Ferromagnetism and Antiferromagnetism of Correlated Topological Insulator with Flat Band

TL;DR

This study investigates magnetic phases in a topological flat band system using mean field and RPA methods, revealing conditions for ferromagnetic and antiferromagnetic order, and identifying a quarter-filled topological insulator phase.

Contribution

It provides a detailed phase diagram of magnetic orders in a correlated topological flat band system, highlighting the emergence of a quarter-filled topological insulator induced by ferromagnetism.

Findings

Antiferromagnetic order is more stable near half-filling.

Ferromagnetic order dominates at large doping.

Quarter filling leads to a topological insulator phase.

Abstract

In this paper, based on the mean field approach and random-phase-approximation, we study the magnetic properties of the spinful Haldane model on honeycomb lattice of topological flat band with on-site repulsive Coulomb interaction. We find that the antiferromagnetic (AF) order is more stable than ferromagnetic (FM) order at (or near) half-filling; while away from half-filling the phase diagram becomes complex: At large doping, FM order is more stable than AF order due to the flatness of band structure. In particular, we find that at quarter filling case, the system becomes a Q=1$ topological insulator which is induced by the FM order.