On the rotational alignment of graphene domains grown on Ge(110) and Ge(111)

We have used low-energy electron diffraction and microscopy to compare the growth of graphene on hydrogen-free Ge(111) and Ge(110) from an atomic carbon flux. Growth on Ge(110) leads to significantly better rotational alignment of graphene domains with the substrate. To explain the poor rotational alignment on Ge(111), we have investigated experimentally and theoretically how the adatom reconstructions on Ge interact with graphene. We find that the ordering transition of the adatom reconstruction of Ge(111) is not significantly perturbed by graphene. Density functional theory calculations show that graphene on reconstructed Ge(110) has large-amplitude corrugations, whereas it is remarkably flat on reconstructed Ge(111). We argue that the absence of corrugations prevents graphene islands from locking into a preferred orientation.