Journal
SOLID STATE COMMUNICATIONS
Volume 151, Issue 16, Pages 1075-1083Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.ssc.2011.05.016
Keywords
Graphene nanoribbons; Heterostructures; Electronic properties; Transport properties
Categories
Funding
- MICINN-Spain [FIS2009-08744, FIS2008-00124]
- NSF [DMR-1005035]
- Division Of Materials Research
- Direct For Mathematical & Physical Scien [1005035] Funding Source: National Science Foundation
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We consider bilayer graphene in the presence of spin-orbit coupling, in order to assess its behavior as a topological insulator. The first Chern number n for the energy bands of single-layer graphene and that for the energy bands of bilayer graphene are computed and compared. It is shown that for a given valley and spin, n for a Bernal-stacked bilayer is doubled with respect to that for the monolayer. This implies that this form of bilayer graphene will have twice as many edge states as single-layer graphene, which we confirm with numerical calculations and analytically in the case of an armchair terminated surface. Bernal-stacked bilayer graphene is a weak topological insulator, whose surface spectrum is susceptible to gap opening under spin-mixing perturbations. We assess the stability of the associated topological bulk state of bilayer graphene under various perturbations. In contrast, we show that AA-stacked bilayer graphene is not a topological insulator unless the spin-orbit coupling is bigger than the interlayer hopping. Finally, we consider an intermediate situation in which only one of the two layers has spin-orbit coupling, and find that although individual valleys have non-trivial Chern numbers for the case of Bernal stacking, the spectrum as a whole is not gapped, so the system is not a topological insulator. (C) 2011 Elsevier Ltd. All rights reserved.
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