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We introduce an explicit scheme to realize Chern insulating phases employingcold atoms trapped in a state-dependent optical lattice and laser-inducedtunneling processes. The scheme uses two internal states, a ground state and along-lived excited state, respectively trapped in separate triangular andhoneycomb optical lattices. A resonant laser coherently coupling the twointernal states enables hopping between the two sublattices with a Peierls-likephase factor. Although laser-induced hopping by itself does not lead totopological bands with non-zero Chern numbers, we find that such bands emergewhen adding an auxiliary lattice that perturbs the lattice structure,effectively turning it at low energies into a realization of the Haldane model:A two-dimensional honeycomb lattice breaking time-reversal symmetry. Weinvestigate the parameters of the resulting tight-binding model usingfirst-principles band structure calculations to estimate the relevant regimesfor experimental implementation.

Design of laser-coupled honeycomb optical lattices supporting Chern insulators