Reconciling the electronic and geometric corrugations of the hexagonal boron nitride and graphene nanomeshes

Monolayer hexagonal boron nitride on Rh(111) and graphene on Ru(0001) illustrate a trend of divergence between the density functional theory (DFT) calculated geometric corrugation, and scanning tunneling microscope (STM) measured apparent corrugation, of metal-supported 2D films that feature chemically distinct regions. Notably, the geometric and apparent corrugations differ by up to 2 Å for boron nitride/Rh(111), whereas both the DFT-simulated and the experimentally observed STM images agree in the apparent corrugation over a wide range of bias voltages. The disparity is due to unequal contributions of the low/high-lying atoms to the local density of states in the vicinity of the Fermi level. This phenomenon has important implications for the structural characterization of certain supported 2D films, which are being explored for novel electronic and material applications.