Bifurcation of the Edge-State Width in the Two-Dimensional Topological Insulator

Abstract

We examine the properties of edge states in a two-dimensional topological insulator. Based on the Kane-Mele model, we derive two coupled equations for the energy and the effective width of edge states at a given momentum in a semi-infinite honeycomb lattice with a zigzag boundary. It is revealed that, in a one-dimensional Brillouin zone, the edge states merge into the continuous bands of the bulk states through a bifurcation of the edge-state width. We discuss the implications of the results to the experiments in monolayer or thin films of topological insulators.

5 pages, 5 figures

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• Emerging topological bound states in Haldane model zigzag nanoribbons
• Analytical study of the edge states in the bosonic Haldane model
• Explicit derivation of the chiral and (generic) helical edge states for the Kane-Mele model: Closed expressions for the wave function, dispersion relation, and spin rotation
• Implementing Microwave Impedance Microscopy in a Dilution Refrigerator
• Topological study of a Bogoliubov-de Gennes system of pseudo spin-$1/2$ bosons with conserved magnetization in a honeycomb lattice
• Boundary criticality in two-dimensional interacting topological insulators