Analytic Theory of Edge Modes in Topological Insulators

Abstract

Spectrum and wave function of gapless edge modes are derived analytically for a tight-binding model of topological insulators on square lattice. Particular attention is paid to dependence on edge geometries such as the straight (1,0) and zigzag (1,1) edges in the thermodynamic limit. The key technique is to identify operators that combine to annihilate the edge state in the effective one-dimensional (1D) model with momentum along the edge. In the (1,0) edge, the edge mode is present either around the center of 1D Brillouin zone or its boundary, depending on location of the bulk excitation gap. In the (1,1) edge, the edge mode is always present both at the center and near the boundary. Depending on system parameters, however, the mode is absent in the middle of the Brillouin zone. In this case the binding energy of the edge mode near the boundary is extremely small; about $10^{-3}$ of the overall energy scale. Origin of this minute energy scale is discussed.

9pages, 7figurs

References in corpus (17)

• Quantum Spin Hall Effect in Graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Topological Insulators in Three Dimensions
• 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
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Quantum Spin Hall Effect
• The Quantum Spin Hall Effect: Theory and Experiment
• The Helical Liquid and the Edge of Quantum Spin Hall Systems
• Stability of the quantum spin Hall effect: effects of interactions, disorder, and Z_2 topology
• Finite size effects of helical edge states in HgTe/CdTe quantum wells
• Aspects of Chiral Symmetry and the Lattice
• Surface states and chiral symmetry on the lattice
• Zigzag edge modes in Z2 topological insulator: reentrance and completely flat spectrum
• Edge accumulation and currents of moment in 2D topological insulators

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