Nearly flat band with Chern number C=2 on the dice lattice

We point out the possibility of a nearly flat band with Chern number C = 2 on the dice lattice in a simple nearest-neighbor tight-binding model. This lattice can be naturally formed by three adjacent (111) layers of cubic lattice, which may be realized in certain thin films or artificial heterostructures, such as the SrTiO3/SrIrO3/SrTiO3 trilayer heterostructure grown along the (111) direction. The flatness of two bands is protected by the bipartite nature of the lattice. Including the Rashba spin-orbit coupling on nearest-neighbor bonds causes the flat bands to separate from the others but maintain their flatness. Repulsive interaction will drive spontaneous ferromagnetism on the Kramer pair of the flat bands and split them into two nearly flat bands with Chern number C = +/-2. We thus propose that this may be a route to the quantum anomalous Hall effect and further conjecture that the partial filling of the C = 2 band may realize exotic fractional quantum Hall effects.