Spin-selective insulators in Bose-Fermi mixtures

We investigate an imbalanced mixture composed of two-color fermions and scalar bosons in the hard-core limit, considering repulsive attractive interspecies intraspecies interactions. The interplay between commensurability, interactions imbalance generates three insulating phases: a mixed Mott state two spin-selective insulators characterized by commensurability relations $\rho_B+\rho^{\uparrow,(\downarrow)}_F=1$. For coupling bosons, we found $\rho_B-\rho^{\uparrow,(\downarrow)}_F=0$ for insulators. State-of-the-art cold-atoms setups constitute ideal platforms to implement these unveiled states verify their relations.