Optical conductivity of bilayer dice lattices

We calculate optical conductivity for bilayer dice lattices in commensurate vertically aligned stackings. The interband optical conductivity reveals a rich activation behavior unique for each of the four stackings. We found that the intermediate energy band, which corresponds to the flat band of a single-layer dice lattice, plays a different role for different stackings. The interband selection rules, which are crucial for the single-layer lattice, may become lifted in bilayer lattices. The results for effective and tight-binding models are found to be in qualitative agreement for some of the stackings and the reasons for the discrepancies for others are identified. Our findings propose optical conductivity as an effective tool to distinguish between different stackings in bilayer dice lattices.