We study a low-density system of “spinful” lattice fermions with on-site attraction of different fermionic species in the presence of site disorder acting oppositely on different species (such as a random Zeeman field on opposite spins). In the weak-intersite-hopping regime, the attraction promotes the formation of composite pairs consisting of fermions of different species occupying the same lattice site, while sufficiently strong anticorrelated disorder tends to disintegrate the pairs. We calculate the probability of formation of such pairs depending on the relation between the interaction and the disorder strengths. We also study the transport properties of the system in the phase of composite pairs influenced by the anticorrelated disorder and show that this influence turns out to be parametrically weaker than in the case of a conventional potential disorder. We calculate the shift of the superfluid transition temperature caused by disorder and obtain the temperature dependence of the pairs' mobility in the range of temperatures exceeding that of degeneracy.

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• Composite bosons
• Fermions
• Disordered systems
• Boltzmann theory