  We engineer topological insulating phases in a fermion-fermion mixture on the
honeycomb lattice, without resorting to artificial gauge fields or spin-orbit
couplings and considering only local interactions. Essentially, upon
integrating out the fast component (characterized by a larger hopping
amplitude) in a finite region of dopings, we obtain an effective interaction
between the slow fermions at half-filling, which acquires a Haldane mass with
opposite parity in the two valleys of the Dirac cones, thus triggering a
quantum anomalous Hall effect. We carefully analyze the competition between the
induced Semenoff-type mass (producing charge density wave orders in real space)
versus the Haldane mass (quantum anomalous Hall phase), as a function of the
chemical potential of the fast fermions. If the second species involves
spin-1/2 particles, this interaction may induce a quantum spin Hall phase. Such
fermion-fermion mixtures can be realized in optical lattices or in graphene
heterostructures.
