Hofstadter butterflies and magnetically induced band-gap quenching in graphene antidot lattices

Jesper Goor Pedersen, Thomas Garm Pedersen

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We study graphene antidot lattices (GALs) in magnetic fields. Using a tight-binding model and a recursive Green's function technique that we extend to deal with periodic structures, we calculate Hofstadter butterflies of GALs. We compare the results to those obtained in a simpler gapped graphene model. A crucial difference emerges in the behavior of the lowest Landau level, which in a gapped graphene model is independent of magnetic field. In stark contrast to this picture, we find that in GALs the band gap can be completely closed by applying a magnetic field. While our numerical simulations can only be performed on structures much smaller than can be experimentally realized, we find that the critical magnetic field for which the gap closes can be directly related to the ratio between the cyclotron radius and the neck width of the GAL. In this way, we obtain a simple scaling law for extrapolation of our results to more realistically sized structures and find resulting quenching magnetic fields that should be well within reach of experiments.
Original languageEnglish
Article number235404
JournalPhysical Review B
Issue number23
Pages (from-to)235404
Number of pages8
Publication statusPublished - 2013

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