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The atomic structures and electronic properties of metal-intercalated (metal = Al, Ag, Au, Pt, and Pd) graphene monolayers on SiC(0001) were investigated using first-principles calculations. The unique Dirac cone of graphene near the K point reappeared as the graphite layer was intercalated by these metals at a coverage of 3/8 ML. Furthermore, our results show that metal intercalation leads to n-type doping of graphene. The bands contributed from graphene exhibit small splitting after intercalation, whereas the bands contributed from the intercalated metal layer have significant Rashba spin-orbit splittings in all cases except Al.