Ground-state properties of gapped graphene using the random phase approximation

We study the effect of band gap on the ground-state properties of Dirac electrons in a doped graphene within the random phase approximation at zero temperature. Band gap dependence of the exchange, correlation, and ground-state energies and the compressibility are calculated. In addition, we show that the conductance in the gapped graphene is smaller than gapless one. We also calculate the band-gap dependence of charge compressibility and it decreases with increasing the band-gap values.