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

TL;DR

This paper investigates how electron-electron interactions, including both Hartree and Fock contributions, influence the band gap in electrically biased bilayer graphene, revealing the significance of exchange effects especially at low densities.

Contribution

The study derives and emphasizes the importance of the Fock (exchange) contribution to self screening, which was previously overlooked, in determining the band gap in bilayer graphene.

Findings

Fock contribution is as important as Hartree in screening effects.

Band gap calculations show significant renormalization due to exchange interactions.

Temperature and doping affect the screened band gap in bilayer graphene.

Abstract

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.