Trion formation and unconventional superconductivity in a three-dimensional model with short-range attraction
A three-fermion problem in a three-dimensional lattice with anisotropic hopping is solved by discretizing the Schrödinger equation in momentum space. Interparticle interaction comprises on-site Hubbard repulsion and in-plane nearest-neighbor attraction. By comparing the energy of three-fermion bound clusters (trions) with the energy of one pair plus one free particle, a trion formation threshold is accurately determined, and the region of pair stability is mapped out. It is found that the “close-packed” density of fermion pairs, which is associated with a maximum pair condensation temperature in this model, is the highest in a strongly anisotropic case. It is also argued that pair superconductivity with the highest critical temperature is always close to trion formation, which makes the system prone to phase separation and local charge ordering.
