Lattice-matched versus lattice-mismatched models to describe epitaxial monolayer graphene on Ru(0001)

Abstract

Monolayer graphene grown on Ru(0001) surfaces forms a superstructure with periodic modulations in its geometry and electronic structure. The large dimension and inhomogeneous features of this superstructure make its description and subsequent analysis a challenge for theoretical modeling based on density functional theory. In this work, we compare two different approaches to describe the same physical properties of this surface, focusing on the geometry and the electronic states confined at the surface. In the more complex approach, the actual moiré structure is taken into account by means of large unit cells, whereas in the simplest one, the graphene moiré is completely neglected by representing the system as a stretched graphene layer that adapts pseudomorphically to Ru(0001). As shown in previous work, the more complex model provides an accurate description of the existing experimental observations. More interestingly, we show that the simplified stretched models, which are computationally inexpensive, reproduce qualitatively the main features of the surface electronic structure. They also provide a simple and comprehensive picture of the observed electronic structure, thus making them particularly useful for the analysis of these and maybe other complex interfaces.

Substrate engineering of graphene reactivity: towards high-performance graphene-based catalysts

“…The second approach (which is more often used) employs a much smaller supercell with stretched lattice constant of graphene (to match the Ru (0001) lattice). [15][16][17] Previous studies have convincingly shown that although the second approach (the stretched model) neglects the long-range lattice variation (the moiré pattern), it does generate essentially the same electronic properties of the system as those obtained from the first approach, therefore can correctly describe the interaction between graphene and Ru (0001) and are good for further analysis.…”

“…Density functional theory (DFT)-based computational modeling is the commonly used theoretical tool to understand physical and chemical properties of Ru (0001)-supported graphene. [15][16][17] In literature, two different types of DFT-based approaches have been used. The first one uses a very large supercell (e.g., 11 × 11 graphene unit cells) 17 to describe the so-called moiré pattern originated from the lattice mismatch between graphene and Ru.…”

“…[15][16][17] In literature, two different types of DFT-based approaches have been used. The first one uses a very large supercell (e.g., 11 × 11 graphene unit cells) 17 to describe the so-called moiré pattern originated from the lattice mismatch between graphene and Ru. This approach is able to produce the long-range variation of the lattice that agrees well with experiments, but extremely expensive so that is not applicable for some detailed analysis such as chemical reactivity and catalytic activity of the supported graphene.…”

Tailoring the Magnetism of Co Atoms on Graphene through Substrate Hybridization

“…The degree of hybridization of the first is tailored by choosing a specific metal substrate. For G/Ru(0001), the strong hybridization with the substrate d bands opens a gap of about 2 eV in the graphene π bands just below E F [62,63]. This gap limits the hybridization between Co and graphene orbitals and preserves a largely unscreened Coulomb interaction.…”

Determination of low-strain interfaces via geometric matching

“…However, if the interface cell is large, the atomic bonding configurations will often vary considerably over the cell, so that in some parts of the cell favorable bonding configurations are obtained but in other parts not. Overall this leads to weaker bonding [17].…”