Ferromagnetism in the Hubbard model with Topological/Non-Topological Flat Bands

TL;DR

This paper investigates Hubbard models with flat bands influenced by magnetic flux or spin-orbit coupling, revealing conditions for ferromagnetism and topological properties of the bands.

Contribution

It introduces two classes of Hubbard models with flat bands, analyzing their topological characteristics and proving ferromagnetism induced by Coulomb repulsion.

Findings

Flat bands can have zero or nontrivial Chern numbers.

On-site Coulomb repulsion induces ferromagnetism.

Topological properties depend on the class of the model.

Abstract

We introduce and study two classes of Hubbard models with magnetic flux or with spin-orbit coupling, which have a flat lowest band separated from other bands by a nonzero gap. We study the Chern number of the flat bands, and find that it is zero for the first class but can be nontrivial in the second. We also prove that the introduction of on-site Coulomb repulsion leads to ferromagnetism in both the classes.