Emergent triangular structure in doped extended honeycomb Hubbard model

We investigate the extended honeycomb Hubbard model at $3/4$ filling. By using the mean-field approximation, we find a transition from a normal metal to a ferromagnetic metal at large Coulomb interaction $U$, and a transition to a charge ordered metal at large nearest-neighbor Coulomb interaction $V$. In the presence of both $U$ and $V$, we find a metal-insulator transition, where the insulating state possesses charge and magnetic orders. The charge rich sites are nearly fully occupied, while the charge poor sites form a triangular lattice at nearly half filling. We also apply the variational Monte Carlo method to take into account quantum fluctuations beyond the mean-field treatment, and find this charge ordered state to be stable at sufficiently large $U$ and $V$.