The effects of gap parameter and spin polarization on electronic Hartree and correlation energies of doped graphene nanoribbon

We study the behaviors of both Hartree and correlation energies of undoped gapped armchair graphene nanoribbon using random phase approximation in the context of Hubbard model Hamiltonian. Specially, the effects of spin polarization and gap parameter on electron density dependence of Hartree and correlation energies of armchair graphene nanoribbon has been addressed. Our results show the variation of gap parameter leads to considerable effect on correlation and Hartree energy behavior of spin unpolarized gapped graphene in the middle electron density region. However local Hubbard interaction parameter affects the behaviors of Hartree and correlation energy on the whole range of electron density in zero magnetization case. We also show that a considerable reduction has been observed for density dependence of Hartree and correlation energies of spin polarized gapped graphene nanoribbon.