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

TL;DR

This paper investigates how magnetic fields influence graphene antidot lattices, revealing that magnetic fields can close the band gap, with a scaling law enabling predictions for larger, experimental structures.

Contribution

It introduces a recursive Green's function method for calculating Hofstadter butterflies in GALs and demonstrates magnetic field-induced band gap quenching.

Findings

Magnetic fields can close the band gap in GALs.

A scaling law relates critical magnetic field to structure dimensions.

Predicted quenching fields are experimentally accessible.

Abstract

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 behaviour 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.