Analytic theory of edge modes in topological insulators

Shijun Mao, Yoshio Kuramoto, Ken Ichiro Imura, Ai Yamakage

Research output: Contribution to journalArticlepeer-review

29 Citations (Scopus)


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.

Original languageEnglish
Article number124709
Journaljournal of the physical society of japan
Issue number12
Publication statusPublished - 2010 Dec
Externally publishedYes


  • Effective hamiltonian
  • Flat edge spectrum
  • Reentrant edge mode
  • Zigzag lattice

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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