▎ 摘　　要

We develop a simple way to investigate the energy gap induced by many body effect in optically pumped graphene at different carrier densities. The exchange self-energy and energy dispersions are obtained analytically at the long wave limit. An energy gap depending on the carrier density is observed at the Dirac point. The energy gap induced by many body effect lies in the microwave range which is in accordance with the experimental measurements. Our theoretical results indicate that the exchange interaction via Coulomb interaction can be a mechanism to create an energy gap in optically pumped graphene. (C) 2014 AIP Publishing LLC.