Universal Rule on Chirality‐Dependent Bandgaps in Graphene Antidot Lattices

Abstract

Graphene with periodically patterned antidots has attracted intense research attention as it represents a facile route to open a bandgap for graphene electronics. However, not all graphene antidot lattices (GALs) can open a bandgap and a guiding rule is missing. Here, through systematic first-principles calculations, it is found that bandgaps in triangular GALs are surprisingly well defined by a chirality vector R = n a1 + ma2 connecting two neighboring antidots, where a1 and a2 are the basis vectors of graphene. The bandgap opens in the GALs with (n-m)mod3 = 0 but remains closed in those with (n-m)mod3 = ±1, reminiscent of the gap-chirality rule in carbon nanotubes. Remarkably, the gap value in GALs allows ample modulation by adjusting the length of chirality vectors, shape and size of the antidots. The gap-chirality relation in GALs stems from the chirality-dependent atomic structures of GALs as revealed by a super-atom model as well as Clar sextet analyses. This chirality-dependent bandgap is further shown to be a generic behavior in any parallelogram GAL and thus serves as an essential stepping stone for experimenters to realize graphene devices by antidot engineering.

Bilayered semiconductor graphene nanostructures with periodically arranged hexagonal holes

“…It was predicted that such periodic arrays of holes in graphene lattice transform graphene from semimetal to semiconductor with a tunable band gap by means of the changing of the period and the size of the holes. [9][10][11] Periodical nanopores were experimentally realized by different methods, [12][13][14][15][16] with general confirmation of theoretical predictions. [9,10,[17][18][19][20] The transport measurements show that such materials display an effective energy gap (~100 meV) and an ON-OFF ratio up to 10, which is a promising feature of the graphene antidot scheme.…”

“…[9][10][11] Periodical nanopores were experimentally realized by different methods, [12][13][14][15][16] with general confirmation of theoretical predictions. [9,10,[17][18][19][20] The transport measurements show that such materials display an effective energy gap (~100 meV) and an ON-OFF ratio up to 10, which is a promising feature of the graphene antidot scheme. [21,22] It can be speculated that while in the case of a graphene monolayer such holes act as scattering edges, in the case of a bilayered structure the neighboring graphene edges can connect with each other (as was shown in several experimental papers on formation of a closed-edge structure [23][24][25][26] after an e-beam irradiation of the bilayered graphene).…”

Electron trajectories and magnetotransport in nanopatterned graphene under commensurability conditions

“…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. Indeed, the band-gap behavior predicted for certain lattice geometries [23,24,[38][39][40][41][42][43][44][45] is particularly sensitive to small levels of geometric disorder, which may not be possible to eliminate in experiment [46][47][48][49][50][51]. Although such uniformity is not an essential ingredient for commensurability oscillations, invasive etching processes usually reduce the mean free path significantly so that electrons are principally scattered by defects and not antidots, thus suppressing commensurability effects.…”

Screening and collective modes in disordered graphene antidot lattices

“…It should be noted that there are many other possible realizations of a GAL: Both the antidot shape and its edge structure, as well as the underlying lattice symmetry can be varied in a number of ways. The present model is chosen for several reasons: It is a generic model used in many previous studies, and it displays a gapped band structure, 6,7,35 which is of special interest for the present study (see Fig. 2).…”

“…Subsequently, scores of theoretical papers have addressed various properties of GALs using a variety of theoretical tools (e.g., Dirac cone approximation for the underlying graphene spectrum, 3 density functional theory, 4 or within the tight-binding model 5 ). Rather than attempting to review this vast literature, we merely state that, in our opinion, the electronic structure and its dependence on the underlying lattice symmetry and shape of the antidots, 6,7 as well as transport and optical properties of perfect GALs, are fairly well understood, 4 and what remains to be investigated concerns the role of interactions, disorder, and extension of the present theoretical methods to systems with large unit cells, such as the ones encountered in the laboratory. What really has made GALs interesting is the rapid development in fabrication techniques, and today several methods exist to create (reasonably) regular structures with periods in low tens of nanometers-a length scale at which the created gaps are predicted to be in hundreds of millivolts, i.e., approaching the technologically relevant numbers.…”