Confinement and deconfinement in the potential of antidot arrays of a massless Dirac electron in magnetic fields

Abstract

We have investigated the effect of inter-Landau level mixing on confinement/deconfinement in antidot potentials of states with energies less than the potential height of the antidot array. We find that, depending on the ratio between the size of the antidot R and the magnetic length [Formula: see text], probability densities display confinement or deconfinement in antidot potentials (B is the magnetic field). When R/ℓ < 1 inter-Landau level mixing is strong and probability densities with energy less than the potential height are non-chiral and localized inside antidot potentials. However, in the strong magnetic field limit R/ℓ ≫ 1, where inter-Landau level mixing is small, they are delocalized outside antidot potentials, and are chiral for N = 0 Landau level (LL) states while non-chiral for N = 1. In the non-trivial crossover regime R/ℓ ∼ 1 localized and delocalized probability densities coexist. States that are delocalized outside antidots when R/ℓ > 1 form a nearly degenerate band and their probability densities are independent of k, in contrast to the case of R/ℓ < 1.

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

“…Structures comprising only a single or few antidots are more easily analyzed. For instance, Yang and coworkers 13,14 have included magnetic fields in studies of isolated graphene antidots and small arrays, with perforations modeled as circular electrostatic potentials. The present authors studied an isolated antidot using a mass term barrier.…”

Graphene nanosystems and low-dimensional Chern-Simons topological insulators

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