The fundamental differences between Quantum Spin Hall edge-states at zig-zag and armchair terminations of honeycomb and ruby nets

Abstract

Combining an analytical and numerical approach we investigate the dispersion of the topologically protected spin-filtered edge-states of the Quantum Spin Hall state on honeycomb and ruby nets with zigzag (ZZ) and armchair (AC) edges. We show that the Fermi velocity of the helical edge-states on ZZ edges increases linearly with the strength of the spin-orbit coupling (SOC) whereas for AC edges the Fermi velocity is independent of the SOC. Also the decay length of edge states into the bulk is dramatically different for AC and ZZ edges, displaying an inverse functional dependence on the SOC.

5 pages, 4 figures

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• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Topological Insulators with Inversion Symmetry
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• Interference of Topologically Protected Edge States in Silicene Nanoribbons
• Band topology and quantum spin Hall effect in bilayer graphene
• Controlling edge states in the Kane-Mele model via edge chirality

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• A primer on twistronics: A massless Dirac fermion's journey to moiré patterns and flat bands in twisted bilayer graphene
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