Pairing and superconductivity in the flat band: Creutz lattice

TL;DR

This study investigates how local attractive interactions induce pair superfluidity in the flat band of the Creutz lattice, revealing a BCS to bosonic pair crossover and demonstrating the robustness of pairing compared to a standard ladder.

Contribution

It provides a comprehensive analysis of pairing mechanisms in flat band systems using unbiased numerical methods, extending understanding beyond weak interactions.

Findings

Identification of a BCS to bosonic pair crossover in the Creutz lattice.

Longer ranged pair correlations in the Creutz lattice compared to a fermionic ladder.

Robustness of pairing in flat band systems demonstrated through numerical simulations.

Abstract

We use unbiased numerical methods to study the onset of pair superfluidity in a system that displays flat bands in the noninteracting regime. This is achieved by using a known example of flat band systems, namely the Creutz lattice, where we investigate the role of local attractive interactions in the $U < 0$ Hubbard model. Going beyond the standard approach used in these systems where weak interactions are considered, we map the superfluid behavior for a wide range of interaction strengths and exhibit a crossover between BCS and tightly bound bosonic fermion pairs. We further contrast these results with a standard two-leg fermionic ladder, showing that the pair correlations, although displaying algebraic decay in both cases, are longer ranged in the Creutz lattice, signifying the robustness of pairing in this system.