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Despite the noble electronic properties of graphene, its industrial application has been hindered mainly by the absence of a stable means of producing a band gap at the Dirac point (DP). We report a new route to open a band gap (Eg) at DP in a controlled way by depositing positively charged Na+ ions on single layer graphene formed on 6H-SiC(0001) surface. The doping of low energy Na+ ions is found to deplete the π* band of graphene above the DP, and simultaneously shift the DP downward away from Fermi energy indicating the opening of Eg. The band gap increases with increasing Na+ coverage with a maximum Eg >= 0.70 eV. Our core-level data, C 1s, Na 2p, and Si 2p, consistently suggest that Na+ ions do not intercalate through graphene, but produce a significant charge asymmetry among the carbon atoms of graphene to cause the opening of a band gap. We thus provide a reliable way of producing and tuning the band gap of graphene by using Na+ ions, which may play a vital role in utilizing graphene in future nano-electronic devices. [ABSTRACT FROM AUTHOR]