Multitude of Topological Phase Transitions in Bipartite Dice and Lieb Lattices with Interacting Electrons and Rashba Coupling

TL;DR

This study reveals a rich variety of topological phases with different Chern numbers in interacting electron systems on bipartite dice and Lieb lattices, driven by Hubbard interaction and Rashba coupling, expanding understanding of topological phase control.

Contribution

It demonstrates the emergence of multiple topological phases with varying Chern numbers in interacting bipartite lattices, highlighting the role of electron interactions in topological properties.

Findings

Multiple topological phases with Chern numbers from 0 to 3 were observed.

All phases exhibit ferrimagnetic order.

Large Chern numbers can be achieved through electronic correlations.

Abstract

We report the results of a Hartree-Fock study applied to interacting electrons moving in two different bipartite lattices: the dice and the Lieb lattices, at half-filling. Both lattices develop ferrimagnetic order in the phase diagram $U$-$\lambda$, where $U$ is the Hubbard onsite repulsion and $\lambda$ the Rashba spin-orbit coupling strength. Our main result is the observation of an unexpected multitude of topological phases for both lattices. All these phases are ferrimagnetic, but they differ among themselves in their set of six Chern numbers (six numbers because the unit cells have three atoms). The Chern numbers $|C|$ observed in our study range from 0 to 3, showing that large Chern numbers can be obtained by the effect of electronic correlations, adding to the recently discussed methodologies to increase $|C|$ based on extending the hopping range in tight-binding models, using sudden quenches, or photonic crystals, all without including electronic interactions.