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

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 , probability densities display confinement or deconfinement in antidot potentials (B is the magnetic field). When R/<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/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/1 localized and delocalized probability densities coexist. States that are delocalized outside antidots when R/>1 form a nearly degenerate band and their probability densities are independent of k, in contrast to the case of R/<1.