit splitting on Bi surfaces
• Quantum Spin Hall Effect and Enhanced Magnetic Response by Spin-Orbit Coupling
• Momentum-Resolved Landau-Level Spectroscopy of Dirac Surface State in Bi2Se3
• Transmission of topological surface states through surface barriers
• Direct mass measurements beyond the proton drip-line
• Edge and Interfacial States in a 2D Topological Insulator:Bi(111) Bilayer on Bi${}_2$Te${}_2$Se
• Magnetic field induced localization in 2D topological insulators

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