Zero-energy states in corrugated bilayer graphene

Abstract

Anomalous quantum Hall effects in single-layer and bilayer graphene are related with nontrivial topological properties of electron states (Berry phases $\pi$ and 2$\pi$, 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.

minor changes (misprints are fixed, a bit more explanations in the mathematical part are added)

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Cited by in corpus (32)

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• Properties of Graphene: A Theoretical Perspective
• Gauge fields in graphene
• Non-Abelian gauge potentials in graphene bilayers
• Local Compressibility Measurements of Correlated States in Suspended Bilayer Graphene
• Landau Level Spectrum of ABA- and ABC-stacked Trilayer Graphene
• Midgap states in corrugated graphene: Ab-initio calculations and effective field theory
• Valley-momentum locking in a graphene superlattice with Y-shaped Kekulé bond texture
• Pedestrian index theorem a la Aharonov-Casher for bulk threshold modes in corrugated multilayer graphene
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• Topologically confined states at corrugations of gated bilayer graphene
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