We study $N$ interacting massless Dirac fermions confined in a two-dimensional quantum dot. Physical realizations of this problem include a graphene monolayer and the surface state of a strong topological insulator. We consider both a magnetic confinement and an infinite mass confinement. The ground-state energy is computed as a function of the effective interaction parameter $\alpha$ from the Hartree-Fock approximation and, alternatively, by employing the Müller exchange functional. For $N=2$, we compare those approximations to exact diagonalization results. The Hartree-Fock energies are highly accurate for the most relevant interaction range $\alpha \lesssim 2$, but the Müller functional leads to an unphysical instability when $\alpha \gtrsim 0.756$. Up to 20 particles were studied using Hartree-Fock calculations. Wigner molecule formation was observed for strong but realistic interactions, accompanied by a rich peak structure in the addition energy spectrum.

• Received 2 November 2010

DOI:https://doi.org/10.1103/PhysRevB.83.085409