Berry's Phase for Standing Wave Near Graphene Edge

Details Berry's Phase for Standing Wave Near Graphene Edge Berry's Phase for Standing Wave Near Graphene Edge

2010-02-24

arxiv.org/abs/1002.4443v2

New J. Phys. 12 (2010) 083023

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

6 pages, 4 figures

Scientific paper

10.1088/1367-2630/12/8/083023

Standing waves near the zigzag and armchair edges, and their Berry's phases are investigated. It is suggested that the Berry's phase for the standing wave near the zigzag edge is trivial, while that near the armchair edge is non-trivial. A non-trivial Berry's phase implies the presence of a singularity in parameter space. We have confirmed that the Dirac singularity is absent (present) in the parameter space for the standing wave near the zigzag (armchair) edge. The absence of the Dirac singularity has a direct consequence in the local density of states near the zigzag edge. The transport properties of graphene nanoribbons observed by recent numerical simulations and experiments are discussed from the point of view of the Berry's phases for the standing waves.

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