Bandgap opening/closing of graphene antidot lattices with zigzag-edged hexagonal holes

Abstract

How to predict the bandgap size of graphene antidot lattices (GALs) is a key problem in the field of graphene-based nanoelectronics. Here, we have obtained the universal rules on bandgap opening/closing of GALs with zigzag-edged hexagonal holes (ZH-GALs), as well as the means to control the bandgap size. In the simple case that the electronic property depends on the choice of the supercell, the quantitative relationship between Eg and the density/diameter of antidots is fitted. Turning to complex structures, we reveal that the bandgap opening in ZH-GALs results mainly from the intervalley scattering. In this interpretation, according to their relative position, the antidots can be divided into three categories. A relatively large bandgap appears in ZH-GALs, only when the numbers of the three categories are unequal. This could be explained based on a mechanism similar to diffraction. A formula according to the explanation is provided to estimate the bandgap, which can be used to predict the electronic properties of GALs and guide the design of semiconductor and photoelectronic devices based on GALs.

Floquet Graphene Antidot Lattices

“…Comparable to varying the width of a nanoribbon, varying the size of the supercell and/or the diameter of the holes of the graphene antidot lattice amounts to controlling quantum confinement and the electronic band gap. Subsequent work has showed that the shape of the holes, edge termination, and edge magnetism can have a profound effect on the way that the energy gap scales with the geometric parameters of the antidot structure [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22].…”

The effect of different hydrogen terminations on the structural and electronic properties in the triangular array graphene nanomeshes

“…Theoretical calculations have predicted that lattice modication by perforating would realize a transition of properties of graphene from semimetallic to semiconducting, where the opened band gap could be tuned by the size, shape, density and symmetry of the perforated hole. 13,17,[25][26][27][28][29][30][31][32][33][34] For instance, Pedersen et al found a simple scaling rule for band gap with respect to the numbers of removed and original total carbon atoms in a unit cell. 13 But previous theoretical works have not sufficiently considered the arrays of perforated holes in graphene, especially, another interesting issue about different terminations of the hole edges affecting the structural stability and the electronic properties of GNM has been less addressed.…”

Counterpropagating topological interface states in graphene patchwork structures with regular arrays of nanoholes

“…One idea is to introduce a regular array of holes, also known as antidot lattice, into graphene, with the remaining body dubbed as graphene nanomesh [8][9][10][11][12][13][14][15][16]. Depending on the hole alignment, the band structure of superstructured graphene can be either gapless or gapped, and in gapped cases the gap size is tunable [8,9,[17][18][19][20][21][22][23][24][25].Historically, gap introduction in a honeycomb lattice model, or mass attachment to emergent relativistic electrons, has been cornerstones in discovering new topological phases of matter. For instance, with an appropriate time reversal symmetry (TRS) breaking term, the honeycomb lattice model can derive the quantum anomalous Hall state [26], which is a typical topological state characterized by the Chern number [27].…”