Fractional-filling Mott domains in two dimensional optical superlattices

Ultracold bosons in optical superlattices are expected to exhibit fractional-filling insulating phases for sufficiently large repulsive interactions. On strictly 1D systems, the exact mapping between hard-core bosons and free spinless fermions shows that any periodic modulation in the lattice parameters causes the presence of fractional-filling insulator domains. Here, we focus on two recently proposed realistic 2D structures where such mapping does not hold, i.e. the two-leg ladder and the trimerized kagome' lattice. Based on a cell strong-coupling perturbation technique, we provide quantitatively satisfactory phase diagrams for these structures, and give estimates for the occurrence of the fractional-filling insulator domains in terms of the inter-cell/intra-cell hopping amplitude ratio.