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arXiv 0802.1409cond-mat.mes-hall
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波纹双层石墨烯中的零能态

Zero-energy states in corrugated bilayer graphene

M. I. Katsnelson, M. F. Prokhorova

摘要:

单层和双层石墨烯中的反常量子霍尔效应与电子态的非平凡拓扑性质(分别为Berry相$π$和2 $π$)有关。众所周知,Atiyah-Singer指数定理保证,对于单层的情况,存在零能量状态的情况下,非均匀磁场假设总通量是非零的。这导致,特别是,在波纹石墨烯中的midgap状态的外观和拓扑保护波纹单层石墨烯中的零能量朗道能级。在这里,我们将这一定理的情况下,双层石墨烯,并证明了零能量模式的存在。

英文摘要:

Anomalous quantum Hall effects in single-layer and bilayer graphene are related with nontrivial topological properties of electron states (Berry phases $π$ and 2$π$, respectively). It was known that the Atiyah-Singer index theorem guarantees, for the case of the single-layer, existence of zero-energy states for the case of inhomogeneous magnetic fields assuming that the total flux is non-zero. This leads, in particular, to appearance of midgap states in corrugated graphene and topologically protects zero-energy Landau level in corrugated single-layer graphene. Here we apply this theorem to the case of bilayer graphene and prove the existence of zero-energy modes for this case.

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