Tuning the Electronic Structure of Graphene by Controlling Spatial Confinement

TL;DR

The paper investigates how spatial confinement via graphene nanoribbon (GNR) arrays can tune the electronic structure of ABA-stacked bilayer and trilayer graphene. It uses the six-parameter Slonczewski–Weiss–McClure tight-binding Hamiltonian to model sandwiched (S) and non-sandwiched (NS) GNR configurations, exploring armchair and zigzag edges and varying GNR widths. Key findings show that semiconducting AGNRs as middle layers in trilayers maintain graphene-like bands with weak interlayer coupling, while gapless AGNRs can open a direct band gap of about $0.6\,\mathrm{eV}$ in bilayers and modify trilayer dispersions; ZGNRs introduce edge-state features that can resemble trilayer behavior as width increases. These results provide design principles for band-gap engineering and potential infrared absorption in graphene-based heterostructures, though they do not include structural relaxation and primarily address near-Fermi energies.

Abstract

The electronic properties of a material depend on the spatial freedom of the electron wavefunction. A well-known example is graphite, which is a conventional gapless semiconductor, while a single layer of it, graphene, exhibits extremely high electronic conductivity. Nevertheless, graphene ribbons can have different physical properties, such as a tunable band gap, from gapless to large band gap semiconductor. The purpose of this study is to investigate the electronic structure of graphene few-layers composed of a layer of graphene nanoribbons and graphene sheet(s), where quasi-one-dimensional nanoribbons can interact with two-dimensional sheet of graphite. Using the tight-binding model for graphite, we show how different configuration of such heterostructures can affect the electronic structure, in which is different from their components electronic structure. Namely, a gap of ~0.6 eV can be opened in a bilayer configuration composed of a layer of gapless armchair nanoribbon stacked on graphene.

Figures (10)

• Figure 1: (a) The top (left) and side (right) views of the 5A3-S atomic structure with our naming convention. (b) The side (top) and top views (bottom) of the 5A3-NS model, where the AGNR array is not sandwiched. The unit cell borders are shown by dashed lines, and the two sublattices are shown by red and blue colors just in this figure.
• Figure 2: The electronic band structures of (a) 3A4-S, together with the Brillouin zone path, and (b) 4A4-S and (c) 5A4-S heterostructures. The band structure of the corresponding perfect systems are shown by dashed gray lines for reference.
• Figure 3: The electronic band structure of wide (a) semimetal 20A2-S, and (b) semiconducting 24A2-S. The site-resolved probability amplitude for the marked states are shown in the inset, black filled circles for the middle layer, and blue is for other layers. (c) The electronic band structure of 24A2-S without interlayer interactions. The band structure for perfect cases are shown with dashed gray lines.
• Figure 4: The band structure of (a) 4Z4-S and (b) the absolute value of the wavefunction square for the selected states, marked on panel (a).
• Figure 5: The electronic band structure of (a) 4A3-NS, (b)5A3-NS (with $\abs{\psi}^2$ for the marked states), and (c) 23A3-NS systems.