Wigner localization in a graphene quantum dot with a mass gap

In spite of unscreened Coulomb interactions close to charge neutrality, relativistic massless electrons in graphene allegedly behave as noninteracting particles. A clue to this paradox is that both interaction and kinetic energies scale with particle density in the same way. In contrast, in a dilute gas of nonrelativistic electrons, the different scaling drives the transition to Wigner crystal. Here we show that Dirac electrons in a graphene quantum dot with a mass gap localize in the manner of Wigner for realistic values of device parameters. Our theoretical evidence relies on many-body observables obtained through the exact diagonalization of the interacting Hamiltonian, which allows us to take all electron correlations into account. We predict that the experimental signatures of Wigner localization are the suppression of the fourfold periodicity of the filling sequence and the quenching of excitation energies, both of which may be accessed through Coulomb blockade spectroscopy. Our findings are relevant to other carbon-based nanostructures exhibiting a mass gap.