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.
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