Stacking-induced Chern insulator

Graphene can be turned into a semimetal with broken time-reversal symmetry by adding a valley-dependent pseudoscalar potential that shifts the Dirac point energies in opposite directions, as in the modified Haldane model. We consider a bilayer obtained by stacking two time-reversed copies of the modified Haldane model, where conduction and valence bands cross to give rise to a nodal line in each valley. In the AB stacking, the interlayer hopping lifts the degeneracy of the nodal lines and induces a band repulsion, leading surprisingly to a chiral insulator with a Chern number C =±2 . As a consequence, a pair of chiral edge states appears at the boundaries of a ribbon bilayer geometry. In contrast, the AA stacking does not show nontrivial topological phases. We discuss possible experimental implementations of our results.