  We investigate edge properties of a gapful rectangular graphene quantum dot
in a staggered potential. In such a system gap states with discrete and closely
spaced energy levels exist that are spatially located on the left or right
zigzag edge. We find that, although the bulk states outside the energy gap are
nearly unaffected, spin degeneracy of each gap state is lifted by the staggered
potential. We have computed the occupation numbers of spin-up and -down gap
states at various values of the strength of the staggered potential. The
electronic and magnetic properties of the zigzag edges depend sensitively on
these numbers. We discuss the possibility of applying this system as a single
electron spintronic device.
