Excitons in Graphene and the Influence of the Dielectric Envi ronment

Department of Physics and Material Sciences Center,Philipps University Marburg, Renthof 5, D-35032 Marburg, Germany(Dated: July 29, 2011)The exciton Wannier equation for graphene is solved for different background dielectric constants. It is shownthat freestanding graphene features strong Coulomb effects with a very large exciton binding energy exceeding3eV. A second-order transition to a weak Coulomb regime is found if the effective background dielectric con-stant exceeds a critical value. All bound-state solutions vanish for epitaxial graphene on a substrate with largebackground permittivity, such as SiC.