Flat edge modes of graphene and of Z 2 topological insulator
1 Department of Quantum Matter, AdSM, Hiroshima University, Higashi-Hiroshima, 739-8530, Japan
2 Department of Physics, Tohoku University, Sendai, 980-8578, Japan
3 Department of Physics, Tsinghua University, Beijing, 100084, PR China
Nanoscale Research Letters 2011, 6:358 doi:10.1186/1556-276X-6-358Published: 21 April 2011
A graphene nano-ribbon in the zigzag edge geometry exhibits a specific type of gapless edge modes with a partly flat band dispersion. We argue that the appearance of such edge modes are naturally understood by regarding graphene as the gapless limit of a Z2 topological insulator. To illustrate this idea, we consider both Kane-Mele (graphene-based) and Bernevig-Hughes-Zhang models: the latter is proposed for HgTe/CdTe 2D quantum well. Much focus is on the role of valley degrees of freedom, especially, on how they are projected onto and determine the 1D edge spectrum in different edge geometries.