By means of synchrotron-radiation-based core-level spectroscopies we demonstrate that the degree of corrugation in graphene nanomesh on lattice-mismatched transition-metal substrates critically depends on the strength of chemical bonding at the interface. The degree of interfacial orbital hybridization between graphene and metal states is rising in the series Pt(111)-Ir(111)-Rh(111)-Ru(0001). This growing strength of hybridization is accompanied by a gradual change in graphene morphology from nearly flat to strongly corrugated. We provide a comparison of the pore size and period for the cases of graphene and $h\text{-BN}$ nanomesh on Rh(111).

The atomic and electronic structure of the lattice-mismatched $h\text{−}\mathrm{B}\mathrm{N}∕\mathrm{Pt}\left(111\right)$ and $h\text{−}\mathrm{B}\mathrm{N}∕\mathrm{Rh}\left(111\right)$ interfaces formed by pyrolitic reactions with vaporized borazine has been studied by low-energy electron diffraction, scanning tunneling microscopy, x-ray-absorption spectroscopy, and core-level and valence-band photoemission. It has been found that on Pt(111), $h\text{−}\mathrm{B}\mathrm{N}$ forms a nearly flat monolayer, insignificantly corrugated across the supercell. On Rh(111), $h\text{−}\mathrm{B}\mathrm{N}$ grows in form of a nanomesh, as originally observed by Corso et al. [Science 303, 217 (2004)]. The structural difference between the $h\text{−}\mathrm{B}\mathrm{N}∕\mathrm{Pt}\left(111\right)$ and $h\text{−}\mathrm{B}\mathrm{N}∕\mathrm{Rh}\left(111\right)$ interfaces is associated with the strength of chemical interaction between $h\text{−}\mathrm{B}\mathrm{N}$ and the substrate surface. A stronger orbital hybridization on Rh(111) results in a stronger attraction of the monolayer to the metal surface at favorable adsorption sites resulting in a highly corrugated structure (nanomesh). It has been shown that the electronic structure of the outer (elevated) and inner (attracted to the surface) nanomesh sites is very different as a result of different chemical bonding to the substrate (weak and strong, respectively).

A very rich Fe-C phase diagram makes the formation of graphene on iron surfaces a challenging task. Here we demonstrate that the growth of graphene on epitaxial iron films can be realized by chemical vapor deposition at relatively low temperatures, and that the formation of carbides can be avoided in excess of the carbon-containing precursors. The resulting graphene monolayer creates a novel periodically corrugated pattern on Fe(110). Using low-energy electron microscopy and scanning tunneling microscopy, we show that it is modulated in one dimension forming long waves with a period of $\sim 4\mathrm{nm}$ parallel to the [001] direction of the substrate, with an additional height modulation along the wave crests. The observed topography of the graphene/Fe superstructure is well reproduced by density functional theory calculations, and found to result from a unique combination of the lattice mismatch and strong interfacial interaction, as probed by core-level photoemission and x-ray absorption spectroscopy.