The dielectric environment dependent exchange self-energy of the energy structure in graphene

We theoretically calculate the energy dispersion in the presence of the screened exchange self-energy in extrinsic monolayer graphene. It is found that the exchange self-energy enhances the renormalized Fermi velocity. With decreasing the dielectric constant, the screening effect and the electron correlation effect increase which induces the Fermi velocity increasing. The screened exchange energy has an energy shift at the Dirac points. The self-energy from the valance band carriers gives the main contribution to the effective energy. We also discuss the electron density dependence of the self-energy.