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

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 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.

Lithographic band structure engineering of graphene

“…Furthermore, magnetotransport measurements match extraordinarily well with tight-binding simulations of antidot lattices as well with a simple model of Dirac fermions in a strongly confining ring geometry [6], and is, thus, well-described as a quantum system consisting of such connected "Dirac rings". Our measurements confirm several theoretical predictions for such band structure engineered graphene, including a sizeable and magnetically tunable band gap [1,6,35], magnetically confined edge-states [36], and non-linear Landau levels [6]. Furthermore, despite the 10 nm-scale patterning of the graphene, the experimental signatures of an interfacial moiré superlattice turn out to be present both before and after nanostructuring.…”

Exclusive sub-lattices for extended and localized states in graphene ribbons: their role in Klein tunneling, disorder and magnetic field effects

“…where the self-energies S R and Σ L of the contact leads are numerically calculated using the recursive Green function method [31,[33][34][35][36]. With these propagators we computed the DOS and the local density of states (LDOS) as described in [31,35,37]. We used Figure 1.…”

“…Also, this normalization will allow us to compare these results with the maps obtained in figure 4 where no disorder was considered. Physically, the model presented here can describe situations in which carbon atoms are substituted by other atoms due to the absorption of molecules present in the environment or by imperfections in the substrate [44][45][46].…”

Emergence of bound states in ballistic magnetotransport of graphene antidots

“…Recent theoretical studies of periodic graphene antidot lattices (GALs) in the ballistic regime has predicted several possible experimental applications [14][15][16][17]. GALs are expected to be suitable for preparing resonant tunneling diodes [14] or graphene waveguides by a regular graphene strip surrounded by a GAL [15].…”