Image potential states in graphene

Using combined ``$\text{LDA}+\text{image}$ potential'' calculations we show that below the vacuum level a single graphene layer possesses a double Rydberg series of even $({n}^{+})$ and odd $({n}^{\ensuremath{-}})$ symmetry image-potential states and argue that the widely discussed interlayer band in graphite is a consequence of the intersheet hybridization of the first even image-potential state. In light of the present results, the unoccupied electronic states with nearly-free-electron properties in carbon nanotubes, fullerenes, and fullerites can be understood to originate from the image-potential states of graphene.