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