Two-component quantum Hall effects in topological flat bands

Abstract

We study quantum Hall states for two-component particles (hardcore bosons and fermions) loading in topological lattice models. By tuning the interplay of interspecies and intraspecies interactions, we demonstrate that two-component fractional quantum Hall states emerge at certain fractional filling factors $\nu =1/2$ for fermions ($\nu =2/3$ for bosons) in the lowest Chern band, classified by features from ground states including the unique Chern number matrix (inverse of $\mathbf{K}$-matrix), the fractional charge and spin pumpings, and two parallel propagating edge modes. Moreover, we also apply our strategy to two-component fermions at integer filling factor $\nu =2$, where a possible topological Neel antiferromagnetic phase is under intense debate very recently. For the typical $\pi$-flux checkerboard lattice, by tuning the onsite Hubbard repulsion, we establish a first-order phase transition directly from a two-component fermionic $\nu =2$ quantum Hall state at weak interaction to a topologically trivial antiferromagnetic insulator at strong interaction, and therefore exclude the possibility of an intermediate topological phase for our system.

8 pages, 8 figures; updated acknowledgements and added references; LA-UR-17-20075

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• Interacting topological insulators: a review
• Many-body Chern number without integration
• Tunning topological phase and quantum anomalous Hall effect by interaction in quadratic band touching systems
• Thermodynamic Response and Neutral Excitations in Integer and Fractional Quantum Anomalous Hall States Emerging from Correlated Flat Bands
• SU(N) fractional quantum Hall effects in topological flat bands
• Continuous phase transition between bosonic integer quantum Hall liquid and trivial insulator: evidences for deconfined quantum criticality
• Microscopic Mechanism of Anyon Superconductivity Emerging from Fractional Chern Insulators
• Topological characterization of hierarchical fractional quantum Hall effects in topological flat bands with SU($N$) symmetry
• Quantum Hall phase diagram of two-component Bose gases: Intercomponent entanglement and pseudopotentials
• Nature of continuous phase transitions in interacting topological insulators
• Chern number matrix of the non-Abelian spin-singlet fractional quantum Hall effect
• Fractional quantum Hall effect of Bose-Fermi mixtures
• Quantum Hall effects of exciton condensate in topological flat bands
• Halperin $(m^{\prime },m,n)$ fractional quantum Hall effect in topological flat bands
• Integer quantum Hall effect of two-component hardcore bosons in a topological triangular lattice
• Anomalous Bilayer Quantum Hall Effect
• Fractional Quantum Hall Effect in n=0 Landau Band of Graphene with Chern Number Matrix
• Interlayer correlated fractional quantum Hall state in the ν = 4/5 bilayer system
• Three-component fractional quantum Hall effect in topological flat bands
• Bosonic Halperin fractional quantum Hall effect at filling factor $\nu =2/5$