We report on several unusual properties of a graphene antidot created by a piecewise constant potential in a magnetic field. We find that the total probability of finding the electron in the barrier can be nearly one while it is almost zero outside the barrier. In addition, for each electron state of a graphene antidot there is a dot state with exactly the same wavefunction but with a different energy. This symmetry is a consequence of Klein tunneling of Dirac electrons. Moreover, in zigzag nanoribbons we find strong coupling between some antidot states and zigzag edge states. Experimental tests of these effects are proposed.
We report on several new basic properties of a parabolic dot in the presence of a magnetic field. The ratio between the potential strength and the Landau level (LL) energy spacing serves as the coupling constant of this problem. In the weak coupling limit the energy spectrum in each Hilbert subspace of an angular momentum consists of discrete LLs of graphene. In the intermediate coupling regime non-resonant states form a closely spaced energy spectrum. We find, counter-intuitively, that resonant quasi-bound states of both positive and negative energies exist in the spectrum. The presence of resonant quasi-bound states of negative energies is a unique property of massless Dirac fermions. As the strong coupling limit is approached resonant and non-resonant states transform into anomalous states, whose probability densities develop a narrow peak inside the well and another broad peak under the potential barrier. These properties may investigated experimentally by measuring optical transition energies that can be described by a scaling function of the coupling constant.
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.
We investigate edge properties of a gapful rectangular graphene quantum dot in a staggered potential. In such a system gap states with discrete and closely spaced energy levels exist that are spatially located on the left or right zigzag edge. We find that, although the bulk states outside the energy gap are nearly unaffected, spin degeneracy of each gap state is lifted by the staggered potential. We have computed the occupation numbers of spin-up and -down gap states at various values of the strength of the staggered potential. The electronic and magnetic properties of the zigzag edges depend sensitively on these numbers. We discuss the possibility of applying this system as a single electron spintronic device.
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