Charge instabilities and topological phases in the extended Hubbard model on the honeycomb lattice with enlarged unit cell

We study spontaneous symmetry breaking in a system of spinless fermions in the honeycomb lattice paying special emphasis to the role of an enlarged unit cell on time reversal symmetry broken phases. We use a tight-binding model with nearest-neighbor hopping t and Hubbard interaction V sub(1) and V sub(2) and extract the phase diagram as a function of electron density and interaction within a mean-field variational approach. The analysis completes the previous work done in Phys. Rev. Lett. 107, 106402 (2011) (http://dx.doi.org/10.1103/PhysRevLett. 107. 106402) where phases with nontrivial topological properties were found with only a nearest-neighbor interaction V sub(1) in the absence of charge decouplings. We see that the topological phases are suppressed by the presence of metallic charge density fluctuations. The addition of next to nearest-neighbor interaction V sub(2) restores the topological nontrivial phases.