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

## TL;DR

This paper investigates how three-fermion bound states (trions) form in a three-dimensional lattice with anisotropic hopping and short-range attraction, revealing their influence on unconventional superconductivity and phase separation.

## Contribution

It provides a detailed analysis of trion formation thresholds and their relation to pair stability and superconductivity in an anisotropic 3D lattice model.

## Key findings

- Trion formation threshold is precisely determined.
- Highest fermion pair density occurs in strongly anisotropic models.
- Superconductivity with high critical temperature is near trion formation, indicating phase separation tendencies.

## Abstract

A three-fermion problem in a three-dimensional lattice with anisotropic hopping is solved by discretizing the Schroedinger 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 is highest in a strongly anisotropic model. 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.