Honeycomb antidot artificial lattice as a prototypical correlated Dirac fermion system

We study theoretically the electronic properties of the artificial quantum dot honeycomb lattice defined in a two-dimensional electron gas, focusing on the possibility of achieving a regime in which electronic correlations play a dominant role. At first, we establish a noninteracting model compatible with recently studied experimen-tally devices. According to the values of the obtained electron-electron interaction integrals, we postulate that the inclusion of inherent electron-gas self-screening is indispensable to reconstruct the experimental observations. Applying the Thomas-Fermi type of screening, we show that the radius of the antidot is crucial to achieve a correlated state in which phenomena like antiferromagnetic ordering and interaction-induced insulating state appear. We estimate the conditions for which the electronically correlated state in an artificial honeycomb lattice can be realized.