Spontaneous breakdown of time reversal symmetry in the doped honeycomb lattice with enlarged unit cell

Enlarging the unit cell of simple lattice models is proposed as a simple means to get spontaneous breakdown of time reversal symmetry ($\mathcal{T}$) and to stabilize non trivial topological phases. As a case study we explore the nearest neighbor tight binding model for spinless fermions interacting through short range Coulomb interactions in the honeycomb lattice. Using a variational mean field approach and an enlarged six atom unit cell we obtain a very rich phase diagram as doping and interaction strength are varied. Two broken $\mathcal{T}$ phases, with orbital currents (fluxes) arranged in a Kekul\'e pattern, show up above the Van Hove filling. One of them realizes a topological Fermi liquid with a finite anomalous Hall conductivity. Instabilities towards charge modulated and superconducting phases are also discussed.