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Projector Quantum-Monte-Carlo Method is used to examine effects of thespin-independent $U_{fd}$ as well as spin-dependent $J_z$ Coulomb interactionbetween the localized $f$ and itinerant $d$ electrons on the stability ofvarious types of charge/spin ordering and superconducting correlations in thespin-one-half Falicov-Kimball model with Hund and Hubbard coupling. The modelis studied for a wide range of $f$ and $d$-electron concentrations and it isfound that the interband interactions $U_{fd}$ and $J_z$ stabilize three basictypes of charge/spin ordering, and namely, (i) the axial striped phases, (ii)the regular $n$-molecular phases and (iii) the phase separated states. It isshown that the d-wave pairing correlations are enhanced within the axialstriped and phase separated states, but not in the regular phases. Moreover, itwas found that the antiferromagnetic spin arrangement within the chains furtherenhances the d-wave paring correlations, while the ferromagnetic one has afully opposite effect.

Enhancement of the d-wave pairing correlations by charge and spin ordering in the spin-one-half Falicov-Kimball model with Hund and Hubbard~coupling