Quantum Anomalous Hall Effect in Flat Band Ferromagnet

TL;DR

This paper presents a theoretical model demonstrating how Coulomb interactions and spin-orbit coupling in a flat-band 2D lattice can induce a transition from a quantum spin Hall to a quantum anomalous Hall phase, revealing new topological states.

Contribution

It introduces a novel theory showing how Coulomb interactions and spin-orbit coupling can produce a quantum anomalous Hall effect in flat-band ferromagnets on 2D decorated lattices.

Findings

Coulomb interactions induce ferrimagnetism in the system.

Spin-orbit coupling leads to a topologically non-trivial band structure.

Coulomb interactions can convert quantum spin Hall into quantum anomalous Hall phase.

Abstract

We proposed a theory of quantum anomalous Hall effect in a flat-band ferromagnet on a two-dimensional (2D) decorated lattice with spin-orbit coupling. Free electrons on the lattice have dispersionless flat bands, and the ground state is highly degenerate when each lattice site is occupied averagely by one electron, i.e., the system is at half filling. The on-site Coulomb interaction can remove the degeneracy and give rise to the ferrimagnetism, which is the coexistence of the ferromagnetic and antiferromagnetic long-range orders. On the other hand the spin-orbit coupling makes the band structure topologically non-trivial, and produces the quantum spin Hall effect with a pair of helical edge states around the system boundary. Based on the rigorous results for the Hubbard model, we found that the Coulomb interaction can provide an effective staggered potential and turn the quantum spin Hall phase into a quantum anomalous Hall phase.