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

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.

12 pages, 12 figures

References in corpus (8)

• The density-matrix renormalization group in the age of matrix product states
• Observation of a localized flat-band state in a photonic Lieb lattice
• Observation of bound states in Lieb photonic lattices
• Fractional Chern Insulators in Topological Flat bands with Higher Chern Number
• Distant-Neighbor Hopping in Graphene and Haldane Models
• Vortex-Peierls States in Optical Lattices
• Flat Bands and Ferrimagnetic Order in Electronically Correlated Dice-Lattice Ribbons
• Interaction-induced topological phase transition and Majorana edge states in low-dimensional orbital-selective Mott insulators

Cited by in corpus (6)

• Even-odd parity transition in strongly correlated locally noncentrosymmetric superconductors : An application to CeRh${}_2$As${}_2$
• Majorana corner states on the dice lattice
• One-dimensional flat bands and Dirac cones in narrow zigzag dice lattice ribbons
• Zigzag dice lattice ribbons: Distinct edge morphologies and structure-spectrum correspondences
• Canted magnetism and ${\mathbb{Z}}_2$ fractionalization in metallic states of the Lieb lattice Hubbard model near quarter filling
• Transversal transport of magnons in a modified Lieb lattice