  We demonstrate a method for synthesizing large scale single layer graphene by
thermal annealing of ruthenium single crystal containing carbon. Low energy
electron diffraction indicates the graphene grows to as large as millimeter
dimensions with good long-range order, and scanning tunneling microscope shows
perfect crystallinity. Analysis of Moire pattern augmented with
first-principles calculations shows the graphene layer is incommensurate with
the underlying Ru(0001) surface forming a N by N superlattice with an average
lattice strain of ~ +0.81%. Our findings offer an effective method for
producing high quality single crystalline graphene for fundamental research and
large-scale graphene wafer for device fabrication and integration.
