Single layer core/shell structures consisting of graphene as core and hexagonal boron nitride as shell are studied using first-principles plane wave method within density functional theory. Electronic energy level structure is analysed as a function of the size of both core and shell. It is found that the confinement of electrons in two dimensional graphene quantum dot is reduced by the presence of boron nitride shell. The energy gap is determined by the graphene states. Comparison of round, hexagonal, rectangular and triangular core/shell structures reveals that their electronic and magnetic states are strongly affected by their geometrical shapes. The energy level structure, energy gap and magnetic states can be modified by external charging. The core part acts as a two-dimensional quantum dot for both electrons and holes. The capacity of extra electron intake of these quantum dots is shown to be limited by the Coulomb blockade in two-dimension.
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