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

Abstract

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 ${V}_{1}$ and ${V}_{2}$ 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) where phases with nontrivial topological properties were found with only a nearest-neighbor interaction ${V}_{1}$ 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 ${V}_{2}$ restores the topological nontrivial phases.