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A three-fermion problem in a three-dimensional lattice with anisotropichopping is solved by discretizing the Schroedinger equation in momentum space.Interparticle interaction comprises on-site Hubbard repulsion and in-planenearest-neighbor attraction. By comparing the energy of three-fermion boundclusters (trions) with the energy of one pair plus one free particle, a trionformation threshold is accurately determined, and the region of pair stabilityis mapped out. It is found that the "close-packed" density of fermion pairs ishighest in a strongly anisotropic model. It is also argued that pairsuperconductivity with the highest critical temperature is always close totrion formation, which makes the system prone to phase separation and localcharge ordering.

Trion formation and unconventional superconductivity in a three-dimensional model with short-range attraction