Flat-band ferromagnetism in a topological Hubbard model

Abstract

We study the flat-band ferromagnetic phase of a topological Hubbard model within a bosonization formalism and, in particular, determine the spin-wave excitation spectrum. We consider a square lattice Hubbard model at 1/4-filling whose free-electron term is the π-flux model with topologically nontrivial and nearly flat energy bands. The electron spin is introduced such that the model either explicitly breaks time-reversal symmetry (correlated flat-band Chern insulator) or is invariant under time-reversal symmetry (correlated flat-band $Z_2$ topological insulator). We generalize for flat-band Chern and topological insulators the bosonization formalism [Phys. Rev. B 71, 045339 (2005)] previously developed for the two-dimensional electron gas in a uniform and perpendicular magnetic field at filling factor ν=1. We show that, within the bosonization scheme, the topological Hubbard model is mapped into an effective interacting boson model. We consider the boson model at the harmonic approximation and show that, for the correlated Chern insulator, the spin-wave excitation spectrum is gapless while, for the correlated topological insulator, gapped. We briefly comment on the possible effects of the boson-boson (spin-wave--spin-wave) coupling.

16 pages, 5 figures

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Cited by in corpus (10)

• Interacting topological insulators: a review
• Towards Three-Dimensional Weyl-SurfaceSemimetals in Graphene Networks
• Compact localized states and flat bands from local symmetry partitioning
• Ferromagnetism and spin excitations in topological Hubbard models with a flatband
• Topological Magnons in a One-dimensional Itinerant Flatband Ferromagnet
• Symmetry breaking and fermionic fractional Chern insulator in topologically trivial bands
• Tuning the topological insulator states of artificial graphene
• Flat-band ferromagnetism and spin waves in the Haldane-Hubbard model
• Itinerant topological magnons and spin excitons in twisted transition metal dichalcogenides: Mapping electron topology to spin counterpart
• Flat-band ferromagnetism in a correlated topological insulator on a honeycomb lattice