We investigate charge transport through electronic surface states of the 6H-SiC͑0001͒-3 ϫ 3 surface. Three intrinsic surface states are located within the wide bulk band gap, in which two ͑S 1 and U 1 ͒ arise from strongly correlated electronic states and the third ͑S 2 ͒ has negligible electron correlation effects. Combined conductance and luminescence experiments with the scanning tunneling microscope show that the Mott-Hubbard surface states ͑S 1 and U 1 ͒ have a high resistance ͑1.0 G⍀͒, while the noncorrelated state ͑S 2 ͒ has a negligible resistance. Consequently, current can be selectively transported through any of these three surface states.