Finite-size version of the excitonic instability in graphene quantum dots

By a combination of Hartree-Fock simulations, exact diagonalization, and perturbative calculations, we investigate the ground-state properties of disorder-free circular quantum dots formed in a graphene monolayer. Taking the reference chemical potential at the Dirac point, we study N <= 15 interacting particles, where the fine structure constant alpha parametrizes the Coulomb interaction. We explore three different models: (i) Sucher's positive projection (no-pair) approach, (ii) a more general Hamiltonian conserving both N and the number of additional electron-hole pairs, and (iii) the full quantum electrodynamics problem, where only N is conserved. We find that electron-hole pair production is important for alpha >= 1. This corresponds to a reconstruction of the filled Dirac sea and is a finite-size version of the bulk excitonic instability. We also address the effects of an orbital magnetic field.