Scaling of excitons in graphene nanodots

The binding energy of an exciton in a semiconductor or an insulator is known to scale linearly with ε_r^-2, where ε_r is its dielectric constant. In graphene however, since the kinetic energy scales linearly with the wave number instead of its square, the exciton binding energy is thus expected to scale with ε_r^-1. In this work we make use of the configuration interaction approach to study the properties of excitons in graphene nanodots embedded in various dielectric environments. With tens of million configurations taken into account in the calculation, we find that the exciton binding energy can be well described by a single scaling rule in which the scaling factor is found to vary with the dimension of the nanodots as well as with the on-site interaction parameter, which agrees well with a recent experiment. The linear relation of the exciton binding energy found with the quasi-particle gap also agrees with the previous work on bulk graphene and other two-dimensional materials.