Open Access Nano Review

Flat edge modes of graphene and of Z 2 topological insulator

Ken-Ichiro Imura12*, Shijun Mao23, Ai Yamakage2 and Yoshio Kuramoto2

Author Affiliations

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

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Nanoscale Research Letters 2011, 6:358  doi:10.1186/1556-276X-6-358

Published: 21 April 2011

Abstract

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.