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

References in corpus (21)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• High temperature fractional quantum Hall states
• Fractional quantum Hall states at zero magnetic field
• Nearly-flat bands with nontrivial topology
• Quantum Spin Hall Effect and Topologically Invariant Chern Numbers
• Fractional quantum Hall effect in the absence of Landau levels
• Fractional Chern Insulators in Topological Flat bands with Higher Chern Number
• Topological flat band models with arbitrary Chern numbers
• Fractional Quantum Hall Effect in Topological Flat Bands with Chern Number Two
• Bloch Model Wavefunctions and Pseudopotentials for All Fractional Chern Insulators
• Flux insertion, entanglement, and quantized responses
• Entanglement signatures of quantum Hall phase transitions
• Quantum Hall Phase Diagram of Half-filled Bilayers in the Lowest and the Second Orbital Landau Levels: Abelian versus Non-Abelian Incompressible Fractional Quantum Hall States
• Fractional Quantum Hall Bilayers at Half-Filling: Tunneling-driven Non-Abelian Phase
• Competing Abelian and non-Abelian topological orders in $\nu =1/3+1/3$ quantum Hall bilayers
• Quantum Hall States in Rapidly Rotating Two-Component Bose Gases
• $U(1)\times U(1)$ Symmetry Protected Topological Order in Gutzwiller Wave Functions
• Quantum Entanglement as a Diagnostic of Phase Transitions in Disordered Fractional Quantum Hall Liquids
• Non-Abelian spin singlet states of two-component Bose gases in artificial gauge fields
• Microscopic Study of Edge Excitations of Spin-Polarized and Spin-Unpolarized $\nu =2/3$ Fractional Quantum Hall Effect
• Generalizing Quantum Hall Ferromagnetism to Fractional Chern Bands