Pairing and superconductivity in quasi one-dimensional flat band systems: Creutz and sawtooth lattices

TL;DR

This paper investigates superconductivity in quasi-one-dimensional flat band lattices, revealing how topological properties influence pairing, with detailed analysis using mean field and DMRG methods.

Contribution

It demonstrates the role of topological flat bands in superconductivity, highlighting differences between topological and non-topological lattices and the limitations of BCS theory.

Findings

Superconducting weight $D_s$ is linear in coupling $U$ at low $U$.

$D_s$ is proportional to the quantum metric in Creutz lattice at small $U$.

Standard BCS mean field is inadequate for systems with inequivalent sublattices.

Abstract

We study the pairing and superconducting properties of the attractive Hubbard model in two quasi one-dimensional topological lattices: the Creutz and sawtooth lattices. They share two peculiar properties: each of their band structures exhibits a flat band with a non-trivial winding number. The difference, however, is that only the Creutz lattice is genuinely topological, owing to a chiral (sub-lattice) symmetry, resulting in a quantized winding number and zero energy edge modes for open boundary conditions. We use mean field and exact density matrix renormalization group in our work. Our three main results are: (a) For both lattice systems, the superconducting weight, $D_s$, is linear in the coupling strength, $U$, for low values of $U$; (b) for small $U$, $D_s$ is proportional to the quantum metric for the Creutz system but not for the sawtooth system because its sublattices are not equivalent; (c) conventional BCS mean field is not appropriate for such systems with inequivalent sublattices. We show that, for a wide range of densities and coupling strengths, these systems are very well described by a full multi-band mean field method where the pairing parameters and the local particle densities on the inequivalent sublattices are variational mean field parameters.