Charge transport gap in graphene antidot lattices

Abstract

Graphene antidot lattices (GALs) offer an attractive approach to band-gap engineering in graphene. Theoretical studies indicate that the size of the opened gap is sensitive to the shape, size, and architecture of the nanoholes introduced into the graphene sheet. We have investigated the temperature-dependent electrical conductivity of GALs comprising 50-nm-diameter nanoholes with a pitch of 80, 100, and 200 nm, respectively. The data reveal the presence of localized states within a transport gap, whose interactions lead to a soft Coulomb gap and associated Efros-Shklovskii variable range hopping (ES-VRH). This conduction type is preserved upon application of magnetic fields up to 1 Tesla, above which a transition to Mott variable range hopping occurs. Such a crossover can alternatively be introduced at zero magnetic fields by increasing either the nanohole spacing or the gate-controlled carrier concentration. Furthermore, at intermediate magnetic fields, the hopping exponent assumes a value of 2/3, as predicted by percolation theory for ES-VRH under this condition.

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

“…As an example, we consider a GAL with a lattice constant of 60 nm and an antidot radius of 25 nm, which represent experimentally feasible feature sizes. 8 The neck width of this GAL is approximately w 54 nm, from which the scaling law predicts a critical flux of c 2.82 × 10 To further illustrate the interplay between the two length scales set by the magnetic field and the neck width of the GAL, we have studied the eigenstate nearest to the Dirac point energy. In particular, we consider the overlap edge |ψ(x,y)| 2 dx dy of the probability density with the edge of the antidot.…”

Electron trajectories and magnetotransport in nanopatterned graphene under commensurability conditions

“…Moreover, the influence of magnetic fields on perfectly periodic GALs and isolated antidots has been studied at the level of full atomistic approaches [25], the Dirac approximation [26], or the simple gapped graphene model [27]. Experimental fabrication of GALs involves invasive techniques such as electron beam or block copolymer lithography [28][29][30][31][32][33][34][35][36][37]. A major issue is the deterioration of the graphene sheet quality and the difficulty in maintaining a uniform size and separation of antidots throughout the lattice.…”

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

“…Such structures are fabricated either by e-beam lithography [16,17] or using diblock copolymer templates [18,19]. Moreover, Oberhuber et al [20] have fabricated GALs with hexagonal antidots.…”