Phase Transitions and the Nature of the Ground State in Triangular Artificial Graphene Quantum Dots

We present theoretical results based on mean-field and exact many-body approaches showing that in artificial triangular graphene quantum dots with zigzag edges (ATGQD), the ground state transitions from a metallic to an antiferromagnetic by changing the distance between sites. The electronic states of these triangular dots in a metallic state have a macroscopically degenerate shell at the fermi level but no such shell exists in a AF state. We determine the effects of electron-electron interactions on the ground state, the total spin, and the excitation spectrum as a function of filling of the ATGQD with electrons. We find that the half-filled charge neutral shell leads to a partially spin polarized state in the metallic state but also in AF state in accordance with Lieb's theorem. In both regimes a relatively large gap separates the spin polarized ground state to the first excited many-body state at half filling of the degenerate shell, but by adding or removing an electron, this gap collapses, and alternate total spin states emerge with energies nearly degenerate to a spin polarized ground state.