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

Imura Ken-Ichiro

Yamakage Ai

Mao Shijun

Hotta Akira

Kuramoto Yoshio

Physical Review B

The spectrum and wave function of helical edge modes in Ζ_2 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-Βk^2. A topological insulator realizes when the parameters Δ and Β fall on the regime, either 0<Δ/Β<4 or 4<Δ/Β<8. At Δ/Β=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/Β, although the main location of the mode moves from the zone center for Δ/Β<4, to the zone boundary for Δ/Β>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/Β=4 where the spectrum becomes independent of the momentum, i.e., flat, over the whole 1D Brillouin zone. Furthermore, for Δ/Β<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.

Physics [ 420 ]

eng

American Physical Society

(c) 2010 American Physical Society

[ISSN] 1098-0121

[DOI] 10.1103/PhysRevB.82.085118

[NCID] AA11187113

[URI] http://link.aps.org/doi/10.1103/PhysRevB.82.085118