  We study a one-dimensional mixture of two-color fermions and scalar bosons at
the hardcore limit, focusing on the effect that the intraspecies next-neighbor
interactions have on the zero-temperature ground state of the system for
different fillings of each carrier. Exploring the problem's parameters, we
observed that the non-local interaction could favor or harm the well-known
mixed Mott and spin-selective Mott insulators. We also found the emergence of
three unusual insulating states with charge density wave (CDW) structures in
which the orders of the carriers are out of phase with each other. For
instance, the immiscible CDW appears only at half-filling bosonic density,
whereas the mixed CDW state is characterized by equal densities of bosons and
fermions. Finally, the spin-selective CDW couples the bosons and only one kind
of fermions. Appropriate order parameters were proposed for each phase to
obtain the critical parameters for the corresponding superfluid-insulator
transition. Our results can inspire or contribute to understanding experiments
in cold-atom setups with long-range interactions or recent reports involving
quasiparticles in semiconductor heterostructures.
