Excitonic physics in a Dirac quantum dot

We present a description of vacuum polarization in a circular Dirac quantum dot in two spatial dimensions assuming alpha-the relative strength of the Coulomb interaction small enough to render an approximation with a single electron (hole) lowest energy level relevant. Applying this approximation, we find that for alpha(c) approximate to 1.05 the lowest level is half filled irrespective of the number of flavors that are present. The ground state can be represented as a superposition of particular (even number) excitonic states which constitute an excitonic cloud that evolves in a crossover manner. The ground state is degenerate with an intervalley excitonic state at alpha(c) approximate to 1.05, a critical strength, that in our approximation marks a point with single electron and exciton resonances.