Graphene has a finite band gap originating from the exchange term of self-energy

Abstract

Graphene is proven to have a finite band gap in the double group of a finite spin–orbit coupling term according to group theory and first-principles calculations. The conduction band minimum and valence band maximum are represented by two different representations. The band gap is then calculated as 0.901 µeV in a generalized gradient approximation but as 0.249 eV in a GW approximation owing to the exchange term of self-energy. The contributions of a substrate and an adsorbate are also assessed.