  Inspired by recent studies of various two-dimensional (2D) metals such as Au,
Fe and Ag, we study the growth of two-dimensional gold patches in graphene
pores by density-functional theory. We find that at room temperature gold atoms
diffuse readily on top of both graphene and two-dimensional gold with energy
barriers less than $0.5$ eV. Furthermore, gold atoms move without barriers from
the top of graphene to its edge and from the top of 2D gold to its edge. The
energy barriers are absent even at the interface of 2D gold and graphene, so
that the gold atoms move effortlessly across the interface. We hope our
demonstration for the propensity of diffusing gold atoms to grow 2D gold
patches in graphene pores will inspire the fabrication of these patches
experimentally.
