Erratum: Graphene Antidot Lattices: Designed Defects and Spin Qubits [Phys. Rev. Lett.100, 136804 (2008)]

Electronic and optical properties of graphene antidot lattices: comparison of Dirac and tight-binding models

“…Generally, the band gap increases as the ratio of antidot to unit-cell area (fill factor) increases. A linear scaling law for GALs with circular antidots was proposed by Pedersen et al [12] suggesting that the band gap scales as E g ≈ K · N 1/2 removed /N total for small values of N 1/2 removed /N total , where N removed is the number of removed atoms and N total is the total number of atoms in the unit cell before the antidot was created. They determined the scaling constant as K ≃ 25 eV, whereas a more exact quasiparticle TB model has revealed a slightly larger constant of K ≃ 29 eV [30].…”

“…This provides a controllable band gap that depends on the geometry of the antidot lattice [12]. Previously, tight-binding (TB) calculations have been made for relatively small unit cells [12][13][14]. Trolle et al [15] have used density functional theory (DFT) and Hubbard TB to show that localized edge states emerge in GALs containing hexagonal antidots with zigzag edges.…”

“…Several strategies for introducing a band gap have been proposed, including graphene nanoribbons (GNRs) [7][8][9], gated bilayer graphene [10] and periodic gating [11]. Another method is to introduce perforations in a periodic pattern, called a graphene antidot lattice (GAL) [12,13]. This provides a controllable band gap that depends on the geometry of the antidot lattice [12].…”

“…Another method is to introduce perforations in a periodic pattern, called a graphene antidot lattice (GAL) [12,13]. This provides a controllable band gap that depends on the geometry of the antidot lattice [12]. Previously, tight-binding (TB) calculations have been made for relatively small unit cells [12][13][14].…”

Magnetic modulation of the tunnelling between defect states in antidot superlattices

“…Prompted by the advantages of the two-dimensional antidot lattices routinely fabricated nowadays, a new structure was proposed recently which seems to offer many attractive features in terms of flexibility, scalability, and operation in the pursuit of achieving solid-state quantum computation. Such scheme is based on quantum-mechanical bound states which form at designed defects in an antidot superlattice defined on a semiconductor heterostructure [17,18,19] or on a graphene sheet [20].…”