Zigzag edge modes in a Z2 topological insulator: Reentrance and completely flat spectrum

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

Research output: Contribution to journalArticlepeer-review

37 Citations (Scopus)


The spectrum and wave function of helical edge modes in Z2 topological insulator are derived on a square lattice using Bernevig-Hughes-Zhang (BHZ) model. The BHZ model is characterized by a "mass" term M (k) =Δ-B k2. A topological insulator realizes when the parameters Δ and B fall on the regime, either 0<Δ/B<4 or 4<Δ/B<8. At Δ/B=4, which separates the cases of positive and negative (quantized) spin Hall conductivities, the edge modes show a corresponding change that depends on the edge geometry. In the (1,0) edge, the spectrum of edge mode remains the same against change in Δ/B, although the main location of the mode moves from the zone center for Δ/B<4, to the zone boundary for Δ/B>4 of the one-dimensional (1D) Brillouin zone. In the (1,1)-edge geometry, the group velocity at the zone center changes sign at Δ/B=4 where the spectrum becomes independent of the momentum, i.e., flat, over the whole 1D Brillouin zone. Furthermore, for Δ/B<1.354, the edge mode starting from the zone center vanishes in an intermediate region of the 1D Brillouin zone, but reenters near the zone boundary, where the energy of the edge mode is marginally below the lowest bulk excitations. On the other hand, the behavior of reentrant mode in real space is indistinguishable from an ordinary edge mode.

Original languageEnglish
Article number085118
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number8
Publication statusPublished - 2010 Aug 27

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


Dive into the research topics of 'Zigzag edge modes in a Z2 topological insulator: Reentrance and completely flat spectrum'. Together they form a unique fingerprint.

Cite this