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We demonstrate a method for synthesizing large scale single layer graphene bythermal annealing of ruthenium single crystal containing carbon. Low energyelectron diffraction indicates the graphene grows to as large as millimeterdimensions with good long-range order, and scanning tunneling microscope showsperfect crystallinity. Analysis of Moire pattern augmented withfirst-principles calculations shows the graphene layer is incommensurate withthe underlying Ru(0001) surface forming a N by N superlattice with an averagelattice strain of ~ +0.81%. Our findings offer an effective method forproducing high quality single crystalline graphene for fundamental research andlarge-scale graphene wafer for device fabrication and integration.

Millimeter-Scale, Highly Ordered Single Crystalline Graphene Grown on Ru (0001) Surface