Pairs, trimers and BCS-BEC crossover near a flat band: the sawtooth lattice

TL;DR

This paper studies how pairing and superconductivity behave in a one-dimensional sawtooth lattice with a flat band, revealing unique effects on the BCS-BEC crossover, the existence of trimers, and the influence of multiband physics.

Contribution

It demonstrates the impact of multiband effects on the BCS-BEC crossover and uncovers the existence of three-body bound states in the sawtooth lattice, contrasting with linear chain models.

Findings

Chemical potential remains near zero-density limit near flat band.

Pairing gap shows strong density dependence and is not peaked at the flat band.

Existence of three-body bound states (trimers) in the sawtooth lattice.

Abstract

We investigate pairing and superconductivity in the attractive Fermi Hubbard model on the one-dimensional sawtooth lattice, which exhibits a flat band by fine-tuning the hopping rates. We first solve the two-body problem, both analytically and numerically, to extract the binding energy and the effective mass of the pairs. Based on the DMRG method, we address the ground-state properties of the many-body system, assuming equal spin populations. We compare our results with those available for a linear chain, where the model is integrable by Bethe ansatz, and show that the multiband nature of the system substantially modifies the physics of the BCS-BEC crossover. Near a flat band, the chemical potential remains always close to its zero-density limit predicted by the two-body physics. In contrast, the pairing gap exhibits a remarkably strong density dependence and, differently from the pair binding energy, it is no longer peaked at the flat-band point. We show that these results can be interpreted in terms of polarization screening effects, due to an anomalous attraction between pairs in the medium and single fermions. Importantly, we unveil that three-body bound states (trimers) exist in the sawtooth lattice, in sharp contrast with the linear chain geometry, and we compute their binding energy. The nature of these states is investigated via a strong coupling variational approach, revealing that they originate from tunneling-induced exchange processes.