Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2010-08-03
J. Phys. Soc. Jpn. 79 (2010) 124709
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
9pages, 7figurs
Scientific paper
10.1143/JPSJ.79.124709
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.
Imura Ken-ichiro
Kuramoto Yoshio
Mao Shijun
Yamakage Ai
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