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. We additionally 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.