We report a multiband transport study of bilayer graphene at high carrier densities. Employing a poly(ethylene)oxide-CsClO$_4$ solid polymer electrolyte gate we demonstrate the filling of the high energy subbands in bilayer graphene samples at carrier densities $|n|geq2.4times 10^{13}$ cm$^{-2}$. We observe a sudden increase of resistance and the onset of a second family of Shubnikov de Haas (SdH) oscillations as these high energy subbands are populated. From simultaneous Hall and magnetoresistance measurements together with SdH oscillations in the multiband conduction regime, we deduce the carrier densities and mobilities for the higher energy bands separately and find the mobilities to be at least a factor of two higher than those in the low energy bands.
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