Competing topological phases in few-layer graphene
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Competing topological phases in few-layer graphene Pierre Carmier · Oleksii Shevtsov · Christoph Groth · Xavier Waintal
Published online: 11 April 2013 © Springer Science+Business Media New York 2013
Abstract We investigate the effect of spin-orbit coupling on the band structure of graphene-based two-dimensional Dirac fermion gases in the quantum Hall regime. Taking monolayer graphene as our first candidate, we show that a quantum phase transition between two distinct topological states—the quantum Hall and the quantum spin Hall phases—can be driven by simply tuning the Fermi level with a gate voltage. This transition is characterized by the existence of a chiral spin-polarized edge state propagating along the interface separating the two topological phases. We then apply our analysis to the more difficult case of bilayer graphene. Unlike in monolayer graphene, spin-orbit coupling by itself has indeed been predicted to be unsuccessful in driving bilayer graphene into a topological phase, due to the existence of an even number of pairs of spin-polarized edge states. While we show that this remains the case in the quantum Hall regime, we point out that by additionally breaking the layer inversion symmetry, a non-trivial quantum spin Hall phase can re-emerge in bilayer graphene at low energy. We consider two different symmetry-breaking mechanisms: inducing spin-orbit coupling only in the upper layer, and applying a perpendicular electric field. In both cases, the presence at low energy of an odd number of pairs of edge states can be driven by an exchange field. The related situation in trilayer graphene is also discussed. Keywords Topological phase · Graphene · Band structure
P. Carmier () · O. Shevtsov · C. Groth · X. Waintal CEA-INAC/UJF Grenoble 1, SPSMS UMR-E 9001, Grenoble 38054, France e-mail: [email protected]
1 Introduction Topological insulators are bulk insulators which possess robust conducting surface states [1, 2]. Paradigmatic twodimensional examples of this class are the quantum Hall (QH) and the quantum spin Hall (QSH) phases, which are characterized by respectively chiral and helical onedimensional edge states. While the former can be generated by simply applying a strong perpendicular magnetic field and has been rather extensively studied since the 1980s, the latter requires the presence of spin-orbit coupling and has received very little experimental evidence. Indeed, despite the wide interest shown in the literature for the QSH phase (and for topological phases in general) since the seminal works by Kane and Mele [3, 4], experimental traces of this phase have remained scarce, with the exception of the remarkable works on HgTe quantum wells [5–7] (see also the experiment involving InAs [8]). Recent studies [9–11] have revived the possibility of generating a QSH in graphene [12, 13], by showing that low concentrations of suitably chosen adatoms, randomly deposited on graphene, could open a large non-trivial gap in graphene’s otherwise semimetallic band structure, and yield transport properties
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