Screening of the band gap in electrically biased bilayer graphene: From Hartree to Hartree-Fock

It is well known that a direct band gap may be opened in bilayer graphene via the application of a perpendicular electric field (bias). The bias and the chemical potential are controlled by electrostatic gating where the top and bottom gate voltages are tuned separately. The value of the band gap opened by the bias field is influenced by the self screening of the bilayer graphene. The Hartree contribution to the self screening is well known in literature, with Hartree screening significantly renormalizing the gap. In the present work we derive the Fock contribution to the self screening and demonstrate that it is equally important and in the low density regime even more important than the Hartree contribution. We calculate the Hartree-Fock screened band gap as a function of electron doping at zero temperature and also as a function of temperature at zero doping.