Density-functional investigation of molecular graphene: CO on Cu(111)

Man-made artificial graphene has attracted significant attention in the past few years due to the possibilities to construct designer Dirac fermions with unexpected topological properties and applications in nanoelectronics. Here we use a first-principles approach within density-functional theory to study molecular graphene similarly to the experiment by Gomes et al. [Nature (London) 483, 306 (2012)]. The system comprises carbon monoxide molecules arranged on a copper (111) surface in such a way that a honeycomb lattice is obtained with the characteristic electronic properties of graphene. Our results show in detail how carbon monoxide molecules modify the copper surface (and regions beneath) and create a honeycomb lattice of accumulated electrons between the adsorbate molecules. We also demonstrate how the properties of the formed Dirac fermions change as the CO density is tuned, and provide a direct comparison with experimental scanning tunneling microscope images.

Figure 1

Band structure of the $2\times 2$ surface system. Two band crossings at the $K$ point are clearly visible, one just above the Fermi level and the second one further in the valence band. The closest band crossing to the Fermi level can be found at 130 meV indicated by an arrow.

Figure 2

Band structure of the $4\times 4$ surface system. The crossing closest to the Fermi level is located at 190 meV (arrow). In this case, the band structure is more difficult to interpret than in the $2\times 2$ case as the system size (number of Cu atoms in the simulation box) is significantly larger, leading to more bands.

Figure 3

Laterally integrated charge density difference curve of the $2\times 2$ surface system. The red solid line denotes the integration over the full $xy$ plane and the green dashed line is restricted to a cylinder with 1 Å diameter along a vertical axis that goes through the CO molecule. The triangle on top indicates the position of the Cu plane in Fig. 5.

Figure 4

Charge density difference isosurfaces (red, accumulation; blue, depletion) for the $2\times 2$ coverage show how CO molecules push electron density to interstitial areas resulting in a sixfold accumulation zone (red color).

Figure 5

Electron localization function (ELF) in color scale for lateral ($xy$ plane, left) and vertical ($xz$ plane, right) cut planes. The dotted white lines shows positions of the respective cut planes in the neighboring panels. The crosses show the position of C and O atoms, and the diamonds show the Cu positions. Note that the system (unit cell) is periodically repeated.

Figure 6

Simulated STM image calculated with a small bias for the $4\times 4$ surface using the Tersoff-Hamann scheme [27]. The figure illustrates how the flat areas between the CO molecules form a honeycomb lattice. The zero of the height corresponds to a position at about 7 Å above the uppermost copper layer. Blue crosses give positions of the copper atoms in the surface.