期刊
PHYSICAL REVIEW B
卷 84, 期 19, 页码 -出版社
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.84.195452
关键词
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资金
- NANOSIMGRAPHENE [ANR-09-NANO-016-01, ANR/P3N2009]
- European Marie Curie ITN NanoCTM
We develop a method to predict the existence of edge states in graphene ribbons for a large class of boundaries. This approach is based on the bulk-edge correspondence between the quantized value of the Zak phase Z(k(parallel to)), which is a Berry phase across an appropriately chosen one-dimensional Brillouin zone, and the existence of a localized state of momentum k(parallel to) at the boundary of the ribbon. This bulk-edge correspondence is rigorously demonstrated for a one-dimensional toy model as well as for graphene ribbons with zigzag edges. The range of k(parallel to) for which edge states exist in a graphene ribbon is then calculated for arbitrary orientations of the edges. Finally, we show that the introduction of an anisotropy leads to a topological transition in terms of the Zak phase, which modifies the localization properties at the edges. Our approach gives a new geometrical understanding of edge states, and it confirms and generalizes the results of several previous works.
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